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@pkra
Last active July 4, 2018 07:15
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TeX sample extracted from math.SE tutorial
<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Math.SE extracted Samples</title>
</head>
<body>
<p>Licensed under <a href="https://creativecommons.org/licenses/by-sa/3.0/" rel="license">cc by-sa 3.0</a>. Original source: <a href="http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference">meta.math.stackexchange</a> (cc by-sa 3.0), with <a href="http://blog.stackoverflow.com/2009/06/attribution-required/" rel="license">attribution required</a>.</p>
<div>\(\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}\)</div>
<div>\[\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}\]</div>
<div>\(\alpha, \beta, … \omega\)</div>
<div>\(\Gamma, \Delta, …, \Omega\)</div>
<div>\(x_i^2\)</div>
<div>\(\log_2 x\)</div>
<div>\(10^10\)</div>
<div>\(10^{10}\)</div>
<div>\({x^y}^z\)</div>
<div>\(x^{y^z}\)</div>
<div>\(x_i^2\)</div>
<div>\(x_{i^2}\)</div>
<div>\((2+3)[4+4]\)</div>
<div>\(\{\}\)</div>
<div>\((\frac{\sqrt x}{y^3})\)</div>
<div>\(\left(\frac{\sqrt x}{y^3}\right)\)</div>
<div>\((x)\)</div>
<div>\([x]\)</div>
<div>\(\{ x \}\)</div>
<div>\(|x|\)</div>
<div>\(\vert x \vert\)</div>
<div>\(\Vert x \Vert\)</div>
<div>\(\langle x \rangle\)</div>
<div>\(\lceil x \rceil\)</div>
<div>\(\lfloor x \rfloor\)</div>
<div>\(\left.\frac12\right\rbrace\)</div>
<div>\(\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)\)</div>
<div>\(\sum_1^n\)</div>
<div>\(\sum_{i=0}^\infty i^2\)</div>
<div>\(\prod\)</div>
<div>\(\int\)</div>
<div>\(\bigcup\)</div>
<div>\(\bigcap\)</div>
<div>\(\iint\)</div>
<div>\(\iiint\)</div>
<div>\(\frac ab\)</div>
<div>\(\frac{a+1}{b+1}\)</div>
<div>\({a+1\over b+1}\)</div>
<div>\(\cfrac{a}{b}\)</div>
<div>\(\mathbb{CHNQRZ}\)</div>
<div>\(\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathbf{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathtt{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathrm{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathsf{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\mathcal{ ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\)</div>
<div>\(\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \mathfrak{abcdefghijklmnopqrstuvwxyz}\)</div>
<div>\(\sqrt{x^3}\)</div>
<div>\(\sqrt[3]{\frac xy}\)</div>
<div>\(\sin x\)</div>
<div>\(sin x\)</div>
<div>\[\lim_{x\to 0}\]</div>
<div>\(\lt\, \gt\, \le\, \leq\, \leqq\, \leqslant\, \ge\, \geq\, \geqq\, \geqslant\, \neq\)</div>
<div>\(\not\lt\)</div>
<div>\(\times\, \div\, \pm\, \mp\)</div>
<div>\(x\cdot y\)</div>
<div>\(\cup\, \cap\, \setminus\, \subset\, \subseteq \,\subsetneq \,\supset\, \in\, \notin\, \emptyset\, \varnothing\)</div>
<div>\({n+1 \choose 2k}\)</div>
<div>\(\to\, \rightarrow\, \leftarrow\, \Rightarrow\, \Leftarrow\, \mapsto\)</div>
<div>\(\land\, \lor\, \lnot\, \forall\, \exists\, \top\, \bot\, \vdash\, \vDash\)</div>
<div>\(\star\, \ast\, \oplus\, \circ\, \bullet\)</div>
<div>\(\approx\, \sim \, \simeq\, \cong\, \equiv\, \prec, \lhd\)</div>
<div>\(\infty\, \aleph_0\)</div>
<div>\(\nabla\, \partial\)</div>
<div>\(\Im\, \Re\)</div>
<div>\(a\equiv b\pmod n\)</div>
<div>\(a_1, a_2, \ldots ,a_n\)</div>
<div>\(a_1+a_2+\cdots+a_n\)</div>
<div>\(\epsilon\, \varepsilon\)</div>
<div>\(\phi\, \varphi\)</div>
<div>\(\ell\)</div>
<div>\(\TeX\)</div>
<div>\(\LaTeX\)</div>
<div>\(\TeX\)</div>
<div>\(a b\)</div>
<div>\(a\,b\)</div>
<div>\(a\;b\)</div>
<div>\(a\quad b\)</div>
<div>\(a\qquad b\)</div>
<div>\(\{x\in s\mid x\text{ is extra large}\}\)</div>
<div>\(\hat x\)</div>
<div>\(\widehat{xy}\)</div>
<div>\(\bar x\)</div>
<div>\(\overline{xyz}\)</div>
<div>\(\vec x\)</div>
<div>\(\overrightarrow{xy}\)</div>
<div>\(\overleftrightarrow{xy}\)</div>
<div>\(\frac d{dx}x\dot x = \dot x^2 + x\ddot x\)</div>
<div>\(\$\)</div>
<div>\(\{\)</div>
<div>\(\_\)</div>
<div>\(\backslash\)</div>
<div>\(\LaTeX\)</div>
<div>\(\mathrm{B}\)</div>
<div>\(\sin\)</div>
<div>\(\operatorname{Spec} A\)</div>
<div>\(_5C_3\)</div>
<div>\(\TeX\)</div>
<div>\(\TeX\)</div>
<div>\(\LaTeX\)</div>
<div>\(\mathrm{d}x\)</div>
<div>\[
\begin{matrix}
1 &amp; x &amp; x^2 \\
1 &amp; y &amp; y^2 \\
1 &amp; z &amp; z^2 \\
\end{matrix}
\]
</div>
<div>\(\begin{pmatrix}1&amp;2\\3&amp;4\\ \end{pmatrix}\)</div>
<div>\(\begin{bmatrix}1&amp;2\\3&amp;4\\ \end{bmatrix}\)</div>
<div>\(\begin{Bmatrix}1&amp;2\\3&amp;4\\ \end{Bmatrix}\)</div>
<div>\(\begin{vmatrix}1&amp;2\\3&amp;4\\ \end{vmatrix}\)</div>
<div>\(\begin{Vmatrix}1&amp;2\\3&amp;4\\ \end{Vmatrix}\)</div>
<div>\(\cdots\)</div>
<div>\(\ddots\)</div>
<div>\(\vdots\)</div>
<div>\begin{pmatrix}
1 &amp; a_1 &amp; a_1^2 &amp; \cdots &amp; a_1^n \\
1 &amp; a_2 &amp; a_2^2 &amp; \cdots &amp; a_2^n \\
\vdots &amp; \vdots&amp; \vdots &amp; \ddots &amp; \vdots \\
1 &amp; a_m &amp; a_m^2 &amp; \cdots &amp; a_m^n
\end{pmatrix}</div>
<div>\[
\left[\begin{array}{cc|c}
1&amp;2&amp;3\\
4&amp;5&amp;6
\end{array}\right]
\]
</div>
<div>\[
\begin{pmatrix}
a &amp; b \\
c &amp; d\\
\hline
1 &amp; 0\\
0 &amp; 1
\end{pmatrix}
\]
</div>
<div>\(\bigl( \begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix} \bigr)\)</div>
<div>\begin{align}
\sqrt{37} &amp; = \sqrt{\frac{73^2-1}{12^2}} \\
&amp; = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\
&amp; = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
&amp; = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\
&amp; \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
\end{align}</div>
<div>\[
\begin{align} f(x)&amp;=\left(x^3\right)+\left(x^3+x^2+x^1\right)+\left(x^3+x^2\right)\\ f'(x)&amp;=\left(\left(3x^2+2x+1\right)+\left(3x^2+2x\right)\right)\\ f''(x)&amp;=\left(6x+2\right)\\ \end{align}
\]</div>
<div>\({}{}{}{}{}{}{}{}\)</div>
<div>\(\Psi\)</div>
<div>\(\delta\)</div>
<div>\(\zeta\)</div>
<div>\(\ge\)</div>
<div>\(\subseteq\)</div>
<div>\(\LaTeX\)</div>
<div>\(\LaTeX\)</div>
<div>f(n) =
\begin{cases}
n/2, &amp; \text{if $n$ is even} \\
3n+1, &amp; \text{if $n$ is odd}
\end{cases}</div>
<div>\[
\left.
\begin{array}{l}
\text{if $n$ is even:}&amp;n/2\\
\text{if $n$ is odd:}&amp;3n+1
\end{array}
\right\}
=f(n)
\]
</div>
<div>f(n) =
\begin{cases}
\frac{n}{2}, &amp; \text{if $n$ is even} \\[2ex]
3n+1, &amp; \text{if $n$ is odd}
\end{cases}</div>
<div>\begin{array}{c|lcr}
n &amp; \text{Left} &amp; \text{Center} &amp; \text{Right} \\
\hline
1 &amp; 0.24 &amp; 1 &amp; 125 \\
2 &amp; -1 &amp; 189 &amp; -8 \\
3 &amp; -20 &amp; 2000 &amp; 1+10i
\end{array}
</div>
<div>\[
% outer vertical array of arrays
\begin{array}{c}
% inner horizontal array of arrays
\begin{array}{cc}
% inner array of minimum values
\begin{array}{c|cccc}
\text{min} &amp; 0 &amp; 1 &amp; 2 &amp; 3\\
\hline
0 &amp; 0 &amp; 0 &amp; 0 &amp; 0\\
1 &amp; 0 &amp; 1 &amp; 1 &amp; 1\\
2 &amp; 0 &amp; 1 &amp; 2 &amp; 2\\
3 &amp; 0 &amp; 1 &amp; 2 &amp; 3
\end{array}
&amp;
% inner array of maximum values
\begin{array}{c|cccc}
\text{max}&amp;0&amp;1&amp;2&amp;3\\
\hline
0 &amp; 0 &amp; 1 &amp; 2 &amp; 3\\
1 &amp; 1 &amp; 1 &amp; 2 &amp; 3\\
2 &amp; 2 &amp; 2 &amp; 2 &amp; 3\\
3 &amp; 3 &amp; 3 &amp; 3 &amp; 3
\end{array}
\end{array}
\\
% inner array of delta values
\begin{array}{c|cccc}
\Delta&amp;0&amp;1&amp;2&amp;3\\
\hline
0 &amp; 0 &amp; 1 &amp; 2 &amp; 3\\
1 &amp; 1 &amp; 0 &amp; 1 &amp; 2\\
2 &amp; 2 &amp; 1 &amp; 0 &amp; 1\\
3 &amp; 3 &amp; 2 &amp; 1 &amp; 0
\end{array}
\end{array}
\]
</div>
<div>\(\mathsf{Show\ Math\ As\ }\blacktriangleright\mathsf{\ TeX\ Commands}\)</div>
<div>\(all italics, weird-looking spacing, an' odd apostrophes\)</div>
<div>\(\LaTeX\)</div>
<div>\[
\begin{array}{ll} \hfill\mathrm{Bad}\hfill &amp; \hfill\mathrm{Better}\hfill \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}&amp; e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx &amp; \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}
\]</div>
<div>\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}&amp; e^{i\pi/2} \\
\int_{-\frac\pi2}^\frac\pi2 \sin x\,dx &amp; \int_{-\pi/2}^{\pi/2}\sin x\,dx \\
\end{array}</div>
<div>\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
\{x|x^2\in\Bbb Z\} &amp; \{x\mid x^2\in\Bbb Z\} \\
\end{array}</div>
<div>\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
\int\int_S f(x)\,dy\,dx &amp; \iint_S f(x)\,dy\,dx \\
\int\int\int_V f(x)\,dz\,dy\,dx &amp; \iiint_V f(x)\,dz\,dy\,dx
\end{array}</div>
<div>\(\TeX\)</div>
<div>\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
\iiint_V f(x)dz dy dx &amp; \iiint_V f(x)\,dz\,dy\,dx
\end{array}</div>
<div>\(\left\{x\middle | \frac{x^2}{2} \in \mathbb{z}\right\}\)</div>
<div>\[
\require{cancel}\begin{array}{rl}
\verb|y+\cancel{x}| &amp; y+\cancel{x}\\
\verb|\cancel{y+x}| &amp; \cancel{y+x}\\
\verb|y+\bcancel{x}| &amp; y+\bcancel{x}\\
\verb|y+\xcancel{x}| &amp; y+\xcancel{x}\\
\verb|y+\cancelto{0}{x}| &amp; y+\cancelto{0}{x}\\
\verb+\frac{1\cancel9}{\cancel95} = \frac15+&amp; \frac{1\cancel9}{\cancel95} = \frac15 \\
\end{array}
\]
</div>
<div>\[
\require{enclose}\begin{array}{rl}
\verb|\enclose{horizontalstrike}{x+y}| &amp; \enclose{horizontalstrike}{x+y}\\
\verb|\enclose{verticalstrike}{\frac xy}| &amp; \enclose{verticalstrike}{\frac xy}\\
\verb|\enclose{updiagonalstrike}{x+y}| &amp; \enclose{updiagonalstrike}{x+y}\\
\verb|\enclose{downdiagonalstrike}{x+y}| &amp; \enclose{downdiagonalstrike}{x+y}\\
\verb|\enclose{horizontalstrike,updiagonalstrike}{x+y}| &amp; \enclose{horizontalstrike,updiagonalstrike}{x+y}\\
\end{array}
\]
</div>
<div>\(19/95 = 1/5\)</div>
<div>\(\cancelto{\cancelto{\cancelto{x^{2+x}}{\cancelto{x^2}{x}+4}}4}0\)</div>
<div>\(\LaTeX\)</div>
<div>
\[
\left\{
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{array}
\right.
\]
</div>
<div>
\[
\begin{cases}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{cases}
\]
</div>
<div>\[\left\{\begin{aligned} a_1x+b_1y+c_1z&amp;=d_1+e_1 \\
a_2x+b_2y&amp;=d_2 \\
a_3x+b_3y+c_3z&amp;=d_3 \end{aligned} \right. \]</div>
<div>\[
\left\{\begin{array}{ll}a_1x+b_1y+c_1z &amp;=d_1+e_1 \\ a_2x+b_2y &amp;=d_2 \\ a_3x+b_3y+c_3z &amp;=d_3 \end{array} \right.
\]</div>
<div>
\[\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\[2ex]
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\[2ex]
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}
\]
</div>
<div>
\[
\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}
\]
</div>
<div>\[
\left\{ \begin{array}{l} 0 = c_x-a_{x0}-d_{x0}\dfrac{(c_x-a_{x0})\cdot d_{x0}}{\|d_{x0}\|^2} + c_x-a_{x1}-d_{x1}\dfrac{(c_x-a_{x1})\cdot d_{x1}}{\|d_{x1}\|^2} \\[2ex] 0 = c_y-a_{y0}-d_{y0}\dfrac{(c_y-a_{y0})\cdot d_{y0}}{\|d_{y0}\|^2} + c_y-a_{y1}-d_{y1}\dfrac{(c_y-a_{y1})\cdot d_{y1}}{\|d_{y1}\|^2} \end{array} \right.
\]
</div>
<div>\(\longrightarrow\)</div>
<div>
\[
\begin{array}{|rc|}
\hline
\verb+\color{black}{text}+ &amp; \color{black}{text} \\
\verb+\color{gray}{text}+ &amp; \color{gray}{text} \\
\verb+\color{silver}{text}+ &amp; \color{silver}{text} \\
\verb+\color{white}{text}+ &amp; \color{white}{text} \\
\hline
\verb+\color{maroon}{text}+ &amp; \color{maroon}{text} \\
\verb+\color{red}{text}+ &amp; \color{red}{text} \\
\verb+\color{yellow}{text}+ &amp; \color{yellow}{text} \\
\verb+\color{lime}{text}+ &amp; \color{lime}{text} \\
\verb+\color{olive}{text}+ &amp; \color{olive}{text} \\
\verb+\color{green}{text}+ &amp; \color{green}{text} \\
\verb+\color{teal}{text}+ &amp; \color{teal}{text} \\
\verb+\color{aqua}{text}+ &amp; \color{aqua}{text} \\
\verb+\color{blue}{text}+ &amp; \color{blue}{text} \\
\verb+\color{navy}{text}+ &amp; \color{navy}{text} \\
\verb+\color{purple}{text}+ &amp; \color{purple}{text} \\
\verb+\color{fuchsia}{text}+ &amp; \color{magenta}{text} \\
\hline
\end{array}
\]</div>
<div>\(r, g, b\)</div>
<div>\(0–15\)</div>
<div>
\[
\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ &amp; \color{#000}{text} &amp; &amp; &amp;
\verb+#00F+ &amp; \color{#00F}{text} &amp; &amp; \\
&amp; &amp; \verb+#0F0+ &amp; \color{#0F0}{text} &amp;
&amp; &amp; \verb+#0FF+ &amp; \color{#0FF}{text}\\
\verb+#F00+ &amp; \color{#F00}{text} &amp; &amp; &amp;
\verb+#F0F+ &amp; \color{#F0F}{text} &amp; &amp; \\
&amp; &amp; \verb+#FF0+ &amp; \color{#FF0}{text} &amp;
&amp; &amp; \verb+#FFF+ &amp; \color{#FFF}{text}\\
\hline
\end{array}
\]
</div>
<div>\begin{array}{|rrrrrrrr|}
\hline
\verb+#000+ &amp; \color{#000}{text} &amp; \verb+#005+ &amp; \color{#005}{text} &amp; \verb+#00A+ &amp; \color{#00A}{text} &amp; \verb+#00F+ &amp; \color{#00F}{text} \\
\verb+#500+ &amp; \color{#500}{text} &amp; \verb+#505+ &amp; \color{#505}{text} &amp; \verb+#50A+ &amp; \color{#50A}{text} &amp; \verb+#50F+ &amp; \color{#50F}{text} \\
\verb+#A00+ &amp; \color{#A00}{text} &amp; \verb+#A05+ &amp; \color{#A05}{text} &amp; \verb+#A0A+ &amp; \color{#A0A}{text} &amp; \verb+#A0F+ &amp; \color{#A0F}{text} \\
\verb+#F00+ &amp; \color{#F00}{text} &amp; \verb+#F05+ &amp; \color{#F05}{text} &amp; \verb+#F0A+ &amp; \color{#F0A}{text} &amp; \verb+#F0F+ &amp; \color{#F0F}{text} \\
\hline
\verb+#080+ &amp; \color{#080}{text} &amp; \verb+#085+ &amp; \color{#085}{text} &amp; \verb+#08A+ &amp; \color{#08A}{text} &amp; \verb+#08F+ &amp; \color{#08F}{text} \\
\verb+#580+ &amp; \color{#580}{text} &amp; \verb+#585+ &amp; \color{#585}{text} &amp; \verb+#58A+ &amp; \color{#58A}{text} &amp; \verb+#58F+ &amp; \color{#58F}{text} \\
\verb+#A80+ &amp; \color{#A80}{text} &amp; \verb+#A85+ &amp; \color{#A85}{text} &amp; \verb+#A8A+ &amp; \color{#A8A}{text} &amp; \verb+#A8F+ &amp; \color{#A8F}{text} \\
\verb+#F80+ &amp; \color{#F80}{text} &amp; \verb+#F85+ &amp; \color{#F85}{text} &amp; \verb+#F8A+ &amp; \color{#F8A}{text} &amp; \verb+#F8F+ &amp; \color{#F8F}{text} \\
\hline
\verb+#0F0+ &amp; \color{#0F0}{text} &amp; \verb+#0F5+ &amp; \color{#0F5}{text} &amp; \verb+#0FA+ &amp; \color{#0FA}{text} &amp; \verb+#0FF+ &amp; \color{#0FF}{text} \\
\verb+#5F0+ &amp; \color{#5F0}{text} &amp; \verb+#5F5+ &amp; \color{#5F5}{text} &amp; \verb+#5FA+ &amp; \color{#5FA}{text} &amp; \verb+#5FF+ &amp; \color{#5FF}{text} \\
\verb+#AF0+ &amp; \color{#AF0}{text} &amp; \verb+#AF5+ &amp; \color{#AF5}{text} &amp; \verb+#AFA+ &amp; \color{#AFA}{text} &amp; \verb+#AFF+ &amp; \color{#AFF}{text} \\
\verb+#FF0+ &amp; \color{#FF0}{text} &amp; \verb+#FF5+ &amp; \color{#FF5}{text} &amp; \verb+#FFA+ &amp; \color{#FFA}{text} &amp; \verb+#FFF+ &amp; \color{#FFF}{text} \\
\hline
\end{array}</div>
<div>\(\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}\)</div>
<div>\(\demo\overline A\)</div>
<div>\(\demo\underline B\)</div>
<div>\(\demo\widetilde C\)</div>
<div>\(\demo\widehat D\)</div>
<div>\(\demo\fbox {$E$}\)</div>
<div>\(\demo\underleftarrow{F}\qquad\)</div>
<div>\(\xleftarrow{abc}\)</div>
<div>\(\demo\underrightarrow{G}\qquad\)</div>
<div>\(\xrightarrow{abc}\)</div>
<div>\(\demo\underleftrightarrow{H}\)</div>
<div>\(\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}\)</div>
<div>\((n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)\)</div>
<div>\[\underbrace{a\cdot a\cdots a}_{b\text{ times}}\]</div>
<div>\(\varliminf\)</div>
<div>\(\varlimsup\)</div>
<div>\(\check{I}\)</div>
<div>\(\acute{J}\)</div>
<div>\(\grave{K}\)</div>
<div>\(\vec u\ \vec{AB}\)</div>
<div>\(\bar z\)</div>
<div>\(\hat x\)</div>
<div>\(\tilde x\)</div>
<div>\(\dot x,\ddot x,\dddot x\)</div>
<div>\(\mathring A\)</div>
<div>\(\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}\)</div>
<div> \[
x = a_0 + \cfrac{1^2}{a_1
+ \cfrac{2^2}{a_2
+ \cfrac{3^2}{a_3 + \cfrac{4^4}{a_4 + \cdots}}}}
\]
</div>
<div> \[
x = a_0 + \frac{1^2}{a_1
+ \frac{2^2}{a_2
+ \frac{3^2}{a_3 + \frac{4^4}{a_4 + \cdots}}}}
\]
</div>
<div> \[
x = a_0 + \frac{1^2}{a_1+}
\frac{2^2}{a_2+}
\frac{3^2}{a_3 +} \frac{4^4}{a_4 +} \cdots
\]
</div>
<div>\([a_0; a_1, a_2, a_3, \ldots]\)</div>
<div>\[ \cfrac{a_{1}}{b_{1}+\cfrac{a_{2}}{b_{2}+\cfrac{a_{3}}{b_{3}+\ddots }}}= {\genfrac{}{}{}{}{a_1}{b_1}} {\genfrac{}{}{0pt}{}{}{+}} {\genfrac{}{}{}{}{a_2}{b_2}} {\genfrac{}{}{0pt}{}{}{+}} {\genfrac{}{}{}{}{a_3}{b_3}} {\genfrac{}{}{0pt}{}{}{+\dots}} \]</div>
<div>\(\LaTeX\)</div>
<div>\[\underset{j=1}{\overset{\infty}{\LARGE\mathrm K}}\frac{a_j}{b_j}=\cfrac{a_1}{b_1+\cfrac{a_2}{b_2+\cfrac{a_3}{b_3+\ddots}}}.\]</div>
<div>\[\mathop{\LARGE\mathrm K}_{i=1}^\infty \frac{a_i}{b_i}\]</div>
<div>
\[
\require{AMScd}
\begin{CD}
A @&gt;a&gt;&gt; B\\
@V b V V= @VV c V\\
C @&gt;&gt;d&gt; D
\end{CD}
\]
</div>
<div>
\[
\begin{CD}
A @&gt;&gt;&gt; B @&gt;{\text{very long label}}&gt;&gt; C \\
@. @AAA @| \\
D @= E @&lt;&lt;&lt; F
\end{CD}
\]
</div>
<div>
\[
\require{AMScd}
\begin{CD}
RCOHR'SO_3Na @>{\text{Hydrolysis,$\Delta, Dil.HCl$}}&gt;&gt; (RCOR')+NaCl+SO_2+ H_2O
\end{CD}
\]
</div>
<div>\( \newcommand{\SES}[3]{ 0 \to #1 \to #2 \to #3 \to 0 }\)</div>
<div>\[ \SES{A}{B}{C} \]</div>
<div>\(\implies\)</div>
<div>\(\Rightarrow\)</div>
<div>\(\iff\)</div>
<div>\(\impliedby\)</div>
<div>\(\to\)</div>
<div>\(f\colon A \to B\)</div>
<div>\(\gets\)</div>
<div>\(T:\mathbb R\to \mathbb R,\; x\mapsto x+1\)</div>
<div>\(p\land((q\lor r)\to s)\)</div>
<div>\[x+2=4-x\implies x=1.\]</div>
<div>\[ a := x^2-y^3 \tag{*}\label{*} \]</div>
<div>\[ a+y^3 \stackrel{\eqref{*}}= x^2 \]</div>
<div>\(\eqref{*}\)</div>
<div>\(\ref{*}\)</div>
<div>\(\eqref{*}\)</div>
<div>\[(1)\qquad\qquad\sum\limits_{j}k\tag*{}\]</div>
<div>\((1)\)</div>
<div>
\[
f\left(\left[ \frac{1+\left\{x,y\right\}}{\left(\frac{x}{y}+\frac{y}{x}\right)\left(u+1\right)}+a\right]^{3/2}\right).
\]
</div>
<div>
\[
\begin{aligned}
a=&amp;\left(1+2+3+ \cdots \right. \\
&amp; \cdots+ \left. \infty-2+\infty-1+\infty\right).
\end{aligned}
\]
</div>
<div>
\[
\left\langle q\middle\|\frac{\frac{x}{y}}{\frac{u}{v}} \middle| p \right\rangle.
\]
</div>
<div>\(\Big(\dots\Big)\)</div>
<div>\[\operatorname{arsinh}(x)\]</div>
<div>\(arsinh(x)\)</div>
<div>
\[
\operatorname*{Res}_{z=1}\left(\frac1{z^2-z}\right)=1
\]
</div>
<div>\(\verb*{\rm ...}*\)</div>
<div>\(\verb*{\rm arsinh}*\)</div>
<div>\({\rm arsinh}\)</div>
<div>\(\operatorname{arsinh}x\)</div>
<div>\({\rm arsinh}x\)</div>
<div>\({\tt operatorname}\)</div>
<div>\(\text{arsinh }x\)</div>
<div>\(\operatorname{arsinh}x\)</div>
<div>\(\lim \limits_{x \to 1} \frac{x^2-1}{x-1}\)</div>
<div>\(\lim\)</div>
<div>\(lim\)</div>
<div>\(\lim \limits_{x \to 1}\)</div>
<div>\(\to\)</div>
<div>\(x \to 1\)</div>
<div>\(\lim\)</div>
<div>\(x \to 1\)</div>
<div>\(\lim \limits_{x \to 1} \frac{x^2-1}{x-1}\)</div>
<div>\[\lim_{x\to 1}?\]</div>
<div>\[\mathop{+}\limits_{i=1}^k\text{ instead of }+_{i=1}^k\]</div>
<div>\(\lim\limits_{x\to 1}\)</div>
<div>\(\lim_{x\to 1}\)</div>
<div>\(\lim_{x\to 1}\)</div>
<div>\(\lim\limits_{x\to 1}\)</div>
<div>\(x\to 1\)</div>
<div>\(\lim \limits_{x \to 1}\)</div>
<div>\(\lim\limits_{x\mapsto 1}\dfrac1x\)</div>
<div>\(\TeX\)</div>
<div>\(\lim_{x\mapsto 1}\frac1x\)</div>
<div>\(\TeX\)</div>
<div>\(\lvert x\rvert\)</div>
<div>\(\lVert v\rVert\)</div>
<div>\[|x|, ||v|| \quad\longrightarrow\quad \lvert x\rvert, \lVert v\rVert\]</div>
<div>\(\|x\|\)</div>
<div>\(\lVert x \rVert\)</div>
<div>
\[
\bbox[yellow]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (1)
}
\]
</div>
<div>
\[
\bbox[yellow,5px]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (1)
}
\]
</div>
<div>
\[
\bbox[5px,border:2px solid red]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (2)
}
\]
</div>
<div>
\[
\bbox[yellow,5px,border:2px solid red]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (1)
}
\]
</div>
<div>\begin{align}
v + w &amp; = 0 &amp;&amp;\text{Given} \tag 1\\
-w &amp; = -w + 0 &amp;&amp; \text{additive identity} \tag 2\\
-w + 0 &amp; = -w + (v + w) &amp;&amp; \text{equations $(1)$ and $(2)$}
\end{align}</div>
<div>\[\spadesuit\quad\heartsuit\quad\diamondsuit\quad\clubsuit\]</div>
<div>\[\color{red}{\heartsuit}\quad\color{red}{\diamondsuit}\]</div>
<div>\[♠\quad♡\quad♢\quad♣\\
♤\quad♥\quad♦\quad♧\]
</div>
<div>\(\Rightarrow\)</div>
<div>\(\Leftarrow\)</div>
<div>\(\Leftrightarrow\)</div>
<div>\(\implies\)</div>
<div>\(\impliedby\)</div>
<div>\(\iff\)</div>
<div>
\[
\require{enclose}
\begin{array}{r}
13 \\[-3pt]
4 \enclose{longdiv}{52} \\[-3pt]
\underline{4}\phantom{2} \\[-3pt]
12 \\[-3pt]
\underline{12}
\end{array}
\]
</div>
<div>\[x^3−6x^2+11x−6=(x−{\color{red}1})(x^2−5x+6)+{\color{blue}0}\]</div>
<div>\[\begin{array}{c|rrrr}&amp; x^3 &amp; x^2 &amp; x^1 &amp; x^0\\ &amp; 1 &amp; -6 &amp; 11 &amp; -6\\ {\color{red}1} &amp; \downarrow &amp; 1 &amp; -5 &amp; 6\\ \hline &amp; 1 &amp; -5 &amp; 6 &amp; |\phantom{-} {\color{blue}0} \end{array}\]</div>
<div>\(90°\)</div>
<div>\(90^\circ\)</div>
<div>\[\sum_{n=1}^\infty \frac{1}{n^2} \to
\textstyle \sum_{n=1}^\infty \frac{1}{n^2} \to
\displaystyle \sum_{n=1}^\infty \frac{1}{n^2}\]</div>
<div>\(\displaystyle \lim_{t \to 0} \int_t^1 f(t)\, dt\)</div>
<div>\(\lim_{t \to 0} \int_t^1 f(t)\, dt\)</div>
<div>\(\overline a+\overline b=\overline {a\cdot b}\)</div>
<div>\(\sqrt{a}-\sqrt{b}\)</div>
<div>\(\sqrt{\mathstrut a} - \sqrt{\mathstrut b}\)</div>
<div>\(\sqrt{\vphantom{b} a} - \sqrt{b}\)</div>
<div>\(\dfrac{1}{\sqrt{\vphantom{b} a} - \sqrt{b}}\)</div>
<div>\(\smash{\dfrac{1}{\sqrt{\vphantom{b} a} - \sqrt{b}}}\)</div>
<div>\(n\)</div>
<div>\(T_1,\ldots,T_n\)</div>
<div>\(T_1\gets 1\)</div>
<div>\(k\)</div>
<div>\(2\)</div>
<div>\(n\)</div>
<div>\(T_k\gets (k−1)T_{k−1}\)</div>
<div>\(k\)</div>
<div>\(2\)</div>
<div>\(n\)</div>
<div>\(j\)</div>
<div>\(k\)</div>
<div>\(n\)</div>
<div>\(T_j\gets (j −k)T_{j−1} + (j −k+2)T_j\)</div>
<div>\(\;T_1,T_2,\ldots,T_n\)</div>
<div>\(n\)</div>
<div>\(T_1,\ldots,T_n\)</div>
<div>\(T_1\gets 1\)</div>
<div>\(\;k\;\)</div>
<div>\(2\;\)</div>
<div>\(\;n\)</div>
<div>\(\phantom{{}++{}}\)</div>
<div>\(T_k\gets (k−1)T_{k−1}\)</div>
<div>\(\;k\;\)</div>
<div>\(2\;\)</div>
<div>\(\;n\)</div>
<div>\(\phantom{{}++{}}\)</div>
<div>\(\;j\;\)</div>
<div>\(\;k\;\)</div>
<div>\(\;n\)</div>
<div>\(\phantom{{}++{}}\)</div>
<div>\(\phantom{{}++{}}\)</div>
<div>\(T_j\gets (j −k)T_{j−1} + (j −k+2)T_j\)</div>
<div>\(\;T_1,T_2,\ldots,T_n\)</div>
<div>\(\LaTeX\)</div>
<div>\[e=mc^2 \tag{1}\label{eq1}\]</div>
<div>\(\eqref{eq1}\)</div>
<div>\(\eqref{eq1}\)</div>
<div>
\[
\begin{equation}\begin{aligned}
a &amp;= b + c \\
&amp;= d + e + f + g \\
&amp;= h + i
\end{aligned}\end{equation}\tag{2}\label{eq2}
\]
</div>
<div>\(\eqref{eq2}\)</div>
<div>\(\eqref{eq2}\)</div>
<div>\begin{align}
a &amp;= b + c \tag{3}\label{eq3} \\
x &amp;= yz \tag{4}\label{eq4}\\
l &amp;= m - n \tag{5}\label{eq5}
\end{align}</div>
<div>\(\eqref{eq3}\)</div>
<div>\(\eqref{eq4}\)</div>
<div>\(\eqref{eq5}\)</div>
<div>\begin{array}{ll}
\text{maximize} &amp; c^T x \\
\text{subject to}&amp; d^T x = \alpha \\
&amp;0 \le x \le 1.
\end{array}</div>
<div>\begin{alignat}{5}
\max \quad &amp; z = &amp; x_1 &amp; + &amp; 12 x_2 &amp; &amp; &amp; &amp;&amp; \\
\mbox{s.t.} \quad &amp; &amp; 13 x_1 &amp; + &amp; x_2 &amp; + &amp; 12x_3 &amp; \geq 5 &amp;&amp; \tag{constraint 1} \\
&amp; &amp; x_1 &amp; &amp; &amp; + &amp; x_3 &amp; \leq 16 &amp;&amp; \tag{constraint 2} \\
&amp; &amp; 15 x_1 &amp; + &amp; 201 x_2 &amp; &amp; &amp; = 14 &amp;&amp; \tag{constraint 3} \\
&amp; &amp; \rlap{x_i \ge 0, i = 1, 2, 3}
\end{alignat}</div>
<div>\(\max\)</div>
<div>\(z\)</div>
<div>\(\pm\)</div>
<div>\(\rm\LaTeX\)</div>
<div>\(\rm\LaTeX\)</div>
<div>
\[
\begin{bmatrix}
1 &amp; 2 &amp; 2 \\
2 &amp; 3 &amp; 4 \\
4 &amp; 4 &amp; 2
\end{bmatrix}.
\]
</div>
<div>\(z\)</div>
<div>\(z\)</div>
<div>\begin{array}{rrrrrr|r}
&amp; x_1 &amp; x_2 &amp; s_1 &amp; s_2 &amp; s_3 &amp; \\ \hline
s_1 &amp; 0 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 8 \\
s_2 &amp; 1 &amp; -1 &amp; 0 &amp; 1 &amp; 0 &amp; 4 \\
s_3 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 1 &amp; 12 \\ \hline
&amp; -1 &amp; -1 &amp; 0 &amp; 0 &amp; 0 &amp; 0
\end{array}</div>
<div>\begin{array}{rrrrrrr|rr}
&amp; x_1 &amp; x_2 &amp; s_1 &amp; s_2 &amp; s_3 &amp; w &amp; &amp; \text{ratio} \\ \hline
s_1 &amp; 0 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 8 &amp; - \\
w &amp; 1^* &amp; -1 &amp; 0 &amp; -1 &amp; 0 &amp; 1 &amp; 4 &amp; 4 \\
s_3 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; 12 &amp; 12 \\ \hdashline
&amp; 1 &amp; -1 &amp; 0 &amp; -1 &amp; 0 &amp; 0 &amp; 4 &amp; \\ \hline
s_1 &amp; 0 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 8 &amp; \\
x_1 &amp; 1 &amp; -1 &amp; 0 &amp; -1 &amp; 0 &amp; 1 &amp; 4 &amp; \\
s_3 &amp; 0 &amp; 2 &amp; 0 &amp; 2 &amp; 1 &amp; -1 &amp; 8 &amp; \\ \hdashline
&amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; -1 &amp; 0 &amp;
\end{array}</div>
<div>\begin{array}{rrrrrrrr|r}
&amp; x_1 &amp; x_2 &amp; x_3 &amp; x_4 &amp; x_5 &amp; x_6 &amp; x_7 &amp; \\ \hline
x_4 &amp; 0 &amp; -3 &amp; 7 &amp; 1 &amp; 0 &amp; 0 &amp; 2 &amp; 2M -4 \\
x_5 &amp; 0 &amp; -9 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; -1 &amp; -M -3 \\
x_6 &amp; 0 &amp; 6 &amp; -1 &amp; 0 &amp; 0 &amp; 1 &amp; -4^* &amp; -4M +8 \\
x_1 &amp; 1 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; M \\ \hline
&amp; 0 &amp; 1 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 2 &amp; 2M \\
\text{ratio} &amp; &amp; &amp; 1 &amp; &amp; &amp; &amp; 1/2 &amp;
\end{array}</div>
<div>\begin{array}{rrrrrrr|r}
&amp; x_1 &amp; x_2 &amp; x_3 &amp; s_1 &amp; s_2 &amp; s_3 &amp; \\ \hline
s_1 &amp; -2 &amp; 0 &amp; -2 &amp; 1 &amp; 0 &amp; 0 &amp; -60 \\
s_2 &amp; -2 &amp; -4^* &amp; -5 &amp; 0 &amp; 1 &amp; 0 &amp; -70 \\
s_3 &amp; 0 &amp; -3 &amp; -1 &amp; 0 &amp; 0 &amp; 1 &amp; -27 \\ \hdashline
&amp; 8 &amp; 10 &amp; 25 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
\text{ratio} &amp; -4 &amp; -5/2 &amp; -5 &amp; &amp; &amp; &amp; \\ \hline
s_1 &amp; -2^* &amp; 0 &amp; -2 &amp; 1 &amp; 0 &amp; 0 &amp; -60 \\
x_2 &amp; 1/2 &amp; 1 &amp; 5/4 &amp; 0 &amp; -1/4 &amp; 0 &amp; 35/2 \\
s_3 &amp; 3/2 &amp; 0 &amp; 11/4 &amp; 0 &amp; -3/4 &amp; 1 &amp; 51/2 \\ \hdashline
&amp; 3 &amp; 0 &amp; 25/2 &amp; 0 &amp; 5/2 &amp; 0 &amp; -175 \\
\text{ratio} &amp; -3/2 &amp; &amp; 25/4 &amp; &amp; &amp; &amp; \\ \hline
x_1 &amp; 1 &amp; 0 &amp; 1 &amp; -1/2 &amp; 0 &amp; 0 &amp; 30 \\
x_2 &amp; 0 &amp; 1 &amp; 3/4 &amp; 1/4 &amp; -1/4 &amp; 0 &amp; 5/2 \\
s_3 &amp; 0 &amp; 0 &amp; 5/4 &amp; 3/4 &amp; -3/4^* &amp; 1 &amp; -39/2 \\ \hdashline
&amp; 0 &amp; 0 &amp; 19/2 &amp; 3/2 &amp; 5/2 &amp; 0 &amp; -265 \\
\text{ratio} &amp; &amp; &amp; &amp; &amp; \dots &amp; &amp; \\ \hline
x_1 &amp; 1 &amp; 0 &amp; 1 &amp; -1/2 &amp; 0 &amp; 0 &amp; 30 \\
x_2 &amp; 0 &amp; 1 &amp; 1/3 &amp; 0 &amp; 0 &amp; -1/3 &amp; 9 \\
s_2 &amp; 0 &amp; 0 &amp; -5/3 &amp; -1 &amp; 1 &amp; -4/3 &amp; 26 \\ \hdashline
&amp; 0 &amp; 0 &amp; 41/3 &amp; 4 &amp; 0 &amp; 10/3 &amp; -330
\end{array}</div>
<div>\[
\require{extpfeil} % produce extensible horizontal arrows
\begin{array}{ccc} % arrange LPPs
% first row
% first LPP
\begin{array}{ll}
\max &amp; z = c^T x \\
\text{s.t.} &amp; A x \le b \\
&amp; x \ge 0
\end{array}
&amp; \xtofrom{\text{duality}} &amp;
% second LPP
\begin{array}{ll}
\min &amp; v = b^T y \\
\text{s.t.} &amp; A^T y \ge c \\
&amp; y \ge 0
\end{array} \\
({\cal PC}) &amp; &amp; ({\cal DC}) \\
\text{add } {\Large \downharpoonleft} \text{slack var} &amp; &amp; \text{minus } {\Large \downharpoonright} \text{surplus var}\\ % Change to your favorite arrow style
%
% second row
% third LPP
\begin{array}{ll}
\max &amp; z = c^T x \\
\text{s.t.} &amp; A x + s = b \\
&amp; x,s \ge 0
\end{array}
&amp; \xtofrom[\text{some steps skipped}]{\text{duality}} &amp;
% fourth LPP
\begin{array}{ll}
\min &amp; v = b^T y \\
\text{s.t.} &amp; A^T y - t = c \\
&amp; y,t \ge 0
\end{array} \\
({\cal PS}) &amp; &amp; ({\cal DS})
%
\end{array}
\]
</div>
<div>\(\sum_{i=n}^\mathbb{N}\)</div>
<div>\(\sum\)</div>
</body>
</html>
<!DOCTYPE html><html><head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Math.SE extracted Samples</title>
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<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">∑</span></span></span><span class="mjx-stack" style="vertical-align: -0.31em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.422em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 4.646em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 6.57em; top: -1.87em;"><span class="mjx-mrow" style=""><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.435em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 6.57em; bottom: -0.687em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 4.646em;" class="mjx-line"></span></span><span style="height: 1.808em; vertical-align: -0.486em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em; padding-left: 0.721em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.74em; padding-bottom: 0.74em;">∑</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.21em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 7.39em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 7.39em; top: -1.667em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-denominator" style="width: 7.39em; bottom: -0.778em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 7.39em;" class="mjx-line"></span></span><span style="height: 2.445em; vertical-align: -0.778em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\alpha, \beta, … \omega"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">α</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.446em; padding-right: 0.007em;">β</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">…</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">ω</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Gamma, \Delta, …, \Omega"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">Γ</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Δ</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">…</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Ω</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x_i^2"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-stack" style="vertical-align: -0.311em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\log_2 x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">log</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.377em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="10^10"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">10</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="10^{10}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">10</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">10</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{x^y}^z"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span></span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.594em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x^{y^z}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.435em; padding-left: 0.069em; padding-right: 0.06em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x_i^2"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-stack" style="vertical-align: -0.311em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x_{i^2}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.365em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.347em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="(2+3)[4+4]"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">[</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">]</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\{\}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="(\frac{\sqrt x}{y^3})"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.135em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.605em; top: -1.766em;"><span class="mjx-msqrt" style=""><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.236em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.605em; bottom: -1.043em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.347em; padding-left: 0.069em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.135em;" class="mjx-line"></span></span><span style="height: 1.987em; vertical-align: -0.738em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\left(\frac{\sqrt x}{y^3}\right)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.135em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.605em; top: -1.766em;"><span class="mjx-msqrt" style=""><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.236em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.605em; bottom: -1.043em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.347em; padding-left: 0.069em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.135em;" class="mjx-line"></span></span><span style="height: 1.987em; vertical-align: -0.738em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="(x)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="[x]"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">[</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">]</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\{ x \}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="|x|"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\vert x \vert"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Vert x \Vert"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\langle x \rangle"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">⟨</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">⟩</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lceil x \rceil"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">⌈</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">⌉</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lfloor x \rfloor"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">⌊</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">⌋</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\left.\frac12\right\rbrace"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="width: 0.12em;"></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.495em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.7em; top: -1.372em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.7em; bottom: -0.665em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.495em;" class="mjx-line"></span></span><span style="height: 1.441em; vertical-align: -0.47em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">}</span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">(</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">(</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">)</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">)</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sum_1^n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">∑</span></span></span><span class="mjx-stack" style="vertical-align: -0.31em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.422em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sum_{i=0}^\infty i^2"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">∑</span></span></span><span class="mjx-stack" style="vertical-align: -0.31em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.422em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\prod"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">∏</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\int"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\bigcup"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">⋃</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\bigcap"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">⋂</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\iint"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∬</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\iiint"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∭</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\frac ab"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.515em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.729em; top: -1.157em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.729em; bottom: -0.704em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.515em;" class="mjx-line"></span></span><span style="height: 1.316em; vertical-align: -0.498em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\frac{a+1}{b+1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.419em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 2.007em; top: -1.454em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 2.007em; bottom: -0.775em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.419em;" class="mjx-line"></span></span><span style="height: 1.577em; vertical-align: -0.548em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{a+1\over b+1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.419em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 2.007em; top: -1.454em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 2.007em; bottom: -0.775em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.419em;" class="mjx-line"></span></span><span style="height: 1.577em; vertical-align: -0.548em;" class="mjx-vsize"></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\cfrac{a}{b}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.67em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.948em; top: -1.816em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.948em; bottom: -1.266em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.67em;" class="mjx-line"></span></span><span style="height: 2.18em; vertical-align: -0.895em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathbb{CHNQRZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.593em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathbf{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em; padding-right: 0.101em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.593em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.593em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.372em; padding-bottom: 0.372em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.593em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.593em; padding-right: 0.002em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.593em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-B" style="padding-top: 0.151em; padding-bottom: 0.372em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.225em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em; padding-right: 0.003em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathtt{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.225em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.225em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em; padding-right: 0.011em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.02em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathrm{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.066em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.519em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.519em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.519em; padding-right: 0.007em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.519em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathsf{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.041em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.446em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathcal{ ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.021em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.007em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.006em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.036em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.11em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.446em; padding-right: 0.004em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.097em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.446em; padding-right: 0.161em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.519em; padding-bottom: 0.372em; padding-right: 0.159em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.037em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.036em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.288em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.061em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.045em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.046em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.094em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.446em; padding-right: 0.046em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-cal-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.042em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.213em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.02em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.153em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.081em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.156em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.095em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.128em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.272em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.137em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.081em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.29em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.161em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.136em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.306em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.067em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.018em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.002em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.037em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.148em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.249em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.16em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.228em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.221em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.187em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.249em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-script-R" style="padding-top: 0.519em; padding-bottom: 0.225em; padding-right: 0.211em;">Z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \mathfrak{abcdefghijklmnopqrstuvwxyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">E</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.446em; padding-right: 0.001em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">I</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">J</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.014em;">K</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">P</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">Q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.007em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.019em;">U</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">V</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.008em;">W</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">X</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">Y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.519em; padding-bottom: 0.446em;">Z</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">f</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.298em; padding-bottom: 0.519em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">q</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.015em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.446em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.298em; padding-bottom: 0.519em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">z</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sqrt{x^3}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.081em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sqrt[3]{\frac xy}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mroot"><span class="mjx-root" style="font-size: 58.9%; vertical-align: 0.477em; width: 0px;"><span class="mjx-mn" style="padding-left: 0.561em;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">√</span></span><span class="mjx-box" style="padding-top: 0.224em; border-top: 1px solid;"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.546em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.772em; top: -1.159em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.772em; bottom: -0.718em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.546em;" class="mjx-line"></span></span><span style="height: 1.327em; vertical-align: -0.507em;" class="mjx-vsize"></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sin x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">sin</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="sin x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\lim_{x\to 0}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lt\, \gt\, \le\, \leq\, \leqq\, \leqslant\, \ge\, \geq\, \geqq\, \geqslant\, \neq"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">&lt;</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">&gt;</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;">≤</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;">≤</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.519em; padding-bottom: 0.446em;">≦</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.372em; padding-bottom: 0.446em;">⩽</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;">≥</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;">≥</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.519em; padding-bottom: 0.446em;">≧</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.372em; padding-bottom: 0.446em;">⩾</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">≠</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\not\lt"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">≮</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\times\, \div\, \pm\, \mp"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">×</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">÷</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">±</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">∓</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x\cdot y"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\cup\, \cap\, \setminus\, \subset\, \subseteq \,\subsetneq \,\supset\, \in\, \notin\, \emptyset\, \varnothing"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">∪</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">∩</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∖</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⊂</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;">⊆</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">⊊</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⊃</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">∈</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∉</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.446em;">∅</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">∅</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{n+1 \choose 2k}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mrow"><span class="mjx-TeXmathchoice"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span></span></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.328em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.878em; top: -1.319em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.878em; bottom: -0.524em;"><span class="mjx-mrow" style=""><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span></span></span></span><span style="height: 1.303em; vertical-align: -0.37em;" class="mjx-vsize"></span></span><span class="mjx-TeXmathchoice"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\to\, \rightarrow\, \leftarrow\, \Rightarrow\, \Leftarrow\, \mapsto"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">←</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⇒</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⇐</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">↦</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\land\, \lor\, \lnot\, \forall\, \exists\, \top\, \bot\, \vdash\, \vDash"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">∧</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">∨</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">¬</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">∀</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">∃</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">⊤</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">⊥</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">⊢</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">⊨</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\star\, \ast\, \oplus\, \circ\, \bullet"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">⋆</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">∗</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">⊕</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">∘</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">∙</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\approx\, \sim \, \simeq\, \cong\, \equiv\, \prec, \lhd"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">≈</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">∼</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">≃</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char" style="padding-top: 0.298em; padding-bottom: 0.004em;"><span class="mjx-charbox MJXc-TeX-main-R" style="padding-bottom: 0.314em; margin-right: -0.222em;">≅</span></span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">≡</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">≺</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">⊲</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\infty\, \aleph_0"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">ℵ</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\nabla\, \partial"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">∇</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.035em;">∂</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Im\, \Re"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">I</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-frak-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="a\equiv b\pmod n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">≡</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-TeXmathchoice"><span class="mjx-mspace" style="width: 0.444em; height: 0px;"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">mod</span></span><span class="mjx-mspace" style="width: 0.333em; height: 0px;"></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="a_1, a_2, \ldots ,a_n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">…</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="a_1+a_2+\cdots+a_n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\epsilon\, \varepsilon"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">ϵ</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">ε</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\phi\, \varphi"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">ϕ</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em;">φ</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\ell"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">ℓ</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\TeX"><span class="mjx-mrow" style="width: 2.065em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\LaTeX"><span class="mjx-mrow" style="width: 2.72em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mspace" style="margin-right: -0.325em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.327em; padding: 0px 0.469em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -0.463em 0px -0.016em; position: relative; top: -0.21em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.17em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\TeX"><span class="mjx-mrow" style="width: 2.065em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="a b"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="a\,b"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="a\;b"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="a\quad b"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="a\qquad b"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mspace" style="width: 2em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\{x\in s\mid x\text{ is extra large}\}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">∈</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∣</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">&nbsp;is extra large</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\hat x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.213em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">^</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\widehat{xy}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.257em; padding-bottom: 0.06em; padding-left: 0.034em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.519em; padding-bottom: 0.225em;">ˆ</span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\bar x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.096em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">¯</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\overline{xyz}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; height: 0.096em; padding-bottom: 0.283em; padding-top: 0.141em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin: 0px -0.07em 0px -0.069em;">¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; letter-spacing: -0.242em; margin: 0px 0.031em 0px -0.17em;">¯¯¯¯¯¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin-right: -0.07em; margin-bottom: 0px; margin-top: 0px;">¯</span></span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\vec x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.248em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-vec-R" style="padding-top: 0.519em; padding-bottom: 0.225em;">→</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\overrightarrow{xy}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="padding-bottom: 0.06em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.299em 0px -0.084em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.056em 0px -0.271em;">→</span></span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\overleftrightarrow{xy}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="padding-bottom: 0.06em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.41em 0px -0.055em;">←</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.056em 0px -0.41em;">→</span></span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\frac d{dx}x\dot x = \dot x^2 + x\ddot x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.916em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.295em; top: -1.41em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.295em; bottom: -0.704em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.916em;" class="mjx-line"></span></span><span style="height: 1.495em; vertical-align: -0.498em;" class="mjx-vsize"></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.17em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">˙</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.17em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">˙</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.6em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.165em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">¨</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\$"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">$</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\{"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\_"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">_</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\backslash"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∖</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\LaTeX"><span class="mjx-mrow" style="width: 2.72em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mspace" style="margin-right: -0.325em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.327em; padding: 0px 0.469em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -0.463em 0px -0.016em; position: relative; top: -0.21em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.17em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathrm{B}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sin"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">sin</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\operatorname{Spec} A"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">Spec</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="_5C_3"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char"></span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">5</span></span></span></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.045em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\TeX"><span class="mjx-mrow" style="width: 2.065em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\TeX"><span class="mjx-mrow" style="width: 2.065em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\LaTeX"><span class="mjx-mrow" style="width: 2.72em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mspace" style="margin-right: -0.325em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.327em; padding: 0px 0.469em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -0.463em 0px -0.016em; position: relative; top: -0.21em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.17em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathrm{d}x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{matrix}
1 &amp; x &amp; x^2 \\
1 &amp; y &amp; y^2 \\
1 &amp; z &amp; z^2 \\
\end{matrix}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -1.742em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.252em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0.5em; width: 0.572em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; width: 0.961em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.482em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0.082em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.252em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0.076em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\begin{pmatrix}1&amp;2\\3&amp;4\\ \end{pmatrix}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">(</span></span><span class="mjx-mtable" style="vertical-align: -0.95em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">)</span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\begin{bmatrix}1&amp;2\\3&amp;4\\ \end{bmatrix}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">[</span></span><span class="mjx-mtable" style="vertical-align: -0.95em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">]</span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\begin{Bmatrix}1&amp;2\\3&amp;4\\ \end{Bmatrix}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">{</span></span><span class="mjx-mtable" style="vertical-align: -0.95em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">}</span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\begin{vmatrix}1&amp;2\\3&amp;4\\ \end{vmatrix}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.676em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∣</span><span class="mjx-char MJXc-TeX-main-R" style="line-height: 0.402em; margin-bottom: 0.014em; margin-top: -0.114em;">∣</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∣</span></span></span><span class="mjx-mtable" style="vertical-align: -0.95em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="vertical-align: -0.676em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∣</span><span class="mjx-char MJXc-TeX-main-R" style="line-height: 0.402em; margin-bottom: 0.014em; margin-top: -0.114em;">∣</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∣</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\begin{Vmatrix}1&amp;2\\3&amp;4\\ \end{Vmatrix}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.675em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span><span class="mjx-char MJXc-TeX-main-R" style="line-height: 0.4em; margin-bottom: 0.014em; margin-top: -0.114em;">∥</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span><span class="mjx-mtable" style="vertical-align: -0.95em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="vertical-align: -0.675em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span><span class="mjx-char MJXc-TeX-main-R" style="line-height: 0.4em; margin-bottom: 0.014em; margin-top: -0.114em;">∥</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\cdots"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\ddots"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 1.256em; padding-bottom: 0.298em;">⋱</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\vdots"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 1.035em; padding-bottom: 0.372em;">⋮</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{pmatrix}
1 &amp; a_1 &amp; a_1^2 &amp; \cdots &amp; a_1^n \\
1 &amp; a_2 &amp; a_2^2 &amp; \cdots &amp; a_2^n \\
\vdots &amp; \vdots&amp; \vdots &amp; \ddots &amp; \vdots \\
1 &amp; a_m &amp; a_m^2 &amp; \cdots &amp; a_m^n
\end{pmatrix}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -2.276em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎛</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.554em; margin-bottom: -0.1em; margin-top: 0px;">⎜
⎜</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎝</span></span></span><span class="mjx-mtable" style="vertical-align: -2.945em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.393em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0.5em; width: 1.185em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0.5em; width: 1.185em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-stack" style="vertical-align: -0.315em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0.5em; width: 1.282em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; width: 1.185em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-stack" style="vertical-align: -0.315em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.593em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-stack" style="vertical-align: -0.315em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-stack" style="vertical-align: -0.315em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 2.145em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: 0.22em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 1.035em; padding-bottom: 0.372em;">⋮</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: 0.22em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 1.035em; padding-bottom: 0.372em;">⋮</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: 0.22em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 1.035em; padding-bottom: 0.372em;">⋮</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 1.256em; padding-bottom: 0.298em;">⋱</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: 0.22em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 1.035em; padding-bottom: 0.372em;">⋮</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.26em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-stack" style="vertical-align: -0.157em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.14em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-stack" style="vertical-align: -0.157em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="vertical-align: -2.276em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎞</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.554em; margin-bottom: -0.1em; margin-top: 0px;">⎟
⎟</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎠</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\left[\begin{array}{cc|c}
1&amp;2&amp;3\\
4&amp;5&amp;6
\end{array}\right]
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">[</span></span><span class="mjx-mtable" style="vertical-align: -1.171em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.221em 0.463em 0px 0.5em; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.463em; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">5</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">]</span></span></span></span></span></span></span>
</div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{pmatrix}
a &amp; b \\
c &amp; d\\
\hline
1 &amp; 0\\
0 &amp; 1
\end{pmatrix}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -1.902em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎛</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.506em; margin-bottom: -0.1em; margin-top: 0px;">⎜
⎜</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎝</span></span></span><span class="mjx-mtable" style="vertical-align: -2.571em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; width: 0.529em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; width: 0.523em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; border-bottom: 1.3px solid;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; border-bottom: 1.3px solid;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="vertical-align: -1.902em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎞</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.506em; margin-bottom: -0.1em; margin-top: 0px;">⎟
⎟</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎠</span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\bigl( \begin{smallmatrix} a &amp; b \\ c &amp; d \end{smallmatrix} \bigr)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span></span></span><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-mtable" style="vertical-align: -0.605em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 0.855em;"><span class="mjx-mtd" style="padding: 0px 0.167em 0px 0px; width: 0.529em;"><span class="mjx-mrow" style="margin-top: -0.281em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.167em; width: 0.523em;"><span class="mjx-mrow" style="margin-top: -0.281em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 0.855em;"><span class="mjx-mtd" style="padding: 0.1em 0.167em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.281em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.1em 0px 0px 0.167em;"><span class="mjx-mrow" style="margin-top: -0.281em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{align}
\sqrt{37} &amp; = \sqrt{\frac{73^2-1}{12^2}} \\
&amp; = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\
&amp; = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
&amp; = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\
&amp; \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
\end{align}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -7.817em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 3.26em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: right; width: 1.833em;"><span class="mjx-mrow" style="margin-top: 0.87em;"><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.066em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">37</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: left; width: 9.019em;"><span class="mjx-mrow"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msqrt MJXc-space3"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">√</span></span><span class="mjx-box" style="padding-top: 0.157em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 3.311em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 3.311em; top: -1.593em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.605em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="width: 3.311em; bottom: -0.972em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">12</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 3.311em;" class="mjx-line"></span></span><span style="height: 2.565em; vertical-align: -0.972em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 3.41em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: 0.854em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msqrt MJXc-space3"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">√</span></span><span class="mjx-box" style="padding-top: 0.141em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.589em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.589em; top: -1.593em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.605em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="width: 1.589em; bottom: -0.972em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">12</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.589em;" class="mjx-line"></span></span><span style="height: 2.565em; vertical-align: -0.972em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 3.311em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 3.311em; top: -1.593em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.605em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="width: 3.311em; bottom: -1.004em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.605em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 3.311em;" class="mjx-line"></span></span><span style="height: 2.597em; vertical-align: -1.004em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 3.426em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: 0.87em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msqrt MJXc-space3"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">√</span></span><span class="mjx-box" style="padding-top: 0.157em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.589em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.589em; top: -1.593em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.605em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="width: 1.589em; bottom: -0.972em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">12</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.589em;" class="mjx-line"></span></span><span style="height: 2.565em; vertical-align: -0.972em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">√</span></span><span class="mjx-box" style="padding-top: 0.141em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 3.311em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 3.311em; top: -1.593em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.605em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="width: 3.311em; bottom: -1.004em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.605em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 3.311em;" class="mjx-line"></span></span><span style="height: 2.597em; vertical-align: -1.004em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 3.41em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: 0.742em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 1.2em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.2em; top: -1.378em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-denominator" style="width: 1.2em; bottom: -0.756em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">12</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.2em;" class="mjx-line"></span></span><span style="height: 2.134em; vertical-align: -0.756em;" class="mjx-vsize"></span></span><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">√</span></span><span class="mjx-box" style="padding-top: 0.254em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 1.589em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.589em; top: -1.368em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="width: 1.589em; bottom: -1.004em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.605em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.589em;" class="mjx-line"></span></span><span style="height: 2.371em; vertical-align: -1.004em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 2.629em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: 0.475em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">≈</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 1.2em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.2em; top: -1.378em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-denominator" style="width: 1.2em; bottom: -0.756em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">12</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.2em;" class="mjx-line"></span></span><span style="height: 2.134em; vertical-align: -0.756em;" class="mjx-vsize"></span></span><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 2.811em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 2.811em; top: -1.368em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="width: 2.811em; bottom: -1.004em;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">73</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.605em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 2.811em;" class="mjx-line"></span></span><span style="height: 2.371em; vertical-align: -1.004em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">)</span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{align} f(x)&amp;=\left(x^3\right)+\left(x^3+x^2+x^1\right)+\left(x^3+x^2\right)\\ f'(x)&amp;=\left(\left(3x^2+2x+1\right)+\left(3x^2+2x\right)\right)\\ f''(x)&amp;=\left(6x+2\right)\\ \end{align}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -1.876em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.426em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: right; width: 2.392em;"><span class="mjx-mrow" style="margin-top: -0.098em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: left; width: 15.959em;"><span class="mjx-mrow" style="margin-top: -0.098em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mrow MJXc-space3"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mrow MJXc-space2"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mrow MJXc-space2"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.576em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.098em;"><span class="mjx-msup"><span class="mjx-base" style="margin-right: -0.06em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0.181em; padding-right: 0.071em;"><span class="mjx-mo" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">′</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.098em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mrow MJXc-space3"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mrow MJXc-space2"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">)</span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.252em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.173em;"><span class="mjx-msup"><span class="mjx-base" style="margin-right: -0.06em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0.181em; padding-right: 0.071em;"><span class="mjx-mo" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">′′</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.173em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mrow MJXc-space3"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{}{}{}{}{}{}{}{}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Psi"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">Ψ</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\delta"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.007em;">δ</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\zeta"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.033em;">ζ</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\ge"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;">≥</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\subseteq"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.446em;">⊆</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\LaTeX"><span class="mjx-mrow" style="width: 2.72em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mspace" style="margin-right: -0.325em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.327em; padding: 0px 0.469em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -0.463em 0px -0.016em; position: relative; top: -0.21em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.17em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\LaTeX"><span class="mjx-mrow" style="width: 2.72em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mspace" style="margin-right: -0.325em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.327em; padding: 0px 0.469em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -0.463em 0px -0.016em; position: relative; top: -0.21em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.17em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div>f(n) =
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{cases}
n/2, &amp; \text{if $n$ is even} \\
3n+1, &amp; \text{if $n$ is odd}
\end{cases}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">{</span></span><span class="mjx-mtable" style="vertical-align: -0.897em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.175em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; text-align: left; width: 3.1em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; text-align: left; width: 4.578em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">if&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">&nbsp;is even</span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.119em;"><span class="mjx-mtd" style="padding: 0.1em 0.5em 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.1em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">if&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">&nbsp;is odd</span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="width: 0.12em;"></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\left.
\begin{array}{l}
\text{if $n$ is even:}&amp;n/2\\
\text{if $n$ is odd:}&amp;3n+1
\end{array}
\right\}
=f(n)
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="width: 0.12em;"></span><span class="mjx-mtable" style="vertical-align: -0.988em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.275em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; text-align: left; width: 4.856em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">if&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">&nbsp;is even:</span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; text-align: left; width: 2.822em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.2em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">if&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">&nbsp;is odd:</span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">}</span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span>
</div>
<div>f(n) =
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{cases}
\frac{n}{2}, &amp; \text{if $n$ is even} \\[2ex]
3n+1, &amp; \text{if $n$ is odd}
\end{cases}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.511em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.667em; padding-bottom: 0.298em; margin-bottom: -0.209em;">⎧</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎨</span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: -0.426em; padding-bottom: 1.182em;">⎩</span></span></span><span class="mjx-mtable" style="vertical-align: -1.435em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.82em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; text-align: left; width: 3.1em;"><span class="mjx-mrow" style="margin-top: -0.18em;"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.566em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.8em; top: -1.159em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.8em; bottom: -0.665em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.566em;" class="mjx-line"></span></span><span style="height: 1.29em; vertical-align: -0.47em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; text-align: left; width: 4.578em;"><span class="mjx-mrow" style="margin-top: -0.18em;"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">if&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">&nbsp;is even</span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.549em;"><span class="mjx-mtd" style="padding: 0.53em 0.5em 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.53em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">if&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">&nbsp;is odd</span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="width: 0.12em;"></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{array}{c|lcr}
n &amp; \text{Left} &amp; \text{Center} &amp; \text{Right} \\
\hline
1 &amp; 0.24 &amp; 1 &amp; 125 \\
2 &amp; -1 &amp; 189 &amp; -8 \\
3 &amp; -20 &amp; 2000 &amp; 1+10i
\end{array}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -2.587em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.452em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.221em 0.463em 0px 0.4em; border-bottom: 1.3px solid; width: 0.6em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.463em; border-bottom: 1.3px solid; text-align: left; width: 1.778em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Left</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; border-bottom: 1.3px solid; width: 2.947em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Center</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; text-align: right; width: 3.067em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">Right</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0.24</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">125</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">189</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">8</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">20</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2000</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">10</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
% outer vertical array of arrays
\begin{array}{c}
% inner horizontal array of arrays
\begin{array}{cc}
% inner array of minimum values
\begin{array}{c|cccc}
\text{min} &amp; 0 &amp; 1 &amp; 2 &amp; 3\\
\hline
0 &amp; 0 &amp; 0 &amp; 0 &amp; 0\\
1 &amp; 0 &amp; 1 &amp; 1 &amp; 1\\
2 &amp; 0 &amp; 1 &amp; 2 &amp; 2\\
3 &amp; 0 &amp; 1 &amp; 2 &amp; 3
\end{array}
&amp;
% inner array of maximum values
\begin{array}{c|cccc}
\text{max}&amp;0&amp;1&amp;2&amp;3\\
\hline
0 &amp; 0 &amp; 1 &amp; 2 &amp; 3\\
1 &amp; 1 &amp; 1 &amp; 2 &amp; 3\\
2 &amp; 2 &amp; 2 &amp; 2 &amp; 3\\
3 &amp; 3 &amp; 3 &amp; 3 &amp; 3
\end{array}
\end{array}
\\
% inner array of delta values
\begin{array}{c|cccc}
\Delta&amp;0&amp;1&amp;2&amp;3\\
\hline
0 &amp; 0 &amp; 1 &amp; 2 &amp; 3\\
1 &amp; 1 &amp; 0 &amp; 1 &amp; 2\\
2 &amp; 2 &amp; 1 &amp; 0 &amp; 1\\
3 &amp; 3 &amp; 2 &amp; 1 &amp; 0
\end{array}
\end{array}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -6.992em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 7.242em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; width: 19.128em;"><span class="mjx-mrow"><span class="mjx-mtable" style="vertical-align: -3.271em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 7.042em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; width: 8.8em;"><span class="mjx-mrow"><span class="mjx-mtable" style="vertical-align: -3.271em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.221em 0.463em 0px 0.4em; border-bottom: 1.3px solid; width: 1.667em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">min</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.463em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; width: 8.994em;"><span class="mjx-mrow"><span class="mjx-mtable" style="vertical-align: -3.271em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.221em 0.463em 0px 0.4em; border-bottom: 1.3px solid; width: 1.861em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">max</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.463em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 7.242em;"><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mtable" style="vertical-align: -3.271em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.221em 0.463em 0px 0.4em; border-bottom: 1.3px solid; width: 0.833em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Δ</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.463em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathsf{Show\ Math\ As\ }\blacktriangleright\mathsf{\ TeX\ Commands}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">S</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-sans-R" style="margin-top: -0.217em; padding-bottom: 0.298em;">&nbsp;</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">M</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-sans-R" style="margin-top: -0.217em; padding-bottom: 0.298em;">&nbsp;</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-sans-R" style="margin-top: -0.217em; padding-bottom: 0.298em;">&nbsp;</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">▶</span></span><span class="mjx-texatom MJXc-space2"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-sans-R" style="margin-top: -0.217em; padding-bottom: 0.298em;">&nbsp;</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">T</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">X</span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-sans-R" style="margin-top: -0.217em; padding-bottom: 0.298em;">&nbsp;</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.519em; padding-bottom: 0.298em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-sans-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="all italics, weird-looking spacing, an' odd apostrophes"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.003em;">g</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.003em;">g</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-msup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mo" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">′</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\LaTeX"><span class="mjx-mrow" style="width: 2.72em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mspace" style="margin-right: -0.325em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.327em; padding: 0px 0.469em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -0.463em 0px -0.016em; position: relative; top: -0.21em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.17em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{array}{ll} \hfill\mathrm{Bad}\hfill &amp; \hfill\mathrm{Better}\hfill \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}&amp; e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx &amp; \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -3.433em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; border-bottom: 1.3px solid; width: 5.078em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; width: 5.565em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: left;"><span style="margin-top: -0.2em;"></span></span></span><span class="mjx-mtr" style="height: 1.878em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: left;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.73em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.644em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 83.3%; width: 0.773em; top: -1.064em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span></span><span class="mjx-denominator" style="font-size: 83.3%; width: 0.773em; bottom: -0.688em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1px solid; top: -0.296em; width: 0.644em;" class="mjx-line"></span></span><span style="height: 1.46em; vertical-align: -0.573em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.73em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.932em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 83.3%; width: 1.118em; top: -1.294em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span></span></span><span class="mjx-denominator" style="font-size: 83.3%; width: 1.118em; bottom: -0.688em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1px solid; top: -0.296em; width: 0.932em;" class="mjx-line"></span></span><span style="height: 1.652em; vertical-align: -0.573em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: 0.278em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 2.666em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: left;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span></span><span class="mjx-stack" style="vertical-align: -0.453em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0.324em; padding-right: 0.071em;"><span class="mjx-mfrac" style=""><span class="mjx-box MJXc-stacked" style="width: 0.644em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 83.3%; width: 0.773em; top: -1.064em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span></span><span class="mjx-denominator" style="font-size: 83.3%; width: 0.773em; bottom: -0.688em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1px solid; top: -0.296em; width: 0.644em;" class="mjx-line"></span></span><span style="height: 1.46em; vertical-align: -0.573em;" class="mjx-vsize"></span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.644em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 83.3%; width: 0.773em; top: -1.064em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span></span><span class="mjx-denominator" style="font-size: 83.3%; width: 0.773em; bottom: -0.688em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1px solid; top: -0.296em; width: 0.644em;" class="mjx-line"></span></span><span style="height: 1.46em; vertical-align: -0.573em;" class="mjx-vsize"></span></span></span></span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">sin</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: 0.28em;"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span></span><span class="mjx-stack" style="vertical-align: -0.366em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.256em; padding-left: 0.324em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">sin</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}&amp; e^{i\pi/2} \\
\int_{-\frac\pi2}^\frac\pi2 \sin x\,dx &amp; \int_{-\pi/2}^{\pi/2}\sin x\,dx \\
\end{array}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -3.433em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; border-bottom: 1.3px solid; width: 5.078em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; width: 5.565em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span style="margin-top: -0.2em;"></span></span></span><span class="mjx-mtr" style="height: 1.878em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.73em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.644em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 83.3%; width: 0.773em; top: -1.064em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span></span><span class="mjx-denominator" style="font-size: 83.3%; width: 0.773em; bottom: -0.688em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1px solid; top: -0.296em; width: 0.644em;" class="mjx-line"></span></span><span style="height: 1.46em; vertical-align: -0.573em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.73em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.932em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 83.3%; width: 1.118em; top: -1.294em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span></span></span><span class="mjx-denominator" style="font-size: 83.3%; width: 1.118em; bottom: -0.688em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1px solid; top: -0.296em; width: 0.932em;" class="mjx-line"></span></span><span style="height: 1.652em; vertical-align: -0.573em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: 0.278em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 2.666em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span></span><span class="mjx-stack" style="vertical-align: -0.453em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0.324em; padding-right: 0.071em;"><span class="mjx-mfrac" style=""><span class="mjx-box MJXc-stacked" style="width: 0.644em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 83.3%; width: 0.773em; top: -1.064em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span></span><span class="mjx-denominator" style="font-size: 83.3%; width: 0.773em; bottom: -0.688em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1px solid; top: -0.296em; width: 0.644em;" class="mjx-line"></span></span><span style="height: 1.46em; vertical-align: -0.573em;" class="mjx-vsize"></span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.644em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 83.3%; width: 0.773em; top: -1.064em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span></span><span class="mjx-denominator" style="font-size: 83.3%; width: 0.773em; bottom: -0.688em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1px solid; top: -0.296em; width: 0.644em;" class="mjx-line"></span></span><span style="height: 1.46em; vertical-align: -0.573em;" class="mjx-vsize"></span></span></span></span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">sin</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: 0.28em;"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span></span><span class="mjx-stack" style="vertical-align: -0.366em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.256em; padding-left: 0.324em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">π</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">sin</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
\{x|x^2\in\Bbb Z\} &amp; \{x\mid x^2\in\Bbb Z\} \\
\end{array}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -1.934em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; border-bottom: 1.3px solid; width: 4.7em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; width: 5.256em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span style="margin-top: -0.2em;"></span></span></span><span class="mjx-mtr" style="height: 1.548em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">∈</span></span><span class="mjx-texatom MJXc-space3"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">Z</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∣</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">∈</span></span><span class="mjx-texatom MJXc-space3"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">Z</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
\int\int_S f(x)\,dy\,dx &amp; \iint_S f(x)\,dy\,dx \\
\int\int\int_V f(x)\,dz\,dy\,dx &amp; \iiint_V f(x)\,dz\,dy\,dx
\end{array}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -2.801em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; border-bottom: 1.3px solid; width: 8.276em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; width: 7.417em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span style="margin-top: -0.2em;"></span></span></span><span class="mjx-mtr" style="height: 1.63em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.169em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.517em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.169em;"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∬</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.517em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.651em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.169em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span><span class="mjx-mo MJXc-space1" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.517em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.186em;">V</span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.169em;"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∭</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.517em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.186em;">V</span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\TeX"><span class="mjx-mrow" style="width: 2.065em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{array}{cc}
\mathrm{Bad} &amp; \mathrm{Better} \\
\hline \\
\iiint_V f(x)dz dy dx &amp; \iiint_V f(x)\,dz\,dy\,dx
\end{array}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -1.986em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; border-bottom: 1.3px solid; width: 6.917em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; width: 7.417em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span style="margin-top: -0.2em;"></span></span></span><span class="mjx-mtr" style="height: 1.651em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.169em;"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∭</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.517em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.186em;">V</span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.169em;"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∭</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.517em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.186em;">V</span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\left\{x\middle | \frac{x^2}{2} \in \mathbb{z}\right\}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">{</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-mo" style="vertical-align: -0.379em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em; margin-bottom: -0.291em;">∣</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em; margin-top: -0.291em;">∣</span></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.87em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.23em; top: -1.631em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.435em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.23em; bottom: -0.665em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.87em;" class="mjx-line"></span></span><span style="height: 1.624em; vertical-align: -0.47em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">∈</span></span><span class="mjx-texatom MJXc-space3"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">z</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">}</span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\require{cancel}\begin{array}{rl}
\verb|y+\cancel{x}| &amp; y+\cancel{x}\\
\verb|\cancel{y+x}| &amp; \cancel{y+x}\\
\verb|y+\bcancel{x}| &amp; y+\bcancel{x}\\
\verb|y+\xcancel{x}| &amp; y+\xcancel{x}\\
\verb|y+\cancelto{0}{x}| &amp; y+\cancelto{0}{x}\\
\verb+\frac{1\cancel9}{\cancel95} = \frac15+&amp; \frac{1\cancel9}{\cancel95} = \frac15 \\
\end{array}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -4.571em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.253em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; text-align: right; width: 19.425em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">y+\cancel{x}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; text-align: left; width: 3.44em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-menclose MJXc-space2"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><svg style="width: 0.972em; height: 0.903em; vertical-align: -0.236em; margin-left: -0.972em;"><g stroke-width="1px"><line x1="0.5px" y1="11.3px" x2="12.2px" y2="0.5px"></line></g></svg></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.638em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">\cancel{y+x}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><svg style="width: 2.69em; height: 1.238em; vertical-align: -0.43em; margin-left: -2.69em;"><g stroke-width="1px"><line x1="0.5px" y1="15.8px" x2="35.5px" y2="0.5px"></line></g></svg></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.453em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">y+\bcancel{x}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-menclose MJXc-space2"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><svg style="width: 0.972em; height: 0.903em; vertical-align: -0.236em; margin-left: -0.972em;"><g stroke-width="1px"><line x1="0.5px" y1="0.5px" x2="12.2px" y2="11.3px"></line></g></svg></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.453em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">y+\xcancel{x}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-menclose MJXc-space2"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><svg style="width: 0.972em; height: 0.903em; vertical-align: -0.236em; margin-left: -0.972em;"><g stroke-width="1px"><line x1="0.5px" y1="11.3px" x2="12.2px" y2="0.5px"></line></g></svg><svg style="width: 0.972em; height: 0.903em; vertical-align: -0.236em; margin-left: -0.972em;"><g stroke-width="1px"><line x1="0.5px" y1="0.5px" x2="12.2px" y2="11.3px"></line></g></svg></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.606em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.047em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">y+\cancelto{0}{x}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.047em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msup MJXc-space2"><span class="mjx-base"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><svg style="width: 0.972em; height: 0.903em; vertical-align: -0.236em; margin-left: -0.972em;"><g stroke-width="1px"><g fill="currentColor" transform="translate(0.5 11.8) rotate(-41.56771594726492)"><line x1="0.5px" y1="0" x2="13px" y2="0"></line><path d="M 13,0 L 12,2L 17,0 L 12,-2" stroke="none"></path></g></g></svg></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.557em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -0.209em; padding: 0px 0.5em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -0.691em 0px -0.047em; position: relative; top: -0.1em;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span><span class="mjx-strut"></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 2.238em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: 0.269em;"><span class="mjx-mtext"><span class="mjx-char" style="padding-top: 0.519em; padding-bottom: 0.077em;"><span class="mjx-charbox MJXc-TeX-type-R" style="padding-bottom: 0.233em; margin-right: 0.275em;">\frac{1\cancel9}{\cancel95}&nbsp;</span><span class="mjx-charbox MJXc-TeX-type-R" style="padding-bottom: 0.233em; margin-right: 0.275em;">=&nbsp;</span><span class="mjx-charbox MJXc-TeX-type-R" style="padding-bottom: 0.233em;">\frac15</span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.131em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.6em; top: -1.794em;"><span class="mjx-mrow" style=""><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">9</span></span></span></span><svg style="width: 0.9em; height: 1.138em; vertical-align: -0.247em; margin-left: -0.9em;"><g stroke-width="1px"><line x1="0.5px" y1="14.4px" x2="11.2px" y2="0.5px"></line></g></svg></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.6em; bottom: -1.087em;"><span class="mjx-mrow" style=""><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">9</span></span></span></span><svg style="width: 0.9em; height: 1.138em; vertical-align: -0.247em; margin-left: -0.9em;"><g stroke-width="1px"><line x1="0.5px" y1="14.4px" x2="11.2px" y2="0.5px"></line></g></svg></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">5</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.131em;" class="mjx-line"></span></span><span style="height: 2.038em; vertical-align: -0.769em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 0.495em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.7em; top: -1.372em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.7em; bottom: -0.687em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">5</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.495em;" class="mjx-line"></span></span><span style="height: 1.456em; vertical-align: -0.486em;" class="mjx-vsize"></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\require{enclose}\begin{array}{rl}
\verb|\enclose{horizontalstrike}{x+y}| &amp; \enclose{horizontalstrike}{x+y}\\
\verb|\enclose{verticalstrike}{\frac xy}| &amp; \enclose{verticalstrike}{\frac xy}\\
\verb|\enclose{updiagonalstrike}{x+y}| &amp; \enclose{updiagonalstrike}{x+y}\\
\verb|\enclose{downdiagonalstrike}{x+y}| &amp; \enclose{downdiagonalstrike}{x+y}\\
\verb|\enclose{horizontalstrike,updiagonalstrike}{x+y}| &amp; \enclose{horizontalstrike,updiagonalstrike}{x+y}\\
\end{array}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -3.89em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.438em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; text-align: right; width: 25.2em;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">\enclose{horizontalstrike}{x+y}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; text-align: left; width: 2.69em;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span><span style="border-top: 1px solid; height: 0.582em; vertical-align: -0.43em; width: 2.69em; margin-left: -2.69em;" class="mjx-box"></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 2.127em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: 0.02em;"><span class="mjx-mtext"><span class="mjx-char" style="padding-top: 0.519em; padding-bottom: 0.225em;"><span class="mjx-charbox MJXc-TeX-type-R" style="padding-bottom: 0.233em; margin-right: 0.275em;">\enclose{verticalstrike}{\frac&nbsp;</span><span class="mjx-charbox MJXc-TeX-type-R" style="padding-bottom: 0.233em;">xy}</span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.546em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.772em; top: -1.159em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.772em; bottom: -0.718em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.546em;" class="mjx-line"></span></span><span style="height: 1.327em; vertical-align: -0.507em;" class="mjx-vsize"></span></span></span></span><span style="border-left: 1px solid; height: 1.727em; vertical-align: -0.707em; width: 0.556em; margin-left: -0.63em;" class="mjx-box"></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.638em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">\enclose{updiagonalstrike}{x+y}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span><svg style="width: 2.69em; height: 1.238em; vertical-align: -0.43em; margin-left: -2.69em;"><g stroke-width="1px"><line x1="0.5px" y1="15.8px" x2="35.5px" y2="0.5px"></line></g></svg></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.638em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">\enclose{downdiagonalstrike}{x+y}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span><svg style="width: 2.69em; height: 1.238em; vertical-align: -0.43em; margin-left: -2.69em;"><g stroke-width="1px"><line x1="0.5px" y1="0.5px" x2="35.5px" y2="15.8px"></line></g></svg></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.438em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">\enclose{horizontalstrike,updiagonalstrike}{x+y}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.192em;"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span><span style="border-top: 1px solid; height: 0.582em; vertical-align: -0.43em; width: 2.69em; margin-left: -2.69em;" class="mjx-box"></span><svg style="width: 2.69em; height: 1.238em; vertical-align: -0.43em; margin-left: -2.69em;"><g stroke-width="1px"><line x1="0.5px" y1="15.8px" x2="35.5px" y2="0.5px"></line></g></svg></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="19/95 = 1/5"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">19</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">95</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">5</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\cancelto{\cancelto{\cancelto{x^{2+x}}{\cancelto{x^2}{x}+4}}4}0"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msup"><span class="mjx-base"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span><svg style="width: 0.9em; height: 1.138em; vertical-align: -0.247em; margin-left: -0.9em;"><g stroke-width="1px"><g fill="currentColor" transform="translate(0.5 14.9) rotate(-50.9583926190483)"><line x1="0.5px" y1="0" x2="14.6px" y2="0"></line><path d="M 14.6,0 L 13.6,2L 18.6,0 L 13.6,-2" stroke="none"></path></g></g></svg></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.874em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: 1.834em; padding: 0px 6.229em 0.125em 0px;"><span class="mjx-box" style="width: 0px; margin: -2.734em 0px -0.225em; position: relative; top: -0.1em;"><span class="mjx-mrow"><span class="mjx-msup"><span class="mjx-base"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span></span><svg style="width: 0.9em; height: 1.127em; vertical-align: -0.225em; margin-left: -0.9em;"><g stroke-width="1px"><g fill="currentColor" transform="translate(0.5 14.8) rotate(-50.66687801800788)"><line x1="0.5px" y1="0" x2="14.5px" y2="0"></line><path d="M 14.5,0 L 13.5,2L 18.5,0 L 13.5,-2" stroke="none"></path></g></g></svg></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.696em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: 1.585em; padding: 0px 6.344em 0.336em 0px;"><span class="mjx-box" style="width: 0px; margin: -2.485em 0px -0.436em; position: relative; top: -0.1em;"><span class="mjx-mrow"><span class="mjx-msup"><span class="mjx-base"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-msup"><span class="mjx-base"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><svg style="width: 0.972em; height: 0.903em; vertical-align: -0.236em; margin-left: -0.972em;"><g stroke-width="1px"><g fill="currentColor" transform="translate(0.5 11.8) rotate(-41.56771594726492)"><line x1="0.5px" y1="0" x2="13px" y2="0"></line><path d="M 13,0 L 12,2L 17,0 L 12,-2" stroke="none"></path></g></g></svg></span></span><span class="mjx-sup" style="vertical-align: 0.363em; padding-left: 0px; padding-right: 0.05em;"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: 0.154em; padding: 0px 1.122em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -1.054em 0px -0.036em; position: relative; top: -0.1em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="vertical-align: 0.363em; padding-left: 0px; padding-right: 0.05em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span></span><svg style="width: 3.822em; height: 2.153em; vertical-align: -0.436em; margin-left: -3.822em;"><g stroke-width="1px"><g fill="currentColor" transform="translate(0.5 28.7) rotate(-28.779234196747712)"><line x1="0.5px" y1="0" x2="54.6px" y2="0"></line><path d="M 54.6,0 L 53.6,2L 58.6,0 L 53.6,-2" stroke="none"></path></g></g></svg></span></span><span class="mjx-sup" style="vertical-align: 1.331em; padding-left: 0px; padding-right: 0.05em;"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: 0.154em; padding: 0px 2.472em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -1.054em 0px -0.036em; position: relative; top: -0.1em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="vertical-align: 0.363em; padding-left: 0px; padding-right: 0.05em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\LaTeX"><span class="mjx-mrow" style="width: 2.72em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mspace" style="margin-right: -0.325em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.327em; padding: 0px 0.469em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -0.463em 0px -0.016em; position: relative; top: -0.21em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.17em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\left\{
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{array}
\right.
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.771em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.667em; padding-bottom: 0.298em;">⎧</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.101em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎨</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.101em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: -0.217em; padding-bottom: 1.182em;">⎩</span></span></span><span class="mjx-mtable" style="vertical-align: -1.695em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.23em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; width: 8.781em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.43em;"><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.23em;"><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="width: 0.12em;"></span></span></span></span></span></span>
</div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{cases}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{cases}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.571em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.667em; padding-bottom: 0.298em; margin-bottom: -0.149em;">⎧</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎨</span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: -0.366em; padding-bottom: 1.182em;">⎩</span></span></span><span class="mjx-mtable" style="vertical-align: -1.495em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.13em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: left; width: 8.781em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.23em;"><span class="mjx-mtd" style="padding: 0.1em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.13em;"><span class="mjx-mtd" style="padding: 0.1em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="width: 0.12em;"></span></span></span></span></span></span>
</div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\left\{\begin{aligned} a_1x+b_1y+c_1z&amp;=d_1+e_1 \\
a_2x+b_2y&amp;=d_2 \\
a_3x+b_3y+c_3z&amp;=d_3 \end{aligned} \right. "><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.671em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.667em; padding-bottom: 0.298em;">⎧</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.001em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎨</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.001em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: -0.217em; padding-bottom: 1.182em;">⎩</span></span></span><span class="mjx-mtable" style="vertical-align: -1.595em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.18em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: right; width: 6.539em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: left; width: 4.32em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.33em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.18em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="width: 0.12em;"></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\left\{\begin{array}{ll}a_1x+b_1y+c_1z &amp;=d_1+e_1 \\ a_2x+b_2y &amp;=d_2 \\ a_3x+b_3y+c_3z &amp;=d_3 \end{array} \right.
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.771em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.667em; padding-bottom: 0.298em;">⎧</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.101em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎨</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.101em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: -0.217em; padding-bottom: 1.182em;">⎩</span></span></span><span class="mjx-mtable" style="vertical-align: -1.695em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.23em;"><span class="mjx-mtd" style="padding: 0px 0.5em 0px 0px; text-align: left; width: 6.539em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.5em; text-align: left; width: 4.042em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.43em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.23em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0px 0px 0.5em; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="width: 0.12em;"></span></span></span></span></span></span></div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\[2ex]
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\[2ex]
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -2.123em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.667em; padding-bottom: 0.298em;">⎧</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.242em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪
⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎨</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.242em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪
⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: -0.217em; padding-bottom: 1.182em;">⎩</span></span></span><span class="mjx-mtable" style="vertical-align: -3.047em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 2.013em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: left; width: 8.933em;"><span class="mjx-mrow" style="margin-top: -0.034em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 0.821em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.161em; top: -1.367em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.161em; bottom: -0.731em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.014em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em; padding-right: 0.014em;">q</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.821em;" class="mjx-line"></span></span><span style="height: 1.483em; vertical-align: -0.517em;" class="mjx-vsize"></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 2.543em;"><span class="mjx-mtd" style="padding: 0.53em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.034em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 0.821em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.161em; top: -1.367em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.161em; bottom: -0.731em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.014em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em; padding-right: 0.014em;">q</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.821em;" class="mjx-line"></span></span><span style="height: 1.483em; vertical-align: -0.517em;" class="mjx-vsize"></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 2.038em;"><span class="mjx-mtd" style="padding: 0.53em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.021em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 0.821em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.161em; top: -1.384em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.266em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.161em; bottom: -0.748em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.014em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em; padding-right: 0.014em;">q</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.266em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.821em;" class="mjx-line"></span></span><span style="height: 1.508em; vertical-align: -0.529em;" class="mjx-vsize"></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="width: 0.12em;"></span></span></span></span></span></span>
</div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{cases}
a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\
a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\
a_3x+b_3y+c_3z=\frac{p_3}{q_3}
\end{cases}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -1.263em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.667em; padding-bottom: 0.298em;">⎧</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.198em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪
⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎨</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.198em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪
⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: -0.217em; padding-bottom: 1.182em;">⎩</span></span></span><span class="mjx-mtable" style="vertical-align: -2.187em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.583em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: left; width: 8.933em;"><span class="mjx-mrow" style="margin-top: -0.034em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 0.821em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.161em; top: -1.367em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.161em; bottom: -0.731em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.014em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em; padding-right: 0.014em;">q</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.821em;" class="mjx-line"></span></span><span style="height: 1.483em; vertical-align: -0.517em;" class="mjx-vsize"></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.683em;"><span class="mjx-mtd" style="padding: 0.1em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.034em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 0.821em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.161em; top: -1.367em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.161em; bottom: -0.731em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.014em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em; padding-right: 0.014em;">q</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.821em;" class="mjx-line"></span></span><span style="height: 1.483em; vertical-align: -0.517em;" class="mjx-vsize"></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.608em;"><span class="mjx-mtd" style="padding: 0.1em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.021em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 0.821em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.161em; top: -1.384em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.266em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.161em; bottom: -0.748em;"><span class="mjx-msubsup" style=""><span class="mjx-base" style="margin-right: -0.014em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em; padding-right: 0.014em;">q</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.266em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.821em;" class="mjx-line"></span></span><span style="height: 1.508em; vertical-align: -0.529em;" class="mjx-vsize"></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="width: 0.12em;"></span></span></span></span></span></span>
</div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\left\{ \begin{array}{l} 0 = c_x-a_{x0}-d_{x0}\dfrac{(c_x-a_{x0})\cdot d_{x0}}{\|d_{x0}\|^2} + c_x-a_{x1}-d_{x1}\dfrac{(c_x-a_{x1})\cdot d_{x1}}{\|d_{x1}\|^2} \\[2ex] 0 = c_y-a_{y0}-d_{y0}\dfrac{(c_y-a_{y0})\cdot d_{y0}}{\|d_{y0}\|^2} + c_y-a_{y1}-d_{y1}\dfrac{(c_y-a_{y1})\cdot d_{y1}}{\|d_{y1}\|^2} \end{array} \right.
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -2.177em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.667em; padding-bottom: 0.298em;">⎧</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.251em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪
⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎨</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.251em; margin-bottom: 0.087em; margin-top: -0.137em;">⎪
⎪</span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: -0.217em; padding-bottom: 1.182em;">⎩</span></span></span><span class="mjx-mtable" style="vertical-align: -3.101em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 3.313em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: left; width: 28.306em;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 6.431em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 6.431em; top: -1.59em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span><span class="mjx-denominator" style="width: 6.431em; bottom: -1.093em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 6.431em;" class="mjx-line"></span></span><span style="height: 2.683em; vertical-align: -1.093em;" class="mjx-vsize"></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 6.431em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 6.431em; top: -1.59em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-denominator" style="width: 6.431em; bottom: -1.093em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 6.431em;" class="mjx-line"></span></span><span style="height: 2.683em; vertical-align: -1.093em;" class="mjx-vsize"></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 3.388em;"><span class="mjx-mtd" style="padding: 0.63em 0px 0px 0px; text-align: left;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 6.27em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 6.27em; top: -1.628em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span><span class="mjx-denominator" style="width: 6.27em; bottom: -1.13em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 6.27em;" class="mjx-line"></span></span><span style="height: 2.758em; vertical-align: -1.13em;" class="mjx-vsize"></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 6.27em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 6.27em; top: -1.628em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-denominator" style="width: 6.27em; bottom: -1.13em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 6.27em;" class="mjx-line"></span></span><span style="height: 2.758em; vertical-align: -1.13em;" class="mjx-vsize"></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-mo" style="width: 0.12em;"></span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\longrightarrow"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟶</span></span></span></span></span></span></div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{array}{|rc|}
\hline
\verb+\color{black}{text}+ &amp; \color{black}{text} \\
\verb+\color{gray}{text}+ &amp; \color{gray}{text} \\
\verb+\color{silver}{text}+ &amp; \color{silver}{text} \\
\verb+\color{white}{text}+ &amp; \color{white}{text} \\
\hline
\verb+\color{maroon}{text}+ &amp; \color{maroon}{text} \\
\verb+\color{red}{text}+ &amp; \color{red}{text} \\
\verb+\color{yellow}{text}+ &amp; \color{yellow}{text} \\
\verb+\color{lime}{text}+ &amp; \color{lime}{text} \\
\verb+\color{olive}{text}+ &amp; \color{olive}{text} \\
\verb+\color{green}{text}+ &amp; \color{green}{text} \\
\verb+\color{teal}{text}+ &amp; \color{teal}{text} \\
\verb+\color{aqua}{text}+ &amp; \color{aqua}{text} \\
\verb+\color{blue}{text}+ &amp; \color{blue}{text} \\
\verb+\color{navy}{text}+ &amp; \color{navy}{text} \\
\verb+\color{purple}{text}+ &amp; \color{purple}{text} \\
\verb+\color{fuchsia}{text}+ &amp; \color{magenta}{text} \\
\hline
\end{array}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -11.198em;"><span class="mjx-table" style="border: 1.3px solid;"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; text-align: right; width: 11.025em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">\color{black}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; width: 1.76em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: black;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.454em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">\color{gray}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: gray;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">\color{silver}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: silver;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">\color{white}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; border-bottom: 1.3px solid;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: white;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">\color{maroon}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: maroon;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">\color{red}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: red;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.453em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">\color{yellow}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: yellow;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">\color{lime}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: lime;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">\color{olive}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: olive;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; 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padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">\color{teal}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: teal;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; 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padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.519em; padding-bottom: 0.372em;">\color{fuchsia}{text}</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="r, g, b"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.003em;">g</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="0–15"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: 0.004em; padding-bottom: 0.298em;">–</span></span><span class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">15</span></span></span></span></span></span></div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ &amp; \color{#000}{text} &amp; &amp; &amp;
\verb+#00F+ &amp; \color{#00F}{text} &amp; &amp; \\
&amp; &amp; \verb+#0F0+ &amp; \color{#0F0}{text} &amp;
&amp; &amp; \verb+#0FF+ &amp; \color{#0FF}{text}\\
\verb+#F00+ &amp; \color{#F00}{text} &amp; &amp; &amp;
\verb+#F0F+ &amp; \color{#F0F}{text} &amp; &amp; \\
&amp; &amp; \verb+#FF0+ &amp; \color{#FF0}{text} &amp;
&amp; &amp; \verb+#FFF+ &amp; \color{#FFF}{text}\\
\hline
\end{array}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -2.645em;"><span class="mjx-table" style="border: 1.3px solid;"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; text-align: right; width: 2.1em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#000</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 1.76em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 0, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 2.1em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 1.76em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 2.1em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#00F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 1.76em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 0, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 2.1em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; text-align: right; width: 1.76em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#0F0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 255, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#0FF</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 255, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F00</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 0, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F0F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 0, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#FF0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 255, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">#FFF</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 255, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{array}{|rrrrrrrr|}
\hline
\verb+#000+ &amp; \color{#000}{text} &amp; \verb+#005+ &amp; \color{#005}{text} &amp; \verb+#00A+ &amp; \color{#00A}{text} &amp; \verb+#00F+ &amp; \color{#00F}{text} \\
\verb+#500+ &amp; \color{#500}{text} &amp; \verb+#505+ &amp; \color{#505}{text} &amp; \verb+#50A+ &amp; \color{#50A}{text} &amp; \verb+#50F+ &amp; \color{#50F}{text} \\
\verb+#A00+ &amp; \color{#A00}{text} &amp; \verb+#A05+ &amp; \color{#A05}{text} &amp; \verb+#A0A+ &amp; \color{#A0A}{text} &amp; \verb+#A0F+ &amp; \color{#A0F}{text} \\
\verb+#F00+ &amp; \color{#F00}{text} &amp; \verb+#F05+ &amp; \color{#F05}{text} &amp; \verb+#F0A+ &amp; \color{#F0A}{text} &amp; \verb+#F0F+ &amp; \color{#F0F}{text} \\
\hline
\verb+#080+ &amp; \color{#080}{text} &amp; \verb+#085+ &amp; \color{#085}{text} &amp; \verb+#08A+ &amp; \color{#08A}{text} &amp; \verb+#08F+ &amp; \color{#08F}{text} \\
\verb+#580+ &amp; \color{#580}{text} &amp; \verb+#585+ &amp; \color{#585}{text} &amp; \verb+#58A+ &amp; \color{#58A}{text} &amp; \verb+#58F+ &amp; \color{#58F}{text} \\
\verb+#A80+ &amp; \color{#A80}{text} &amp; \verb+#A85+ &amp; \color{#A85}{text} &amp; \verb+#A8A+ &amp; \color{#A8A}{text} &amp; \verb+#A8F+ &amp; \color{#A8F}{text} \\
\verb+#F80+ &amp; \color{#F80}{text} &amp; \verb+#F85+ &amp; \color{#F85}{text} &amp; \verb+#F8A+ &amp; \color{#F8A}{text} &amp; \verb+#F8F+ &amp; \color{#F8F}{text} \\
\hline
\verb+#0F0+ &amp; \color{#0F0}{text} &amp; \verb+#0F5+ &amp; \color{#0F5}{text} &amp; \verb+#0FA+ &amp; \color{#0FA}{text} &amp; \verb+#0FF+ &amp; \color{#0FF}{text} \\
\verb+#5F0+ &amp; \color{#5F0}{text} &amp; \verb+#5F5+ &amp; \color{#5F5}{text} &amp; \verb+#5FA+ &amp; \color{#5FA}{text} &amp; \verb+#5FF+ &amp; \color{#5FF}{text} \\
\verb+#AF0+ &amp; \color{#AF0}{text} &amp; \verb+#AF5+ &amp; \color{#AF5}{text} &amp; \verb+#AFA+ &amp; \color{#AFA}{text} &amp; \verb+#AFF+ &amp; \color{#AFF}{text} \\
\verb+#FF0+ &amp; \color{#FF0}{text} &amp; \verb+#FF5+ &amp; \color{#FF5}{text} &amp; \verb+#FFA+ &amp; \color{#FFA}{text} &amp; \verb+#FFF+ &amp; \color{#FFF}{text} \\
\hline
\end{array}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -8.245em;"><span class="mjx-table" style="border: 1.3px solid;"><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.4em; text-align: right; width: 2.1em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#000</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 1.76em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 0, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 2.1em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#005</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 1.76em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 0, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 2.1em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#00A</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 1.76em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 0, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 2.1em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#00F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; text-align: right; width: 1.76em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 0, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#500</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 0, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#505</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 0, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#50A</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 0, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#50F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 0, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#A00</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 0, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#A05</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 0, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#A0A</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 0, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#A0F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 0, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F00</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 0, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F05</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 0, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F0A</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 0, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F0F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 0, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#080</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 136, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#085</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 136, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#08A</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 136, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#08F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 136, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#580</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 136, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#585</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 136, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#58A</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 136, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#58F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 136, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#A80</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 136, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#A85</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 136, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#A8A</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 136, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#A8F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 136, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F80</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 136, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F85</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 136, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F8A</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 136, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#F8F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 136, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#0F0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 255, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#0F5</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 255, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#0FA</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 255, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#0FF</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(0, 255, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#5F0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 255, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">#5F5</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 255, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#5FA</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 255, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">#5FF</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(85, 255, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#AF0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 255, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#AF5</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 255, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#AFA</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 255, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#AFF</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(170, 255, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.421em;"><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.4em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#FF0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 255, 0);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">#FF5</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 255, 85);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">#FFA</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 255, 170);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">#FFF</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mstyle" style="color: rgb(255, 255, 255);"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\def\demo#1#2{#1{#2}\ #1{#2#2}\ #1{#2#2#2}}"><span class="mjx-mrow" aria-hidden="true"></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\demo\overline A"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; height: 0.096em; padding-bottom: 0.283em; padding-top: 0.141em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin: 0px -0.07em 0px -0.069em;">¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; letter-spacing: -0.281em; margin: 0px 0.051em 0px -0.19em;">¯¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin-right: -0.07em; margin-bottom: 0px; margin-top: 0px;">¯</span></span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; height: 0.096em; padding-bottom: 0.283em; padding-top: 0.141em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin: 0px -0.07em 0px -0.069em;">¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; letter-spacing: -0.25em; margin: 0px 0.036em 0px -0.175em;">¯¯¯¯¯¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin-right: -0.07em; margin-bottom: 0px; margin-top: 0px;">¯</span></span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; height: 0.096em; padding-bottom: 0.283em; padding-top: 0.141em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin: 0px -0.07em 0px -0.069em;">¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; letter-spacing: -0.244em; margin: 0px 0.033em 0px -0.172em;">¯¯¯¯¯¯¯¯¯¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin-right: -0.07em; margin-bottom: 0px; margin-top: 0px;">¯</span></span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\demo\underline B"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable" style="margin-bottom: -0.223em;"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; padding-top: -0.004em; margin: 0px -0.121em 0px 0px;">–</span><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; padding-top: -0.004em; margin: 0px -0.001em 0px -0.12em;">–</span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-itable" style="margin-bottom: -0.223em;"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; padding-top: -0.004em; margin: 0px -0.001em 0px 0px;">–</span><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; letter-spacing: -0.19em; padding-top: -0.004em; margin: 0px 0.144em 0px -0.145em;">––</span><span class="mjx-char MJXc-TeX-main-R" style="margin-top: 0px; padding-bottom: 0.537em; margin-right: -0.001em; padding-top: -0.004em; margin-bottom: 0px;">–</span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-itable" style="margin-bottom: -0.223em;"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; padding-top: -0.004em; margin: 0px -0.001em 0px 0px;">–</span><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; letter-spacing: -0.155em; padding-top: -0.004em; margin: 0px 0.126em 0px -0.127em;">––––</span><span class="mjx-char MJXc-TeX-main-R" style="margin-top: 0px; padding-bottom: 0.537em; margin-right: -0.001em; padding-top: -0.004em; margin-bottom: 0px;">–</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\demo\widetilde C"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.175em; padding-bottom: 0.06em; padding-left: 0.24em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.225em;">˜</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.189em; padding-bottom: 0.06em; padding-left: 0.038em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 0.519em; padding-bottom: 0.225em;">˜</span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.29em; padding-bottom: 0.06em; padding-left: 0.196em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.593em; padding-bottom: 0.225em;">˜</span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\demo\widehat D"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.257em; padding-bottom: 0.06em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.519em; padding-bottom: 0.225em;">ˆ</span></span></span><span class="mjx-op" style="padding-left: 0.03em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.258em; padding-bottom: 0.06em; padding-left: 0.106em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 0.519em; padding-bottom: 0.225em;">ˆ</span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.334em; padding-bottom: 0.06em; padding-left: 0.297em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.593em; padding-bottom: 0.225em;">ˆ</span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\demo\fbox {$E$}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.126em; border: 1px solid;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.126em; border: 1px solid;"><span class="mjx-mrow"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.126em; border: 1px solid;"><span class="mjx-mrow"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\demo\underleftarrow{F}\qquad"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.219em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">←</span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.056em 0px -0.055em;">←</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.221em 0px -0.389em; letter-spacing: -0.679em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-top: 0px; margin-bottom: 0px; margin-right: -0.084em;">−</span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.056em 0px -0.055em;">←</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.059em 0px -0.227em; letter-spacing: -0.354em;">−−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-top: 0px; margin-bottom: 0px; margin-right: -0.084em;">−</span></span></span></span></span></span></span><span class="mjx-mspace" style="width: 2em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\xleftarrow{abc}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -0.281em; padding: 0px 1.947em 0.036em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.719em 0px -0.036em; position: relative; top: -0.15em; left: 0.389em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.117em 0px -0.055em;">←</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.084em 0px -0.145em;">−</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\demo\underrightarrow{G}\qquad"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.107em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">G</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">G</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.084em 0px -0.084em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.184em 0px -0.352em; letter-spacing: -0.604em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">G</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">G</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.084em 0px -0.084em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.031em 0px -0.199em; letter-spacing: -0.298em;">−−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span></span><span class="mjx-mspace" style="width: 2em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\xrightarrow{abc}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -0.281em; padding: 0px 2.002em 0.036em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.719em 0px -0.036em; position: relative; top: -0.15em; left: 0.278em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.084em 0px -0.084em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.262em 0px -0.43em; letter-spacing: -0.76em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\demo\underleftrightarrow{H}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.118em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">↔</span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.056em 0px -0.055em;">←</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.221em 0px -0.389em; letter-spacing: -0.679em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.056em 0px -0.055em;">←</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.024em 0px -0.192em; letter-spacing: -0.284em;">−−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\overbrace{(n - 2) + \overbrace{(n - 1) + n + (n + 1)} + (n + 2)}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="padding-bottom: 0.06em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-size4-R" style="padding-bottom: 0.488em; padding-top: 0.108em; margin: 0px 0.01em 0px 0.024em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.085em; margin: 0px 0.088em 0px -0.068em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; margin-right: 0.01em; margin-bottom: 0px; margin-top: 0px;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.085em; margin: 0px 0.088em 0px -0.068em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: 0px; padding-bottom: 0.488em; margin-right: 0.024em; padding-top: 0.108em; margin-bottom: 0px;"></span></span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-texatom MJXc-space2"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="padding-bottom: 0.06em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-size4-R" style="padding-bottom: 0.488em; padding-top: 0.108em; margin: 0px 0.01em 0px 0.024em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.093em; margin: 0px 0.092em 0px -0.072em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; margin-right: 0.01em; margin-bottom: 0px; margin-top: 0px;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.093em; margin: 0px 0.092em 0px -0.072em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: 0px; padding-bottom: 0.488em; margin-right: 0.024em; padding-top: 0.108em; margin-bottom: 0px;"></span></span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="(n \underbrace{- 2) + (n \underbrace{- 1) + n + (n +} 1) + (n +} 2)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-texatom MJXc-space1"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-texatom MJXc-space1"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; margin: 0px 0.01em 0px 0.024em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.113em; margin: 0px 0.102em 0px -0.082em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: 0px; padding-bottom: 0.488em; margin-right: 0.01em; padding-top: 0.108em; margin-bottom: 0px;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.113em; margin: 0px 0.102em 0px -0.082em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; margin-right: 0.024em; margin-bottom: 0px; margin-top: 0px;"></span></span></span></span></span></span></span></span></span><span class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; margin: 0px 0.01em 0px 0.024em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.083em; margin: 0px 0.086em 0px -0.066em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: 0px; padding-bottom: 0.488em; margin-right: 0.01em; padding-top: 0.108em; margin-bottom: 0px;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.083em; margin: 0px 0.086em 0px -0.066em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; margin-right: 0.024em; margin-bottom: 0px; margin-top: 0px;"></span></span></span></span></span></span></span></span></span><span class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\underbrace{a\cdot a\cdots a}_{b\text{ times}}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; margin: 0px 0.01em 0px 0.024em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.159em; margin: 0px 0.125em 0px -0.105em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="margin-top: 0px; padding-bottom: 0.488em; margin-right: 0.01em; padding-top: 0.108em; margin-bottom: 0px;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; letter-spacing: -0.159em; margin: 0px 0.125em 0px -0.105em;"></span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.108em; padding-bottom: 0.488em; margin-right: 0.024em; margin-bottom: 0px; margin-top: 0px;"></span></span></span></span></span></span></span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 1.189em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">&nbsp;times</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\varliminf"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-itable" style="margin-bottom: -0.223em;"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; padding-top: -0.004em; margin: 0px -0.001em 0px 0px;">–</span><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; letter-spacing: -0.255em; padding-top: -0.004em; margin: 0px 0.176em 0px -0.177em;">––</span><span class="mjx-char MJXc-TeX-main-R" style="margin-top: 0px; padding-bottom: 0.537em; margin-right: -0.001em; padding-top: -0.004em; margin-bottom: 0px;">–</span></span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\varlimsup"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; height: 0.096em; padding-bottom: 0.283em; padding-top: 0.141em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin: 0px -0.07em 0px -0.069em;">¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; letter-spacing: -0.276em; margin: 0px 0.049em 0px -0.188em;">¯¯¯¯¯¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin-right: -0.07em; margin-bottom: 0px; margin-top: 0px;">¯</span></span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\check{I}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.181em; padding-bottom: 0.06em; padding-left: 0.18em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">ˇ</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.064em;">I</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\acute{J}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.244em; padding-bottom: 0.06em; padding-left: 0.309em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">´</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.078em;">J</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\grave{K}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.244em; padding-bottom: 0.06em; padding-left: 0.301em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">`</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.04em;">K</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\vec u\ \vec{AB}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.248em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-vec-R" style="padding-top: 0.519em; padding-bottom: 0.225em;">→</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.248em; padding-bottom: 0.06em; padding-left: 0.504em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-vec-R" style="padding-top: 0.519em; padding-bottom: 0.225em;">→</span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\bar z"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.096em; padding-bottom: 0.06em; padding-left: 0.067em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">¯</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\hat x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.213em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">^</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\tilde x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.153em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">~</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\dot x,\ddot x,\dddot x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.17em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">˙</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-texatom MJXc-space1"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.165em; padding-bottom: 0.06em; padding-left: 0.064em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">¨</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-texatom MJXc-space1"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="padding-bottom: 0.06em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">...</span></span></span><span class="mjx-op" style="padding-left: 0.103em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\mathring A"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="height: 0.223em; padding-bottom: 0.06em; padding-left: 0.264em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">˚</span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em; padding-left: 1.215em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">@</span></span></span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span></span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-mover MJXc-space3"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em; padding-left: 0.643em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.435em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟼</span></span></span></span></span><span class="mjx-mtext MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.291em; padding-bottom: 0.372em;">&nbsp;</span></span><span class="mjx-mover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; height: 0.439em; padding-bottom: 0.283em; padding-top: 0.141em;"><span class="mjx-mrow" style="vertical-align: top;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">∙</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">∘</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">∘</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">∙</span></span></span></span><span class="mjx-op" style="padding-left: 0.252em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span></span></span></span></span></span></span></div>
<div> <span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
x = a_0 + \cfrac{1^2}{a_1
+ \cfrac{2^2}{a_2
+ \cfrac{3^2}{a_3 + \cfrac{4^4}{a_4 + \cdots}}}}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 11.078em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 11.078em; top: -1.747em;"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="width: 11.078em; bottom: -5.519em;"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 8.497em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 12.017em; top: -2.239em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 12.017em; bottom: -5.51em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 5.976em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 8.451em; top: -2.237em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.59em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 8.451em; bottom: -3.324em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 3.454em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 4.884em; top: -2.265em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.607em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 4.884em; bottom: -1.109em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 3.454em;" class="mjx-line"></span></span><span style="height: 2.386em; vertical-align: -0.784em;" class="mjx-vsize"></span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 5.976em;" class="mjx-line"></span></span><span style="height: 3.932em; vertical-align: -2.35em;" class="mjx-vsize"></span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 8.497em;" class="mjx-line"></span></span><span style="height: 5.479em; vertical-align: -3.896em;" class="mjx-vsize"></span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 11.078em;" class="mjx-line"></span></span><span style="height: 7.266em; vertical-align: -5.519em;" class="mjx-vsize"></span></span></span></span></span></span>
</div>
<div> <span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
x = a_0 + \frac{1^2}{a_1
+ \frac{2^2}{a_2
+ \frac{3^2}{a_3 + \frac{4^4}{a_4 + \cdots}}}}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 7.396em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 7.396em; top: -1.583em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="width: 7.396em; bottom: -3.565em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 4.816em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 6.811em; top: -1.627em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.443em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 6.811em; bottom: -3.358em;"><span class="mjx-mrow" style=""><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 83.3%; vertical-align: -0.267em; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 4.606em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 83.3%; width: 5.526em; top: -1.614em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span><span class="mjx-sup" style="vertical-align: 0.304em; padding-left: 0px; padding-right: 0.05em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="font-size: 83.3%; width: 5.526em; bottom: -2.476em;"><span class="mjx-mrow" style=""><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="vertical-align: -0.336em; padding-right: 0.05em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 3.229em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 3.229em; top: -1.533em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span><span class="mjx-sup" style="vertical-align: 0.316em; padding-left: 0px; padding-right: 0.05em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span></span></span><span class="mjx-denominator" style="width: 3.229em; bottom: -0.971em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="vertical-align: -0.348em; padding-right: 0.05em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span></span></span><span style="border-bottom: 1px solid; top: -0.301em; width: 3.229em;" class="mjx-line"></span></span><span style="height: 2.504em; vertical-align: -0.971em;" class="mjx-vsize"></span></span></span></span><span style="border-bottom: 1px solid; top: -0.296em; width: 4.606em;" class="mjx-line"></span></span><span style="height: 3.409em; vertical-align: -2.064em;" class="mjx-vsize"></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 4.816em;" class="mjx-line"></span></span><span style="height: 3.525em; vertical-align: -2.374em;" class="mjx-vsize"></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 7.396em;" class="mjx-line"></span></span><span style="height: 5.148em; vertical-align: -3.565em;" class="mjx-vsize"></span></span></span></span></span></span>
</div>
<div> <span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
x = a_0 + \frac{1^2}{a_1+}
\frac{2^2}{a_2+}
\frac{3^2}{a_3 +} \frac{4^4}{a_4 +} \cdots
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 1.896em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.896em; top: -1.583em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="width: 1.896em; bottom: -0.854em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.896em;" class="mjx-line"></span></span><span style="height: 2.437em; vertical-align: -0.854em;" class="mjx-vsize"></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.896em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.896em; top: -1.583em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="width: 1.896em; bottom: -0.854em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.896em;" class="mjx-line"></span></span><span style="height: 2.437em; vertical-align: -0.854em;" class="mjx-vsize"></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.896em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.896em; top: -1.582em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.59em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="width: 1.896em; bottom: -0.869em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.896em;" class="mjx-line"></span></span><span style="height: 2.451em; vertical-align: -0.869em;" class="mjx-vsize"></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.896em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.896em; top: -1.602em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.607em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span></span></span><span class="mjx-denominator" style="width: 1.896em; bottom: -0.854em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.896em;" class="mjx-line"></span></span><span style="height: 2.456em; vertical-align: -0.854em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="[a_0; a_1, a_2, a_3, \ldots]"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">[</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.519em;">;</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">…</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">]</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label=" \cfrac{a_{1}}{b_{1}+\cfrac{a_{2}}{b_{2}+\cfrac{a_{3}}{b_{3}+\ddots }}}= {\genfrac{}{}{}{}{a_1}{b_1}} {\genfrac{}{}{0pt}{}{}{+}} {\genfrac{}{}{}{}{a_2}{b_2}} {\genfrac{}{}{0pt}{}{}{+}} {\genfrac{}{}{}{}{a_3}{b_3}} {\genfrac{}{}{0pt}{}{}{+\dots}} "><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 8.366em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 8.366em; top: -1.7em;"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="width: 8.366em; bottom: -4.294em;"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 5.886em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 8.323em; top: -1.816em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 8.323em; bottom: -4.2em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 3.464em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 4.899em; top: -1.816em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 4.899em; bottom: -2.434em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 1.256em; padding-bottom: 0.298em;">⋱</span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 3.464em;" class="mjx-line"></span></span><span style="height: 3.006em; vertical-align: -1.721em;" class="mjx-vsize"></span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 5.886em;" class="mjx-line"></span></span><span style="height: 4.254em; vertical-align: -2.97em;" class="mjx-vsize"></span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 8.366em;" class="mjx-line"></span></span><span style="height: 5.995em; vertical-align: -4.294em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-texatom MJXc-space3"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.118em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.118em; top: -1.174em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span><span class="mjx-denominator" style="width: 1.118em; bottom: -0.927em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.118em;" class="mjx-line"></span></span><span style="height: 2.101em; vertical-align: -0.927em;" class="mjx-vsize"></span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.778em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 0.778em; top: -0.677em;"><span class="mjx-mrow"></span></span><span class="mjx-denominator" style="width: 0.778em; bottom: -0.793em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span></span><span style="height: 1.469em; vertical-align: -0.793em;" class="mjx-vsize"></span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.118em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.118em; top: -1.174em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span class="mjx-denominator" style="width: 1.118em; bottom: -0.927em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.118em;" class="mjx-line"></span></span><span style="height: 2.101em; vertical-align: -0.927em;" class="mjx-vsize"></span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.778em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 0.778em; top: -0.677em;"><span class="mjx-mrow"></span></span><span class="mjx-denominator" style="width: 0.778em; bottom: -0.793em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span></span><span style="height: 1.469em; vertical-align: -0.793em;" class="mjx-vsize"></span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.118em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.118em; top: -1.189em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span class="mjx-denominator" style="width: 1.118em; bottom: -0.942em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.118em;" class="mjx-line"></span></span><span style="height: 2.132em; vertical-align: -0.942em;" class="mjx-vsize"></span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 2.117em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 2.117em; top: -0.677em;"><span class="mjx-mrow"></span></span><span class="mjx-denominator" style="width: 2.117em; bottom: -0.793em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">…</span></span></span></span></span><span style="height: 1.469em; vertical-align: -0.793em;" class="mjx-vsize"></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\LaTeX"><span class="mjx-mrow" style="width: 2.72em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">L</span></span><span class="mjx-mspace" style="margin-right: -0.325em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.327em; padding: 0px 0.469em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -0.463em 0px -0.016em; position: relative; top: -0.21em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.17em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\underset{j=1}{\overset{\infty}{\LARGE\mathrm K}}\frac{a_j}{b_j}=\cfrac{a_1}{b_1+\cfrac{a_2}{b_2+\cfrac{a_3}{b_3+\ddots}}}."><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munder"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em; padding-left: 0.452em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span><span class="mjx-op"><span class="mjx-mstyle"><span class="mjx-mrow" style="font-size: 173%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">K</span></span></span></span></span></span></span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.107em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 1.056em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.056em; top: -1.318em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span></span></span></span><span class="mjx-denominator" style="width: 1.056em; bottom: -1.071em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.056em;" class="mjx-line"></span></span><span style="height: 2.389em; vertical-align: -1.071em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked" style="width: 8.366em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 8.366em; top: -1.7em;"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="width: 8.366em; bottom: -4.294em;"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 5.886em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 8.323em; top: -1.816em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 8.323em; bottom: -4.2em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 3.464em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 4.899em; top: -1.816em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span></span></span></span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 4.899em; bottom: -2.434em;"><span class="mjx-mrow" style=""><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.14em; padding: 0px 0px 0.3em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mstyle" style="font-size: 141.4%;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 1.256em; padding-bottom: 0.298em;">⋱</span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 3.464em;" class="mjx-line"></span></span><span style="height: 3.006em; vertical-align: -1.721em;" class="mjx-vsize"></span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 5.886em;" class="mjx-line"></span></span><span style="height: 4.254em; vertical-align: -2.97em;" class="mjx-vsize"></span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 8.366em;" class="mjx-line"></span></span><span style="height: 5.995em; vertical-align: -4.294em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">.</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\mathop{\LARGE\mathrm K}_{i=1}^\infty \frac{a_i}{b_i}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em; padding-left: 0.452em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span><span class="mjx-op"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle"><span class="mjx-mrow" style="font-size: 173%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">K</span></span></span></span></span></span></span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.14em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mfrac MJXc-space1"><span class="mjx-box MJXc-stacked" style="width: 1.008em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.008em; top: -1.182em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span></span></span><span class="mjx-denominator" style="width: 1.008em; bottom: -0.935em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.008em;" class="mjx-line"></span></span><span style="height: 2.116em; vertical-align: -0.935em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\require{AMScd}
\begin{CD}
A @>a>> B\\
@V b V V= @VV c V\\
C @>>d> D
\end{CD}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -2.651em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.616em;"><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0px; width: 0.76em;"><span class="mjx-mrow" style="margin-top: 0.166em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.15em; padding: 0px 0px 0.2em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"></span></span><span class="mjx-strut"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0.25em; width: 2.75em;"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.248em; padding-top: 0.141em; padding-left: 1.374em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -0.534em; padding: 0px 1.14em 0.035em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.466em 0px -0.035em; position: relative; top: -0.1em; left: 0.333em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.084em 0px -0.084em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.046em 0px -0.214em; letter-spacing: -0.327em;">−−−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0.25em; width: 0.828em;"><span class="mjx-mrow" style="margin-top: 0.166em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.25em; width: 0px;"><span style="margin-top: 0.166em;"></span></span></span><span class="mjx-mtr" style="height: 2.25em;"><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0px;"><span class="mjx-mrow"><span class="mjx-mrow"><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.281em; padding: 0px 0px 0.036em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.719em 0px -0.036em; position: relative; left: -0.429em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span><span class="mjx-mo" style="vertical-align: -0.6em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">⏐</span><span class="mjx-char MJXc-TeX-size1-R" style="line-height: 0.548em; margin-bottom: -0.101em; margin-top: 0px;">⏐</span><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">↓</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow" style="margin-top: 0.125em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.6em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">⏐</span><span class="mjx-char MJXc-TeX-size1-R" style="line-height: 0.548em; margin-bottom: -0.101em; margin-top: 0px;">⏐</span><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">↓</span></span></span><span class="mjx-mstyle" style="font-size: 80%;"><span class="mjx-mrow" style="font-size: 88.4%;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.533em; padding: 0px 0px 0.036em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.467em 0px -0.036em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0px 0px 0.25em;"><span class="mjx-mrow" style="margin-top: 0.125em;"><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.936em;"><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.15em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.15em; padding: 0px 0px 0.2em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"></span></span><span class="mjx-strut"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow" style="margin-top: -0.15em;"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.283em; padding-top: 0.141em; padding-left: 0.264em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -1em; padding: 0px 3.361em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px; position: relative; top: -0.1em; left: 0.333em;"><span class="mjx-mrow"><span class="mjx-mspace" style="width: 2.75em; height: 0px;"></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.084em 0px -0.084em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.046em 0px -0.214em; letter-spacing: -0.327em;">−−−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 1.377em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -0.281em; padding: 0px 1.134em 0.035em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.719em 0px -0.035em; position: relative; left: 0.333em;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow" style="margin-top: -0.15em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0px 0px 0.25em;"><span style="margin-top: -0.15em;"></span></span></span></span></span></span></span></span></span>
</div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{CD}
A @>>> B @>{\text{very long label}}>> C \\
@. @AAA @| \\
D @= E @<<< F
\end{CD}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -2.459em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.869em;"><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0px; width: 0.828em;"><span class="mjx-mrow" style="margin-top: 0.419em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.15em; padding: 0px 0px 0.2em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"></span></span><span class="mjx-strut"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0.25em; width: 2.75em;"><span class="mjx-mrow" style="margin-top: 0.419em;"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.283em; padding-top: 0.141em; padding-left: 0.264em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -1em; padding: 0px 3.361em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px; position: relative; top: -0.1em; left: 0.333em;"><span class="mjx-mrow"><span class="mjx-mspace" style="width: 2.75em; height: 0px;"></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.084em 0px -0.084em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.046em 0px -0.214em; letter-spacing: -0.327em;">−−−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0.25em; width: 0.764em;"><span class="mjx-mrow" style="margin-top: 0.419em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0.25em; width: 4.874em;"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.157em; padding-top: 0.141em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -0.281em; padding: 0px 6.893em 0.231em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.719em 0px -0.231em; position: relative; top: -0.1em; left: 0.333em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">very long label</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.084em 0px -0.084em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.023em 0px -0.191em; letter-spacing: -0.281em;">−−−−−−−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0.25em; width: 0.76em;"><span class="mjx-mrow" style="margin-top: 0.419em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.25em; width: 0px;"><span style="margin-top: 0.419em;"></span></span></span><span class="mjx-mtr" style="height: 2.25em;"><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0px;"><span class="mjx-mrow" style="margin-top: 0.125em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow" style="margin-top: 0.125em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.6em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">↑</span><span class="mjx-char MJXc-TeX-size1-R" style="line-height: 0.548em; margin-bottom: -0.101em; margin-top: 0px;">⏐</span><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">⏐</span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow" style="margin-top: 0.125em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -0.35em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em; margin-bottom: -0.35em;">∥</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em; margin-top: -0.35em;">∥</span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0px 0px 0.25em;"><span class="mjx-mrow" style="margin-top: 0.125em;"><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.3em;"><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0px;"><span class="mjx-mrow" style="margin-top: -0.15em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.15em; padding: 0px 0px 0.2em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"></span></span><span class="mjx-strut"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow" style="margin-top: -0.15em;"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.078em; padding-bottom: 0.422em; margin: 0px -0.056em 0px -0.056em;">=</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.078em; padding-bottom: 0.422em; letter-spacing: -0.272em; margin: 0px 0.074em 0px -0.186em;">===</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.078em; padding-bottom: 0.422em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">=</span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow" style="margin-top: -0.15em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow" style="margin-top: -0.15em;"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.283em; padding-top: 0.141em; padding-left: 1.766em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -1em; padding: 0px 3.361em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px; position: relative; top: -0.1em; left: 0.333em;"><span class="mjx-mrow"><span class="mjx-mspace" style="width: 2.75em; height: 0px;"></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-op"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.056em 0px -0.055em;">←</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.023em 0px -0.191em; letter-spacing: -0.282em;">−−−−−−−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-top: 0px; margin-bottom: 0px; margin-right: -0.084em;">−</span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0.25em 0px 0.25em;"><span class="mjx-mrow" style="margin-top: -0.15em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.25em 0px 0px 0.25em;"><span style="margin-top: -0.15em;"></span></span></span></span></span></span></span></span></span>
</div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\require{AMScd}
\begin{CD}
RCOHR'SO_3Na @>{\text{Hydrolysis,$\Delta, Dil.HCl$}}>> (RCOR')+NaCl+SO_2+ H_2O
\end{CD}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -0.604em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.708em;"><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0px; width: 7.373em;"><span class="mjx-mrow" style="margin-top: 0.433em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span><span class="mjx-msup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mo" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">′</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.085em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.15em; padding: 0px 0px 0.2em 0px;"><span class="mjx-box" style="width: 0px; margin: 0px 0px 0px;"><span class="mjx-mrow"></span></span><span class="mjx-strut"></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0.25em 0px 0.25em; width: 7.278em;"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.157em; padding-top: 0.141em;"><span class="mjx-mpadded" style=""><span class="mjx-block" style="width: 0px; margin-top: -0.259em; padding: 0px 10.293em 0.229em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.741em 0px -0.229em; position: relative; top: -0.1em; left: 0.333em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">Hydrolysis,</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Δ</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">D</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">.</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span></span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px -0.084em 0px -0.084em;">−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin: 0px 0.026em 0px -0.194em; letter-spacing: -0.288em;">−−−−−−−−−−−−</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.222em; padding-bottom: 0.35em; margin-right: -0.056em; margin-bottom: 0px; margin-top: 0px;">→</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0.25em; width: 13.971em;"><span class="mjx-mrow" style="margin-top: 0.433em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span><span class="mjx-msup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mo" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">′</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.085em;">N</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.032em;">S</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.057em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.057em;">H</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">O</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label=" \newcommand{\SES}[3]{ 0 \to #1 \to #2 \to #3 \to 0 }"><span class="mjx-mrow" aria-hidden="true"></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label=" \SES{A}{B}{C} "><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em; padding-right: 0.045em;">C</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\implies"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟹</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Rightarrow"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⇒</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\iff"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟺</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\impliedby"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟸</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\to"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="f\colon A \to B"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">:</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.298em;">A</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">B</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\gets"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">←</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="T:\mathbb R\to \mathbb R,\; x\mapsto x+1"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">:</span></span><span class="mjx-texatom MJXc-space3"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-texatom MJXc-space3"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-ams-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">R</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">↦</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="p\land((q\lor r)\to s)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">∧</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em; padding-right: 0.014em;">q</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.372em;">∨</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="x+2=4-x\implies x=1."><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟹</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1.</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display"><span class="mjx-math" style="width: 100%;" aria-label=" a := x^2-y^3 \tag{*}\label{*} "><span class="mjx-mrow" style="width: 100%;" aria-hidden="true"><span class="mjx-mtable" style="width: 100%; min-width: 9.417em;"><span style="width: 100%; text-align: center;" class="mjx-box"><span class="mjx-table" style="display: inline-table; width: auto; vertical-align: -0.063em;"><span class="mjx-mlabeledtr" style="height: 1.177em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; width: 5.261em;"><span class="mjx-mrow" style="margin-top: -0.098em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.372em;">:<span class="mjx-charbox MJXc-TeX-main-R" style="padding-bottom: 0.314em;">=</span></span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0.082em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-itable" style="vertical-align: top; margin-left: -1.278em;"><span class="mjx-label" style="height: 1.177em;"><span id="mjx-eqn-*" class="mjx-mtd"><span class="mjx-mrow" style="margin-top: -0.098em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(*)</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label=" a+y^3 \stackrel{\eqref{*}}= x^2 "><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-msubsup MJXc-space2"><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0.082em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-texatom MJXc-space3"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.157em; padding-top: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><a href="#mjx-eqn-*"><span class="mjx-mrow MathJax_ref"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(*)</span></span></span></a></span></span></span><span class="mjx-op" style="padding-left: 0.063em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span></span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\eqref{*}"><span class="mjx-mrow" aria-hidden="true"><a href="#mjx-eqn-*"><span class="mjx-mrow MathJax_ref"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(*)</span></span></span></a></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\ref{*}"><span class="mjx-mrow" aria-hidden="true"><a href="#mjx-eqn-*"><span class="mjx-mrow MathJax_ref"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">*</span></span></span></a></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\eqref{*}"><span class="mjx-mrow" aria-hidden="true"><a href="#mjx-eqn-*"><span class="mjx-mrow MathJax_ref"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(*)</span></span></span></a></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display"><span class="mjx-math" style="width: 100%;" aria-label="(1)\qquad\qquad\sum\limits_{j}k\tag*{}"><span class="mjx-mrow" style="width: 100%;" aria-hidden="true"><span class="mjx-mtable" style="width: 100%; min-width: 9.01em;"><span style="width: 100%; text-align: center;" class="mjx-box"><span class="mjx-table" style="display: inline-table; width: auto; vertical-align: 0.457em;"><span class="mjx-mlabeledtr" style="height: 2.364em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; width: 7.41em;"><span class="mjx-mrow" style="margin-top: -0.025em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mspace" style="width: 2em; height: 0px;"></span><span class="mjx-mspace" style="width: 2em; height: 0px;"></span><span class="mjx-munderover MJXc-space1"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.74em; padding-bottom: 0.74em;">∑</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.815em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span></span></span></span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-itable" style="vertical-align: top; margin-left: 0px;"><span class="mjx-label" style="height: 2.364em;"><span id="mjx-eqn-" class="mjx-mtd"><span class="mjx-mrow" style="margin-top: -0.025em;"><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="(1)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
f\left(\left[ \frac{1+\left\{x,y\right\}}{\left(\frac{x}{y}+\frac{y}{x}\right)\left(u+1\right)}+a\right]^{3/2}\right).
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mrow MJXc-space1"><span class="mjx-mo" style="vertical-align: -1.495em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎛</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.403em; margin-bottom: -0.1em; margin-top: 0px;">⎜
⎜</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎝</span></span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mrow"><span class="mjx-mo" style="vertical-align: -1.22em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎡</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.34em; margin-bottom: -0.101em; margin-top: 0px;">⎢
⎢</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎣</span></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 7.427em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 7.427em; top: -1.59em;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mrow MJXc-space2"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">{</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">}</span></span></span></span></span><span class="mjx-denominator" style="width: 7.427em; bottom: -1.889em;"><span class="mjx-mrow"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.546em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.772em; top: -1.159em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.772em; bottom: -0.718em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.546em;" class="mjx-line"></span></span><span style="height: 1.327em; vertical-align: -0.507em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 0.546em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.772em; top: -1.353em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.772em; bottom: -0.524em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.546em;" class="mjx-line"></span></span><span style="height: 1.327em; vertical-align: -0.37em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span><span class="mjx-mrow MJXc-space1"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 7.427em;" class="mjx-line"></span></span><span style="height: 3.479em; vertical-align: -1.889em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo" style="vertical-align: -1.22em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎤</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.34em; margin-bottom: -0.101em; margin-top: 0px;">⎥
⎥</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎦</span></span></span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 2.993em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span class="mjx-mo" style="vertical-align: -1.495em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">⎞</span><span class="mjx-char MJXc-TeX-size4-R" style="line-height: 0.403em; margin-bottom: -0.1em; margin-top: 0px;">⎟
⎟</span><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 0.961em; padding-bottom: 0.888em;">⎠</span></span></span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">.</span></span></span></span></span></span>
</div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\begin{aligned}
a=&amp;\left(1+2+3+ \cdots \right. \\
&amp; \cdots+ \left. \infty-2+\infty-1+\infty\right).
\end{aligned}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -0.975em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.225em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: right; width: 1.585em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: left; width: 12.285em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span><span class="mjx-mo" style="width: 0.12em;"></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.225em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋯</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mrow MJXc-space2"><span class="mjx-mo" style="width: 0.12em;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">.</span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
</div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\left\langle q\middle\|\frac{\frac{x}{y}}{\frac{u}{v}} \middle| p \right\rangle.
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">⟨</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em; padding-right: 0.014em;">q</span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-mo" style="vertical-align: -0.955em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span><span class="mjx-char MJXc-TeX-main-R" style="line-height: 0.549em; margin-bottom: 0.014em; margin-top: -0.114em;">∥
∥</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.986em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 0.986em; top: -1.868em;"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.546em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.772em; top: -1.159em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.772em; bottom: -0.718em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.546em;" class="mjx-line"></span></span><span style="height: 1.327em; vertical-align: -0.507em;" class="mjx-vsize"></span></span></span><span class="mjx-denominator" style="width: 0.986em; bottom: -1.23em;"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.546em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.772em; top: -1.159em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">u</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.772em; bottom: -0.524em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.546em;" class="mjx-line"></span></span><span style="height: 1.19em; vertical-align: -0.37em;" class="mjx-vsize"></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.986em;" class="mjx-line"></span></span><span style="height: 3.098em; vertical-align: -1.23em;" class="mjx-vsize"></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-mo" style="vertical-align: -1.094em;"><span class="mjx-delim-v"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∣</span><span class="mjx-char MJXc-TeX-main-R" style="line-height: 0.619em; margin-bottom: 0.014em; margin-top: -0.114em;">∣
∣</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∣</span></span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.446em;">p</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size4-R" style="padding-top: 1.551em; padding-bottom: 1.551em;">⟩</span></span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">.</span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Big(\dots\Big)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span></span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">…</span></span><span class="mjx-texatom MJXc-space1"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\operatorname{arsinh}(x)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">arsinh</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="arsinh(x)"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">h</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\operatorname*{Res}_{z=1}\left(\frac1{z^2-z}\right)=1
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">Res</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.24em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">(</span></span><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 2.798em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 2.798em; top: -1.368em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="width: 2.798em; bottom: -0.925em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.003em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0.076em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em; padding-right: 0.003em;">z</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 2.798em;" class="mjx-line"></span></span><span style="height: 2.292em; vertical-align: -0.925em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size3-R" style="padding-top: 1.256em; padding-bottom: 1.256em;">)</span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\verb*{\rm ...}*"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtext"><span class="mjx-char" style="padding-top: 0.519em; padding-bottom: 0.077em;"><span class="mjx-charbox MJXc-TeX-type-R" style="padding-bottom: 0.233em; margin-right: 0.275em;">{\rm&nbsp;</span><span class="mjx-charbox MJXc-TeX-type-R" style="padding-bottom: 0.233em;">...}</span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\verb*{\rm arsinh}*"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtext"><span class="mjx-char" style="padding-top: 0.519em; padding-bottom: 0.077em;"><span class="mjx-charbox MJXc-TeX-type-R" style="padding-bottom: 0.233em; margin-right: 0.275em;">{\rm&nbsp;</span><span class="mjx-charbox MJXc-TeX-type-R" style="padding-bottom: 0.233em;">arsinh}</span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{\rm arsinh}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">h</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\operatorname{arsinh}x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">arsinh</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{\rm arsinh}x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">s</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">h</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="{\tt operatorname}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.519em;">p</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">o</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">r</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em;">n</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.225em; padding-right: 0.011em;">m</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-type-R" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\text{arsinh }x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">arsinh&nbsp;</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\operatorname{arsinh}x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">arsinh</span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim \limits_{x \to 1} \frac{x^2-1}{x-1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-mfrac MJXc-space1"><span class="mjx-box MJXc-stacked" style="width: 1.774em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 2.508em; top: -1.702em;"><span class="mjx-mrow" style=""><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.435em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 2.508em; bottom: -0.747em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.774em;" class="mjx-line"></span></span><span style="height: 1.732em; vertical-align: -0.528em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="lim"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">l</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">m</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim \limits_{x \to 1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\to"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x \to 1"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x \to 1"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim \limits_{x \to 1} \frac{x^2-1}{x-1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-mfrac MJXc-space1"><span class="mjx-box MJXc-stacked" style="width: 1.774em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 2.508em; top: -1.702em;"><span class="mjx-mrow" style=""><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.435em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 2.508em; bottom: -0.747em;"><span class="mjx-mrow" style=""><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.774em;" class="mjx-line"></span></span><span style="height: 1.732em; vertical-align: -0.528em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\lim_{x\to 1}?"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">?</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\mathop{+}\limits_{i=1}^k\text{ instead of }+_{i=1}^k"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em; padding-left: 0.551em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span></span><span class="mjx-op" style="padding-left: 0.185em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char"></span></span><span class="mjx-mtext MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">&nbsp;instead of&nbsp;</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span></span><span class="mjx-stack" style="vertical-align: -0.315em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">i</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim\limits_{x\to 1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim_{x\to 1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim_{x\to 1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim\limits_{x\to 1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="x\to 1"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim \limits_{x \to 1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim\limits_{x\mapsto 1}\dfrac1x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.038em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">↦</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-mstyle MJXc-space1"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 0.772em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 0.772em; top: -1.368em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="width: 0.772em; bottom: -0.722em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.772em;" class="mjx-line"></span></span><span style="height: 2.089em; vertical-align: -0.722em;" class="mjx-vsize"></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\TeX"><span class="mjx-mrow" style="width: 2.065em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim_{x\mapsto 1}\frac1x"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">↦</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mfrac MJXc-space1"><span class="mjx-box MJXc-stacked" style="width: 0.546em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 0.772em; top: -1.372em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 0.772em; bottom: -0.524em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.546em;" class="mjx-line"></span></span><span style="height: 1.341em; vertical-align: -0.37em;" class="mjx-vsize"></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\TeX"><span class="mjx-mrow" style="width: 2.065em;" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span><span class="mjx-mspace" style="margin-right: -0.14em; width: 0px; height: 0px;"></span><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.516em; padding: 0px 0.764em 0.246em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.705em 0px -0.025em; position: relative; top: 0.221em;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.026em;">E</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mspace" style="margin-right: -0.115em; width: 0px; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.024em;">X</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lvert x\rvert"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lVert v\rVert"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="|x|, ||v|| \quad\longrightarrow\quad \lvert x\rvert, \lVert v\rVert"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-texatom MJXc-space1"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟶</span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\|x\|"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lVert x \rVert"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">∥</span></span></span></span></span></span></div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\bbox[yellow]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (1)
}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mstyle" style="background-color: yellow;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-munderover MJXc-space3"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.225em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 0.8em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 0.8em; top: -1.144em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-denominator" style="width: 0.8em; bottom: -0.722em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.8em;" class="mjx-line"></span></span><span style="height: 1.865em; vertical-align: -0.722em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 1.276em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mspace" style="width: 2em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></span></span>
</div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\bbox[yellow,5px]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (1)
}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mstyle" style="background-color: yellow;"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: 0.601em; padding: 0px 12.397em 1.09em 0px;"><span class="mjx-box" style="width: 0px; margin: -1.232em 0px -0.722em; position: relative; left: 0.368em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-munderover MJXc-space3"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.225em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 0.8em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 0.8em; top: -1.144em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-denominator" style="width: 0.8em; bottom: -0.722em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.8em;" class="mjx-line"></span></span><span style="height: 1.865em; vertical-align: -0.722em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 1.276em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mspace" style="width: 2em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span>
</div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\bbox[5px,border:2px solid red]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (2)
}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mstyle" style="border: 2px solid red;"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: 0.601em; padding: 0px 12.397em 1.09em 0px;"><span class="mjx-box" style="width: 0px; margin: -1.232em 0px -0.722em; position: relative; left: 0.368em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-munderover MJXc-space3"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.225em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 0.8em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 0.8em; top: -1.144em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-denominator" style="width: 0.8em; bottom: -0.722em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.8em;" class="mjx-line"></span></span><span style="height: 1.865em; vertical-align: -0.722em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 1.276em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mspace" style="width: 2em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span>
</div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\bbox[yellow,5px,border:2px solid red]
{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n
\qquad (1)
}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mstyle" style="border: 2px solid red; background-color: yellow;"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: 0.601em; padding: 0px 12.397em 1.09em 0px;"><span class="mjx-box" style="width: 0px; margin: -1.232em 0px -0.722em; position: relative; left: 0.368em;"><span class="mjx-mrow"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-munderover MJXc-space3"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op" style="padding-left: 0.225em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked" style="width: 0.8em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 0.8em; top: -1.144em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-denominator" style="width: 0.8em; bottom: -0.722em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.8em;" class="mjx-line"></span></span><span style="height: 1.865em; vertical-align: -0.722em;" class="mjx-vsize"></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.961em; padding-bottom: 0.961em;">)</span></span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 1.276em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span><span class="mjx-mspace" style="width: 2em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display"><span class="mjx-math" style="width: 100%;" aria-label="\begin{align}
v + w &amp; = 0 &amp;&amp;\text{Given} \tag 1\\
-w &amp; = -w + 0 &amp;&amp; \text{additive identity} \tag 2\\
-w + 0 &amp; = -w + (v + w) &amp;&amp; \text{equations $(1)$ and $(2)$}
\end{align}"><span class="mjx-mrow" style="width: 100%;" aria-hidden="true"><span class="mjx-mtable" style="width: 100%; min-width: 25.687em;"><span style="width: 100%; text-align: center;" class="mjx-box"><span class="mjx-table" style="display: inline-table; width: auto; vertical-align: 1.363em;"><span class="mjx-mlabeledtr" style="height: 1.225em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: right; width: 3.216em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 1em 0px 0px; text-align: left; width: 7.251em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 1em; text-align: right; width: 0px;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: left; width: 9.063em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">Given</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mlabeledtr" style="height: 1.375em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 1em 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 1em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">additive identity</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.225em;"><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 1em 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mi"></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">v</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">w</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 1em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.15em 0px 0px 0px; text-align: left;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mrow"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">equations&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">&nbsp;and&nbsp;</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span><span class="mjx-itable" style="vertical-align: top; margin-left: -1.278em;"><span class="mjx-label" style="height: 1.225em;"><span id="mjx-eqn-1" class="mjx-mtd"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(1)</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-label" style="height: 1.375em;"><span id="mjx-eqn-2" class="mjx-mtd"><span class="mjx-mrow" style="margin-top: -0.05em;"><span class="mjx-mtext"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(2)</span></span><span class="mjx-strut"></span></span></span></span><span style="height: 1.225em;" class="mjx-label"></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\spadesuit\quad\heartsuit\quad\diamondsuit\quad\clubsuit"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">♠</span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">♡</span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">♢</span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">♣</span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\color{red}{\heartsuit}\quad\color{red}{\diamondsuit}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mstyle" style="color: red;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">♡</span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-mstyle" style="color: red;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">♢</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display"><span class="mjx-math" style="width: 100%;" aria-label="♠\quad♡\quad♢\quad♣\\
♤\quad♥\quad♦\quad♧"><span class="mjx-mrow" style="width: 100%;" aria-hidden="true"><span class="mjx-stack" style="width: 100%; vertical-align: -1.454em;"><span class="mjx-block" style="text-align: center;"><span class="mjx-box"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">♠</span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.372em;">♡</span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.519em;">♢</span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.446em;">♣</span></span></span></span></span></span><span class="mjx-block" style="text-align: center; padding-top: 0.442em;"><span class="mjx-box"><span class="mjx-mspace" style="width: 0px; height: 0px;"></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char" style="padding-top: 0.519em; padding-bottom: 0.225em;"><span class="mjx-charbox MJXc-TeX-unknown-R" style="padding-bottom: 0.3em; width: 0.5em;">♤</span></span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char" style="padding-top: 0.519em; padding-bottom: 0.225em;"><span class="mjx-charbox MJXc-TeX-unknown-R" style="padding-bottom: 0.3em; width: 0.5em;">♥</span></span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char" style="padding-top: 0.519em; padding-bottom: 0.225em;"><span class="mjx-charbox MJXc-TeX-unknown-R" style="padding-bottom: 0.3em; width: 0.5em;">♦</span></span></span></span></span><span class="mjx-mspace" style="width: 1em; height: 0px;"></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char" style="padding-top: 0.519em; padding-bottom: 0.225em;"><span class="mjx-charbox MJXc-TeX-unknown-R" style="padding-bottom: 0.3em; width: 0.5em;">♧</span></span></span></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Rightarrow"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⇒</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Leftarrow"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⇐</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\Leftrightarrow"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⇔</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\implies"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟹</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\impliedby"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟸</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\iff"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">⟺</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div>
<span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="
\require{enclose}
\begin{array}{r}
13 \\[-3pt]
4 \enclose{longdiv}{52} \\[-3pt]
\underline{4}\phantom{2} \\[-3pt]
12 \\[-3pt]
\underline{12}
\end{array}
"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -2.551em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.05em;"><span class="mjx-mtd" style="padding: 0px 0px 0px 0px; text-align: right; width: 2.2em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">13</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.238em;"><span class="mjx-mtd" style="padding: 0.05em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.109em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span><span class="mjx-menclose"><span class="mjx-box" style="padding: 0.2em; margin: 0px 0px 0px 0.3em;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">52</span></span></span></span><svg style="width: 1.7em; height: 1.138em; vertical-align: -0.247em; margin-left: -1.7em;"><g stroke-width="1px"><path d="M 23.1,1 L 1,1 a2.7,7.2 0 0,1 1,13.9"></path></g></svg></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.132em;"><span class="mjx-mtd" style="padding: 0.05em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-munderover"><span class="mjx-itable" style="margin-bottom: -0.223em;"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">4</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: 0.004em; padding-bottom: 0.298em;">–</span></span></span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mphantom"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.1em;"><span class="mjx-mtd" style="padding: 0.05em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">12</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.082em;"><span class="mjx-mtd" style="padding: 0.05em 0px 0px 0px; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-munderover"><span class="mjx-itable" style="margin-bottom: -0.223em;"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">12</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="padding-top: 0.12em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; padding-top: -0.004em; margin: 0px -0.001em 0px 0px;">–</span><span class="mjx-char MJXc-TeX-main-R" style="padding-bottom: 0.537em; letter-spacing: -0.398em; padding-top: -0.004em; margin: 0px 0.247em 0px -0.248em;">–</span><span class="mjx-char MJXc-TeX-main-R" style="margin-top: 0px; padding-bottom: 0.537em; margin-right: -0.001em; padding-top: -0.004em; margin-bottom: 0px;">–</span></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span>
</div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="x^3−6x^2+11x−6=(x−{\color{red}1})(x^2−5x+6)+{\color{blue}0}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">11</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-texatom MJXc-space2"><span class="mjx-mrow"><span class="mjx-mstyle" style="color: red;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">5</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-texatom MJXc-space2"><span class="mjx-mrow"><span class="mjx-mstyle" style="color: blue;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\begin{array}{c|rrrr}&amp; x^3 &amp; x^2 &amp; x^1 &amp; x^0\\ &amp; 1 &amp; -6 &amp; 11 &amp; -6\\ {\color{red}1} &amp; \downarrow &amp; 1 &amp; -5 &amp; 6\\ \hline &amp; 1 &amp; -5 &amp; 6 &amp; |\phantom{-} {\color{blue}0} \end{array}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mtable" style="vertical-align: -2.643em; padding: 0px 0.167em;"><span class="mjx-table"><span class="mjx-mtr" style="height: 1.473em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.221em 0.463em 0px 0.4em; width: 0.5em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.463em; text-align: right; width: 0.961em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">3</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 1.278em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.5em 0px 0.5em; text-align: right; width: 1.278em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.221em 0.4em 0px 0.5em; text-align: right; width: 1.556em;"><span class="mjx-mrow" style="margin-top: -0.148em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.4em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">11</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.419em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em; border-bottom: 1.3px solid;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="color: red;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.519em;">↓</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">5</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; border-bottom: 1.3px solid; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span><span class="mjx-strut"></span></span></span></span><span class="mjx-mtr" style="height: 1.495em;"><span class="mjx-mtd" style="border-right: 1.3px solid; padding: 0.2em 0.463em 0px 0.4em;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.463em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">5</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.5em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">6</span></span><span class="mjx-strut"></span></span></span><span class="mjx-mtd" style="padding: 0.2em 0.4em 0px 0.5em; text-align: right;"><span class="mjx-mrow" style="margin-top: -0.2em;"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">|</span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mphantom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span></span></span></span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mstyle" style="color: blue;"><span class="mjx-mrow"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="90°"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">90</span></span><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.298em;">°</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="90^\circ"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">90</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.591em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mo" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.298em;">∘</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage mjpage__block"><span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math" aria-label="\sum_{n=1}^\infty \frac{1}{n^2} \to
\textstyle \sum_{n=1}^\infty \frac{1}{n^2} \to
\displaystyle \sum_{n=1}^\infty \frac{1}{n^2}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em; padding-left: 0.521em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.74em; padding-bottom: 0.74em;">∑</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.082em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-mfrac MJXc-space1"><span class="mjx-box MJXc-stacked" style="width: 1.189em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.189em; top: -1.368em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="width: 1.189em; bottom: -0.854em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.189em;" class="mjx-line"></span></span><span style="height: 2.221em; vertical-align: -0.854em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mstyle MJXc-space3"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">∑</span></span></span><span class="mjx-stack" style="vertical-align: -0.31em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.422em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span><span class="mjx-mfrac MJXc-space1"><span class="mjx-box MJXc-stacked" style="width: 0.89em; padding: 0px 0.12em;"><span class="mjx-numerator" style="font-size: 70.7%; width: 1.258em; top: -1.372em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="font-size: 70.7%; width: 1.258em; bottom: -0.85em;"><span class="mjx-msubsup" style=""><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sup" style="font-size: 83.3%; vertical-align: 0.347em; padding-left: 0px; padding-right: 0.06em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 0.89em;" class="mjx-line"></span></span><span style="height: 1.572em; vertical-align: -0.601em;" class="mjx-vsize"></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mstyle MJXc-space3"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; padding-bottom: 0.247em; padding-top: 0.141em; padding-left: 0.521em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.151em; padding-bottom: 0.372em;">∞</span></span></span><span class="mjx-op"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 0.74em; padding-bottom: 0.74em;">∑</span></span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.082em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span><span class="mjx-mfrac MJXc-space1"><span class="mjx-box MJXc-stacked" style="width: 1.189em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 1.189em; top: -1.368em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="width: 1.189em; bottom: -0.854em;"><span class="mjx-msubsup"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.409em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 1.189em;" class="mjx-line"></span></span><span style="height: 2.221em; vertical-align: -0.854em;" class="mjx-vsize"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\displaystyle \lim_{t \to 0} \int_t^1 f(t)\, dt"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-munderover"><span class="mjx-itable"><span class="mjx-row"><span class="mjx-cell"><span class="mjx-op"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span></span></span><span class="mjx-row"><span class="mjx-under" style="font-size: 70.7%; padding-top: 0.236em; padding-bottom: 0.141em; padding-left: 0.052em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base" style="margin-right: -0.388em;"><span class="mjx-mo" style="vertical-align: 0.001em; padding-right: 0.388em;"><span class="mjx-char MJXc-TeX-size2-R" style="padding-top: 1.109em; padding-bottom: 1.109em;">∫</span></span></span><span class="mjx-stack" style="vertical-align: -0.921em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 2.201em; padding-left: 0.784em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\lim_{t \to 0} \int_t^1 f(t)\, dt"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-base"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">lim</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">→</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">0</span></span></span></span></span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base" style="margin-right: -0.138em;"><span class="mjx-mo" style="padding-right: 0.138em;"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">∫</span></span></span><span class="mjx-stack" style="vertical-align: -0.366em;"><span class="mjx-sup" style="font-size: 70.7%; padding-bottom: 0.63em; padding-left: 0.324em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-sub" style="font-size: 70.7%; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span></span><span class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.519em; padding-bottom: 0.519em; padding-right: 0.06em;">f</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mspace" style="width: 0.167em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.372em; padding-bottom: 0.298em;">t</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\overline a+\overline b=\overline {a\cdot b}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-munderover"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; height: 0.096em; padding-bottom: 0.283em; padding-top: 0.141em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin: 0px -0.07em 0px -0.069em;">¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; letter-spacing: -0.374em; margin: 0px 0.097em 0px -0.236em;">¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin-right: -0.07em; margin-bottom: 0px; margin-top: 0px;">¯</span></span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-munderover MJXc-space2"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; height: 0.096em; padding-bottom: 0.283em; padding-top: 0.141em; padding-left: 0px;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin: 0px -0.128em 0px -0.069em;">¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin: 0px -0.07em 0px -0.127em;">¯</span></span></span></span><span class="mjx-op"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-munderover MJXc-space3"><span class="mjx-stack"><span class="mjx-over" style="font-size: 70.7%; height: 0.096em; padding-bottom: 0.283em; padding-top: 0.141em;"><span class="mjx-mo" style="vertical-align: top;"><span class="mjx-delim-h"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin: 0px -0.07em 0px -0.069em;">¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; letter-spacing: -0.249em; margin: 0px 0.035em 0px -0.174em;">¯¯¯¯¯¯¯</span><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.301em; padding-bottom: 0.833em; margin-right: -0.07em; margin-bottom: 0px; margin-top: 0px;">¯</span></span></span></span><span class="mjx-op"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.004em; padding-bottom: 0.298em;">⋅</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sqrt{a}-\sqrt{b}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.237em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msqrt MJXc-space2"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.11em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sqrt{\mathstrut a} - \sqrt{\mathstrut b}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">√</span></span><span class="mjx-box" style="padding-top: 0.063em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.225em; padding: 0px 0px 0.275em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.775em 0px -0.275em;"><span class="mjx-mrow"><span class="mjx-mphantom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msqrt MJXc-space2"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-size1-R" style="padding-top: 0.593em; padding-bottom: 0.593em;">√</span></span><span class="mjx-box" style="padding-top: 0.063em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.225em; padding: 0px 0px 0.275em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.775em 0px -0.275em;"><span class="mjx-mrow"><span class="mjx-mphantom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\sqrt{\vphantom{b} a} - \sqrt{b}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.11em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.281em; padding: 0px 0px 0.036em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.719em 0px -0.036em;"><span class="mjx-mrow"><span class="mjx-mphantom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msqrt MJXc-space2"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.11em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\dfrac{1}{\sqrt{\vphantom{b} a} - \sqrt{b}}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 4.046em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 4.046em; top: -1.368em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="width: 4.046em; bottom: -1.15em;"><span class="mjx-mrow"><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.11em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.281em; padding: 0px 0px 0.036em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.719em 0px -0.036em;"><span class="mjx-mrow"><span class="mjx-mphantom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msqrt MJXc-space2"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.11em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 4.046em;" class="mjx-line"></span></span><span style="height: 2.518em; vertical-align: -1.15em;" class="mjx-vsize"></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\smash{\dfrac{1}{\sqrt{\vphantom{b} a} - \sqrt{b}}}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -1em; padding: 0px 4.286em 0px 0px;"><span class="mjx-box" style="width: 0px; margin: -1.368em 0px -1.15em;"><span class="mjx-mrow"><span class="mjx-mstyle"><span class="mjx-mrow"><span class="mjx-mfrac"><span class="mjx-box MJXc-stacked" style="width: 4.046em; padding: 0px 0.12em;"><span class="mjx-numerator" style="width: 4.046em; top: -1.368em;"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span><span class="mjx-denominator" style="width: 4.046em; bottom: -1.15em;"><span class="mjx-mrow"><span class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.11em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mpadded"><span class="mjx-block" style="width: 0px; margin-top: -0.281em; padding: 0px 0px 0.036em 0px;"><span class="mjx-box" style="width: 0px; margin: -0.719em 0px -0.036em;"><span class="mjx-mrow"><span class="mjx-mphantom"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-msqrt MJXc-space2"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.519em; padding-bottom: 0.519em;">√</span></span><span class="mjx-box" style="padding-top: 0.11em; border-top: 1px solid;"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span></span></span></span></span></span></span><span style="border-bottom: 1.3px solid; top: -0.296em; width: 4.046em;" class="mjx-line"></span></span><span style="height: 2.518em; vertical-align: -1.15em;" class="mjx-vsize"></span></span></span></span></span></span><span class="mjx-strut"></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="T_1,\ldots,T_n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">…</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="T_1\gets 1"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">←</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="k"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="2"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="T_k\gets (k−1)T_{k−1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.219em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">←</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.219em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="k"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="2"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="j"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="k"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="T_j\gets (j −k)T_{j−1} + (j −k+2)T_j"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">←</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\;T_1,T_2,\ldots,T_n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">…</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="T_1,\ldots,T_n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.372em;">…</span></span><span class="mjx-mo MJXc-space1"><span class="mjx-char MJXc-TeX-main-R" style="margin-top: -0.144em; padding-bottom: 0.519em;">,</span></span><span class="mjx-msubsup MJXc-space1"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="T_1\gets 1"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.212em; padding-right: 0.071em;"><span class="mjx-mn" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">←</span></span><span class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\;k\;"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="2\;"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\;n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\phantom{{}++{}}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mphantom"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="T_k\gets (k−1)T_{k−1}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.219em; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span></span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.225em; padding-bottom: 0.372em;">←</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-msubsup"><span class="mjx-base" style="margin-right: -0.12em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.12em;">T</span></span></span><span class="mjx-sub" style="font-size: 70.7%; vertical-align: -0.219em; padding-right: 0.071em;"><span class="mjx-texatom" style=""><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\;k\;"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="2\;"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\;n"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">n</span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\phantom{{}++{}}"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mphantom"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"></span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span class="mjx-texatom"><span class="mjx-mrow"></span></span></span></span></span></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\;j\;"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.519em;">j</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></span></div>
<div><span class="mjpage"><span class="mjx-chtml"><span class="mjx-math" aria-label="\;k\;"><span class="mjx-mrow" aria-hidden="true"><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.446em; padding-bottom: 0.298em;">k</span></span><span class="mjx-mspace" style="width: 0.278em; height: 0px;"></span></span></span></span></sp
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