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# markusbuchholz/latex_eq.md

Last active Jun 21, 2021

eq1.--------------------------------------

$$\large x_{n+1} = x_{0} - \frac{f(x_{n})}{f'(x_{n})}$$

eq2.--------------------------------------

$$\large f(x) = x^2 - 999$$

eq3.--------------------------------------

$$\large f(x) = 2x^3 + x^2 +7x + 2$$

eq4.--------------------------------------

$$\large p(x) = \sum_{i=0}^{n} f(x_{i}) \frac{\prod_{j=0, j\neq i}^{n}(x - x_{j})}{\prod_{j=0, j\neq i}^{n}(x_{i} - x_{j})}$$

eq5.--------------------------------------

$$\large \int_{a}^{b} f(x) ,dx = \int_{a}^{c} f(x) ,dx + \int_{c}^{b} f(x) ,dx$$

eq6.--------------------------------------

$$\large \large \int_{a}^{b} f(x) ,dx \approx \frac{b-a}{n}[\sum _{i=0}^{n-1} f(a + (i+0.5)\frac{b-a}{n})]$$

eq7.--------------------------------------

$$\large \large \int_{a}^{b} f(x) ,dx \approx \frac{b-a}{n}[\frac{a}{2} + \frac{b}{2} \sum _{i=0}^{n-1} f(a + i\frac{b-a}{n})]$$

eq8.--------------------------------------

$$\large 2 \int_{-1}^{1} \sqrt{ 1 - x^2 },dx = \pi \approx 3.1415926535$$

eq9.--------------------------------------

$$\large \frac{f(x)}{dx} \approx \frac{f(x+0.5h)-f(x-0.5h)}{h}$$