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