is created by David Witten, a mathematics and computer science student at Vanderbilt University. For more information, see the "About" page.

Taylor Series to Memorize

There are four taylor series that you MUST memorize

MathJax TeX Test Page $$e^x (c = 0)$$ $$P_n(x) = 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + ... + \frac{x^n}{n!}$$ $$=\sum_{n = 0}^{\infty}\frac{x^n}{n!}$$
$$\cos{(x)}$$ $$P_n(x) = 1 - \frac{x^2}{2} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!}...$$ $$=\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n}}{(2n)!}$$
MathJax TeX Test Page $$\sin(x)$$ This is similar to cos $$\sum_{n = 0}^{\infty}(-1)^n \frac{x^{2n +1}}{(2n+1)!}$$
MathJax TeX Test Page $$\frac{1}{1-x}$$ Note that this is identical to $\frac{a}{1-r}$, the geometric series formula, with a = 1. For this reason, the sum is $$\sum_{n = 0}^{\infty}x^n$$
David Witten

Trigonometric Substitution

Taylor Polynomials