Math — Maclaurin Series

e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots

\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots

\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \cdots

\ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \cdots