Taylorreihe
\begin{aligned}
f(x) & = f(a) + f'(a) (x-a) + \frac{f''(a)}{2!} (x-a)^2 + \cdots \\
& = \sum_{k = 0}^\infty \frac{f^{(k)}(a)}{k!}(x-a)^k \\
f(x) & \approx \sum_{k = 0}^n \frac{f^{(k)}(a)}{k!}(x-a)^k
\end{aligned}
Wichtige Formeln
\begin{aligned}
\sin x & = x - \frac{x^3}{3!} + \frac{x^5}{5!} + \cdots \\
\cos x & = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} + \cdots \\
\mathrm{e}^x & = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots \\
\ln (1 + x) & = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \cdots & \text{(für $-1 \lt x \le 1$)}
\end{aligned}