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b/ws2019/ana/lectures/analysis18.tex @@ -166,7 +166,7 @@ \item $\sin x - \sin y = 2 \cos\left( \frac{x+y}{2} \right) \cdot \sin\left( \frac{x - y}{2} \right) $ \\ $\cos x - \cos y = - 2 \cdot \sin \left( \frac{x+y}{2} \right) \cdot - \sin \left( \frac{x - \frac{y}{2}}{} \right)$ + \sin \left( \frac{x - y}{2} \right)$ \end{enumerate} \end{satz} diff --git a/ws2019/ana/lectures/analysis20.tex b/ws2019/ana/lectures/analysis20.tex index 73590db..b11eee5 100644 --- a/ws2019/ana/lectures/analysis20.tex +++ b/ws2019/ana/lectures/analysis20.tex @@ -221,7 +221,7 @@ .\end{align*} mit \begin{align*} - e^{h} &= \sum_{k=0}^{\infty} \frac{h^{k}}{k!} = 1 + \frac{h}{2} + \frac{h^2}{3!} + \ldots \\ + e^{h} &= \sum_{k=0}^{\infty} \frac{h^{k}}{k!} = 1 + h + \frac{h^2}{2} + \frac{h^{3}}{3!} + \ldots \\ \frac{e^{h} - 1}{h} &= 1 + \frac{h}{2} + \frac{h^2}{3!} + \ldots \xrightarrow{h \to 0} \to 1 .\end{align*} \item Sinus / Cosinus.