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z1`U1{oPJliJZ)oc`Ia1Z(ZI8&8Q5=srg4u-TzH_7?+Dv-0XMA*Bie-=vj2zmlh^4S z5&-*}WWjbf998&u`Qbjoh5@TvA})+_&lvdRP1Qc4Zek1c*2D9qNCMN_3;F+r4{g~u zY)>7^6qdjUVL+{dH8QnRhMr`JQ1c9=R?Ui?ml>anUb3S7=j7SpI}#xJs^kt~2Q3Am z#`ecdw6wz+Sil>T==8S)5DiiBkvy<35g{F6HzKpfVH}YirZx7|{WBH+qLr@LZ#z(a z|H)o86rJ8ZD+$>R`26^(UB&Kk@mi9@gg0|Jz(G9FRS|%sssP XJgjYyxj9gHxCMBTX=tQXWsv^|aFjg+ diff --git a/ws2019/ana/lectures/analysis18.tex b/ws2019/ana/lectures/analysis18.tex index 17d1eb9..3f87343 100644 --- a/ws2019/ana/lectures/analysis18.tex +++ b/ws2019/ana/lectures/analysis18.tex @@ -130,7 +130,11 @@ trivial. \end{proof} -\begin{satz}[$\cos$ und $\sin$ sind stetig] +\begin{satz} + $\cos$ und $\sin$ sind stetig. +\end{satz} + +\begin{proof} Restgliedabschätzung von $\exp(x)$ gilt auch für komplexe $z \in \mathbb{C}$ \[ (|R_{n+1}(z)| \le 2 \frac{|z|^{N+1}}{(N+1)!} @@ -152,7 +156,7 @@ $\implies \cos(x_n) \to \cos(a)$ und $\sin(x_n) \to \sin(a)$ \\ $\implies$ Stetigkeit -\end{satz} +\end{proof} \begin{satz}[Additionstheoreme] $\forall x, y \in \R$ gilt: