Editing TU Wien:Analysis UE (diverse)/Übungen SS19/Beispiel 300

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==Lösungsvorschlag von m-zero ==
==Lösungsvorschlag von m-zero ==
<math>\lim_{y \to 0}\bigg(\lim_{x \to 0}f(x,y)\bigg)=\lim_{y \to 0}\frac{y\sin y}{-y}=\lim_{y \to 0}-\sin y=0</math>
<math>\lim_{y \to 0}\bigg(\lim_{x \to 0}f(x,y)\bigg)=\lim_{y \to 0}\frac{y\ sin\ y}{-y}=\lim_{y \to 0}-sin\ y=0</math>


<math>\lim_{x \to 0}\bigg(\lim_{y \to 0}f(x,y)\bigg)=\lim_{x \to 0}\frac{x\cos \frac{1}{x}}{2x}=\lim_{x \to 0}\frac{\cos\ \frac{1}{x}}{2}\ </math> ist wegen <math>\frac{1}{x}</math> undefiniert.
<math>\lim_{x \to 0}\bigg(\lim_{y \to 0}f(x,y)\bigg)=\lim_{x \to 0}\frac{x\ cos\ \frac{1}{x}}{2x}=\lim_{x \to 0}\frac{cos\ \frac{1}{x}}{2}\ </math> ist wegen <math>\frac{1}{x}</math> undefiniert.


Die iterierten Grenzwerte sind also verschieden.
Die iterierten Grenzwerte sind also verschieden.

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