(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello, I can't find any way to prove if this funtion is or isn't differentiable in if [tex](x,y)=(0,0)[/tex] :

[tex]{f(x,y)=\displaystyle\frac{x^{3}}{x^{2}+y^{2}}}[/tex] if [tex](x,y) \neq(0,0)[/tex]

[tex]f(x,y)=0[/tex] if [tex](x,y)=(0,0)[/tex]

3. The attempt at a solution

Partial derivatives don't exist in (0,0), so i have calculate definition of differentiability, and i get:

[tex]\displaystyle\lim_{x,y \to{0,0}}{} \displaystyle\frac{x^{3}}{(x^{2}+y^{2})^{3/2}}[/tex]

Which limit doesn't exit, so it is not differentiable in (0,0).

Is this right?

Thanks!

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# Homework Help: Check differentiability in function

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