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Mathematics
Calculus
Vector calculus - Prove a function is not differentiable at (0,0)
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[QUOTE="physics1000, post: 6831288, member: 696729"] ##f\left(x\right)=\begin{cases}\sqrt{\left|xy\right|}sin\left(\frac{1}{xy}\right)&xy\ne 0\\ 0&xy=0\end{cases}## I showed it partial derivatives exist at ##(0,0)##, also it is continuous as ##(0,0)## but now I have to show if it differentiable or not at ##(0,0)##. According to answers it is not and they proved by showing the vector coordinates at ##(1,1)## does not have a limit. But I dont want a proof like that, I tried using definition and got stuck... I know my Linear transformation is basically 0. but still got in trouble of the definition [/QUOTE]
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Forums
Mathematics
Calculus
Vector calculus - Prove a function is not differentiable at (0,0)
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