Problem 1233 (difficulty: 3/10)

\(\displaystyle f(x,y)=\begin{cases} 0 & \text{if $(x,y)=(0,0)$} \\ (x^2+y^2)\sin {1\over \sqrt{x^2+y^2}} & \text{otherwise} \end{cases}\)

is differentiable everywhere but not continuously.

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