Let
\(\rm f(x,y)=\left\{\begin{matrix}\frac{xy}{\sqrt{x^2+y^2}},&x^2+y^2\ne0\\\ 0,&x=y=0\end{matrix}\right.\)
1
f(x, y) is not continuous at origin
2
f(x, y) is not differentiable at origin
3
fx(0, 0) = f(0, 0)
4
fy(0, 0) = f(0, 0)
Let
\(\rm f(x,y)=\left\{\begin{matrix}\frac{xy}{\sqrt{x^2+y^2}},&x^2+y^2\ne0\\\ 0,&x=y=0\end{matrix}\right.\)