Define f: ℝ2 → ℝ by \(\rm f(x, y)=\left\{\begin{matrix}\frac{y\sqrt{x^2+y^2}}{x}& if\ x\ne 0\\\ 0, &if\ x=0\end{matrix}\right.\)
Which of the following statements are true?
1
\(\rm \frac{\partial f}{\partial x}(0,0)\) exists
2
\(\rm \frac{\partial f}{\partial y}(0,0)\) exists
3
f is not continuous at (0,0)
4
f is not differentiable at (0, 0)