[tex] \rm Let \begin{cases} \rm {x}^{2} \sin\frac{1}{x} + {y}^{2} \sin \frac{1}y ,\: \: \: \: \: \: \: \: xy\ne0 \\ \rm{x}^{2} \sin \frac{1}{x} , \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x \ne0, y = 0 \\ \rm y^{2} \sin \frac{1}{y} , \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y \ne0, x = 0 \\ 0, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm x = y = 0 \end{cases}[/tex]
Which of the following is true at (0,0)?

(A) f is not continuous
(B) ∂f/∂x is continuous but ∂f/∂y is not continuous
(C) f is not differentiable
(D) f is differentiable but both ∂f/∂y are not continuous ​