Consider the function: f(x,y)={x2yx2+y2if (x,y)≠(0,0)0if (x,y)=(0,0)f(x,y) = \begin{cases} \frac{x^2 y}{x^2 + y^2} & \text{if } (x,y) \neq (0,0) \\ 0 & \text{if } (x,y) = (0,0) \end{cases}f(x,y)={x2+y2x2y0if (x,y)=(0,0)if (x,y)=(0,0) Which statement is TRUE?
fff is not continuous at (0,0)(0,0)(0,0)
fff is continuous at (0,0)(0,0)(0,0) but ∂f∂x(0,0)\frac{\partial f}{\partial x}(0,0)∂x∂f(0,0) does not exist
fff is continuous at (0,0)(0,0)(0,0) and both partial derivatives exist at (0,0)(0,0)(0,0)
fff is continuous at (0,0)(0,0)(0,0) and differentiable at (0,0)(0,0)(0,0)