(c) (6 points) The function on the right-hand side of (1) has a removable discontinuity at $x = 1$. Remove it and then show that (1) also holds for $x = 1$. | | | | | |

| 2. Consider $$ f(x, y) = \begin{cases} \dfrac{x y^2}{x^2 + y^2}, & \text{if } (x, y) \neq (0, 0); \\ 0, & \text{if } (x, y) = (0, 0). \end{cases} $$ (a) (3 points) Find the partial derivatives at $(0, 0)$ and the gradient vector $ \nabla f(0, 0) $.