| 5. (a) (7 points) Use a suitable change of variable to compute $$\iint_R (x + y)^2 e^{x^2 - y^2} \mathrm{d}A,$$ where $R$ is the square with vertices $(1,0), (0,1), (-1,0)$ and $(0, -1)$

| 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) $.