1. (4) Let $f(x, y) = \begin{cases} \frac{2x^2}{x^2 + y^2} & (x, y) \neq (0, 0) \\ 0 & (x, y) = (0, 0) \end{cases}$
a) Compute $\lim_{(x,y)\to(1,3)} f(x, y)$.
b) Show that $\lim_{(x,y)\to(0,0)} f(x, y)$ does not exist, by having $(x, y)$ approach $(0, 0)$ along two different paths.
c) Is $f$ continuous at $(1, 3)$? Explain.
d) Is $f$ continuous at $(0, 0)$? Explain.