Show that the function $$f(x,y) = \frac{x^{2}y}{x^{4}+y^{2}}.$$ does not have a limit at $(0,0)$ by examining the following limits.

(a) Find the limit of $f$ as $(x,y) \to (0,0)$ along the line $y = x$.
$\lim\limits_{{}^{(x,y)\to(0,0)}_{y=x}} f(x,y) =$

(b) Find the limit of $f$ as $(x,y)\to(0,0)$ along the curve $y = x^2$.
$\lim\limits_{{}^{(x,y)\to(0,0)}_{y=x^2}} f(x,y) =$

(Be sure that you are able to explain why the results in (a) and (b) indicate that $f$ does not have a limit at (0,0)!