In this problem we show that the function $$f(x,y) = \frac{7x^{2}-y}{x^{2}+y}$$ does not have a limit as $(x,y)\to (0,0)$.

(a) Suppose that we consider $(x,y)\to (0,0)$ along the curve $y = 4 x^2$. Find the limit in this case:
$\lim\limits_{(x,4 x^2)\to(0,0)} \frac{7x^{2}-y}{x^{2}+y} =$

(b) Now consider $(x,y)\to (0,0)$ along the curve $y = 5 x^2$. Find the limit in this case:
$\lim\limits_{(x,5 x^2)\to(0,0)} \frac{7x^{2}-y}{x^{2}+y} =$

(c) Note that the results from (a) and (b) indicate that $f$ has no limit as $(x,y)\to (0,0)$ (be sure you can explain why!).
To show this more generally, consider $(x,y)\to (0,0)$ along the curve $y = m x^2$, for arbitrary $m$. Find the limit in this case:
$\lim\limits_{(x,m x^2)\to(0,0)} \frac{7x^{2}-y}{x^{2}+y} =$
(Be sure that you can explain how this result also indicates that $f$ has no limit as $(x,y)\to(0,0)$.