How do I prove the existence of $\lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^3+y^3}$ How do I prove the existence of
$$\lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^3+y^3}$$
When $y=0$ the limits is $0$
when $y=-x$ it´s $$\lim_{x\to0} \frac{x^2(-x^2)}{x^3- x^3}=\lim_{x\to0} \frac{x^2(-x^2)}{0}$$
I can concluir that the limit no exist??
or how proof the existence?

Along the path $y=x$, 
\begin{align*}
\frac{x^2y^2}{x^3+y^3} = \frac{1}{2}x\rightarrow 0.
\end{align*}
However, along the path $y=x^3-x$,
\begin{align*}
\frac{x^2y^2}{x^3+y^3} = \frac{x^8-2x^6+x^4}{x^9+3x^5-3x^7},
\end{align*}
which does not have a finite limit when $x\rightarrow 0$.
That is, 
\begin{align*}
\lim_{(x, y)\rightarrow (0, 0)} \frac{x^2y^2}{x^3+y^3}
\end{align*}
does not exist.
