Calculate $ \lim_{\left(x,y\right)\to\left(0,0\right)}\frac{xy^{2}}{x^{4}+y^{2}} $ Im trying to calculate (or prove that the limit dosent exists)
$ \lim_{\left(x,y\right)\to\left(0,0\right)}\frac{xy^{2}}{x^{4}+y^{2}} $
Wolfram says the limit does not exists, but for every path I choose the limit ends up being 0.
If someone can tell if the limit exists or not, it would be helpful.
Thanks in advance
HINT
By $x^2=u$ and $y=v$ we obtain
$$\left|\frac{xy^{2}}{x^{4}+y^{2}}\right|= \frac{\sqrt u v^{2}}{u^{2}+v^{2}} $$
HINT
By $x^2=u$ and $y=v$ we obtain
$$\left|\frac{xy^{2}}{x^{4}+y^{2}}\right|= \frac{\sqrt u v^{2}}{u^{2}+v^{2}} $$