# Choosing $2$ paths through $(0,0)$ to show: $\lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 + y^4}$ does not exist

I'm trying to find $2$ paths through $(0,0)$ to show that $\lim_{(x,y) \to (0,0)}\dfrac{xy^2}{x^2 + y^4}$ does not exist.

I only manage to use path $y=x$ but can't find second one. Any thoughts on which path to choose to show that this limit doesn't exist? Thanks!

• Try $x=t^2$, $y=t$. – user137731 Jul 8 '16 at 1:06
• Thanks for the suggestion! – Sandra Jul 8 '16 at 1:24
• Try $y=0$ and $x=y^2$. – user84413 Jul 8 '16 at 4:57

Choose $y=x$ and $y=\sqrt{x}$.