Calculating $\lim_{(x,y) \to(0,0)} \frac{x^2y}{x^2+y^4}$ I can't figure out how to calculate this limit (or prove it does not exist)
$$
\lim_{(x,y) \to(0,0)} \frac{x^2y}{x^2+y^4}
$$
I've tried with restrictions on $y=mx$ and curves of the form $y=x^n$. 
The limit should not exist but even with polar coordinates I can't figure it out

Using polar:  $\lvert\dfrac{r^3\cos^2\theta\sin\theta}{r^2(\cos^2\theta+r^2\sin^2\theta)}\rvert=\lvert\dfrac{r\cos^2\theta \sin\theta}{\cos^2\theta +r^2\sin^2\theta}\rvert\le\lvert\dfrac {r\cos^2\theta \sin\theta}{\cos^2\theta}\rvert=\lvert r\sin\theta\rvert\to0$, if $\theta\neq\dfrac{k\pi}2$.  But it's easy to see the limit is $0$ when $\theta =\dfrac {k\pi}2$.
