I've been working on these two limits all night and can't seem to make any reasonable progress. Any help would be appreciated. Here's the first one:

$\displaystyle \lim_{(x,y) \to (0,0)} \frac{xy^2}{2x-y}$

According to Wolfram Alpha, this limit does not exist. However, I can't seem to find any x,y path that gives any limit other than 0. I tried all lines (x=0, y=0, y=kx), as well as x=y^2 and y=x^2. Any ideas?

And the second one:

$\displaystyle \lim_{(x,y) \to (0,0)} \frac{e^{-\frac{1}{x^2+y^2}}}{x^4+y^4}$

Here, I know that

$\displaystyle \lim_{(x,y) \to (0,0)} \frac{e^{-\frac{1}{x^2+y^2}}}{x^2+y^2} = \lim_{(x,y) \to (0,0)} \frac{\frac{1}{x^2+y^2}}{e^{\frac{1}{x^2+y^2}}} = \lim_{t \to \infty} \frac{t}{e^t} = 0$

I can't find a way to use this though.

Thanks!