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:

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:

Here, I know that

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

Thanks!