Heya guys. I have to study the continuity of the following function at (0,0):

Thus I need to check whether

exists or not.

I converted to polar coordinates:

Thus the limit seems to be 0 except where

If , then

I then used L'Hopital's rule:

since .

However, by using such paths as and , the limit equals 1 and 2, respectively. What's going on that I don't understand here?

Thanks!