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