Consider two different path of approach: .
Do you get different limits?
I had a quick question which might be stupid, but I figured I should ask it as I am uncertain.
Then switching to polar coordinates yield:
Is my notation for the upper limit correct? We want to find the limit as r -> 0 and if the limit exists it doesn't matter how we approach the origin. Therefore can be anything. And if we find that the limit is left with only then it means the limit doesn't exist.