This problem was on a recent quiz. I set $x$ and $y = 0$ and both limits approach $0$. Then I set $y=x$ and that limit also approaches $0$. I would think the answer is that it approaches $0$ but TA says that the limit does not exist. I plugged it into wolfram alpha and it also says limit is $0$.
So, does the limit exist? If so, what is it?