Try approaching on y=x and y=-x.
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.
The first fraction approaches 0 (per the formula in my original post). However, it's still , so that doesn't really help me. Any ideas on how to continue?
Also, could you point me to a good resource on using polar coordinates with limits? I'm not sure that what I did is really OK -- aren't there any conditions that need to be satisfied before I can say that a limit is the same in polar coordinates? Also, I assumed that I can just ignore the angle , as I'm approaching zero, is that correct?
Thanks again, you've been a great help!