Easier: the limits along and are different.
I am trying to find a limit for the 2-variavle function .
So right before changing to polar coordinates, I get something like:
and thus is bounded by 0 and 2: .
(1) Does this mean that the limit exists?
(2) Can we conclude that the numerator and the denomenator are of the same "order"?
(because the ratio of the numerator and the denominator is a constant)
Any help is appreciated!
Okay. I may need to add something. Since, x and y are approching ten the angle is between 0 and 90 degrees so .
You're right, it's much easier, but my approach was to get a limit that is not zero or to determine wether the numerator and denominator are of same order eg. and are of same order...
If you're going to use polars, note that .
Using the change of coordinates we find
Notice that this does not depend on , so making won't make any difference.
Since the limit will change over different paths (depending on the value of ) we can conclude that the limit does not exist.