# Math Help - lim problem with several variables

1. ## lim problem with several variables

Prove that lim (x,y->0,0) (xy)/(x^2+2y^2) does not exist.

Prove that lim (x,y->0,0) (xy)/(x^2+2y^2) does not exist.
I think you want a more formal proof but if not try this:

Assume it exists. Now approach the limit with the path x=0 and y--> 0.

Then approach the path with x=y -->0

You shall see the limits are not the same.

3. I'm actually working on the method of proving there exist an E>0, N in the set of natural numbers, then for each k >= N implies |f(x,y)| > E.

I just don't know how to get there.

4. I had been trying to plug in the x and y differently, but I just don't really get the limits for each one. I should know how to do this, I think they taught us in Cal III.