What is the limit as (x,y) approaches (0,0) for the function x^2/(x+y)?

[Mingy Jongo]

Homework Statement

Find the limit as (x,y) approaches (0,0):

Homework Equations

x^2/(x+y)

The Attempt at a Solution

I have tried replacing y with 0, mx, x^2, etc. (and likewise with x), and all give me a limit of zero. So I tried to think of ways I could use the definition of a limit, squeeze theorem, L'Hopital's rule, etc. to prove it, but there does not appear to be a way. I'm starting to think that a limit might not even exist. Is there something elementary I'm overlooking?

 

[Hammie]

It is a lot easier to show the limit does not exist. All you have to do is find one path towards (0,0) that produces a limit that is not zero. Maybe you could try a quadratic, or a cubic..

 

[Mingy Jongo]

I figured it out a while ago. If y=-x, the limit as x->0 is infinity, not zero.