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Two-variable limit problem

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations


    3. 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?
  2. jcsd
  3. Oct 3, 2011 #2
    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..
  4. Oct 3, 2011 #3
    I figured it out a while ago. If y=-x, the limit as x->0 is infinity, not zero.
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