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Multivariable Calculus: When to use Squeeze Theorem to solve limits?

  1. May 18, 2012 #1
    1. The problem statement, all variables and given/known data
    For example in:
    lim (x,y) -> (0,0) [(xy^2)/(x^2+y^4)]

    This limit does not exist (according to textbook), but if you use squeeze theorem since y^2<(x^2+y^4)
    y^2/(x^2+y^4) <= 1 and therefore

    0 <= (xy^2)/(x^2+y^4) <= x
    as x--> 0
    so
    lim (x,y) -> (0,0) [(xy^2)/(x^2+y^4)] = 0?
     
  2. jcsd
  3. May 18, 2012 #2
    What happens if you look at y=sqrt(x)?
     
  4. May 18, 2012 #3
    I see what you mean but what if i was looking at a different limit and I got 0 every time while using different paths. I still couldn't prove it with squeeze theorem because what if there is just this one path that i never tried.
     
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