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Limits of multivariable functions

  1. May 2, 2014 #1
    1. The problem statement, all variables and given/known data

    The limit as x,y → 0

    [itex]\frac{y^{2}Sin^{2}x}{x^{4}+y^{4}}[/itex]

    2. Relevant equations



    3. The attempt at a solution

    There are pretty straight forward but I have a general question about them. So say in the function above I let y=x and let x approach 0.

    I get 0/0 - inconclusive. Can I fall back on single variable calculus and use L'Hospital's rule to find the limit? For some reason my gut tells me no.
     
  2. jcsd
  3. May 2, 2014 #2

    Zondrina

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    Homework Helper

    If you approach along a straight line, you would need to use L'Hospital's rule to find the limit. What happens if you approach along a parabola? Compare that to approaching along a straight line. What can you conclude?
     
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