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[b]1. The problem statement, all variables and given/known data[/b]A

  1. May 23, 2009 #1
    1. The problem statement, all variables and given/known data
    A few:
    (1) lim(x,y) -> (0,0) of (x^4*y^2)/(x^2 + y^2)2
    (2) lim(x,y) -> (0,0) of x^4 / (y+x^2)

    2. Relevant equations



    3. The attempt at a solution
    (1) i get that it exists and equals 0 by using polar coordinates
    (2) i get that it exists (except for the parabolic path y=-x^2) and equals zero [using (t, mt) and (t, mt^2)]
     
    Last edited: May 23, 2009
  2. jcsd
  3. May 23, 2009 #2

    Dick

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    Re: Limits

    1) looks fine. For 2) how can you have a limit 'except for' something? Look at the path x=t, y=(-t^2). Just because the limit exists on some paths doesn't prove anything.
     
  4. May 23, 2009 #3
    Re: Limits

    yeah but the question says "please ignore the parabolic path y=-x^2" :)
     
  5. May 23, 2009 #4

    Dick

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    Re: Limits

    Since the denominator vanishes on that path, what do you think happens very close to that path?
     
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