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Homework Help: Two variable limit

  1. Feb 17, 2012 #1

    1. The problem statement, all variables and given/known data

    lim (xy²)/(sin(x² + y²))
    (x,y) -> (0,0)

    3. The attempt at a solution
    I think the answer is 0, but I don't know how to get rid of the sin (x² + y²). I thought about using taylor series but I'm not sure if that works with two variables.

    Can someone help me out?
  2. jcsd
  3. Feb 17, 2012 #2
    How about switching to polar coordinates?

    r^2 = x^2 + y^2
  4. Feb 17, 2012 #3
    I suggest you read this:


    "On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.
    Last edited by a moderator: Feb 17, 2012
  5. Feb 18, 2012 #4
    I think I've solved it.
    (xy²)/(sin(x² + y²) = (x² + y²)/(sin(x² + y²) * (xy²/(x²+y²))
    And I know both these limits (1 and 0).
  6. Feb 18, 2012 #5
    Last edited: Feb 18, 2012
  7. Feb 18, 2012 #6


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    By now I see that a PF Moderator has removed your offending post.

    DivisionByZro was merely pointing out to you some of the rules for posting help on this Forum.

    It's your opinion that "... giving an answer directly is still better than no answer at all, ...", but if you continue to try to exercise that behavior in this Forum, I suspect that the Moderators will take your privileges to post.
    Last edited: Feb 18, 2012
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