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Finding The Limit Of A 3D Function

  1. Mar 3, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the limit as X, and Y both approach 0 of (X2Y)/(X2 + Y4)


    2. Relevant equations
    The equation from above.


    3. The attempt at a solution
    I have been doing the technique of approaching from different lines such as y = x, or x = y,
    x = 0, and y = 0. All of them give me a limit of zero, so that will not do. I graphed the function online, and it appears as if the function does have a limit of zero. How would I prove this? I think I need to do something with polar coordinates, but I am not sure how to do that.
     
  2. jcsd
  3. Mar 3, 2013 #2
    EDIT:
    I'd go with SammyS's
     
  4. Mar 3, 2013 #3

    SammyS

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    Yes. Change to polar coordinates.

    [itex]x=r\cos(\theta)[/itex]

    [itex]y=r\sin(\theta)[/itex]
     
    Last edited: Mar 3, 2013
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