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Math Help - [SOLVED] Proving a multi variable limit (using epsilon-delta)

  1. #1
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    [SOLVED] Proving a multi variable limit (using epsilon-delta)

    Hey everyone, long time lurker first time poster. Unfortunately my first post is a request for help!

    Before you ask, yes I've read the sticky on this topic :P However, this is a multi-variable question and I'm really struggling with it. I have to prove this limit using the definition:


    I know the definition and inequalities I have to work with:

    epsilon > 0, delta > 0

    0 < sqrt(x^2 + y^2) < delta
    | f(x) - 0 | < epsilon (1)

    I've attempted to play around with the equation (1), however it seems that I get a delta that is extremely complex. Is there some simplification that I'm overlooking? I noticed, from the sticky, that I can't have delta in terms of x or y. How can I get passed this?

    Thank you very much (I like this emoticon)
    Last edited by MatHematicalprooF; March 22nd 2010 at 11:48 PM.
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  2. #2
    MHF Contributor chisigma's Avatar
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    Try to use polar coordinates, so that is ...

    x= \rho\cdot \cos \theta

    y= \rho\cdot \sin \theta (1)

    Kind regards

    \chi \sigma
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  3. #3
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    Quote Originally Posted by chisigma View Post
    Try to use polar coordinates, so that is ...

    x= \rho\cdot \cos \theta

    y= \rho\cdot \sin \theta (1)

    Kind regards

    \chi \sigma
    Thanks for the advice, but I think this one needs to be solved without the use of polar coordinates. Any ideas?
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  4. #4
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    Does noone have even an inkling on this one? Would really help clarify things for me and for the exam.
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