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Math Help - Urgent! Multivariable Limit Problem!

  1. #1
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    Urgent! Multivariable Limit Problem!

    Can someone please help me find this limit? I have a test tomorrow.

    lim as (x,y) approaches (0,0) of (x+y)/(x-xy+y)

    Thanks for your help!
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  2. #2
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    Quote Originally Posted by 1.2.3.pi.4 View Post
    Can someone please help me find this limit? I have a test tomorrow.

    lim as (x,y) approaches (0,0) of (x+y)/(x-xy+y)

    Thanks for your help!
    Does the limit exist? If so, then it's value is the same regardless of how (0, 0) is approached. eg. Approach along the line y = x ....
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  3. #3
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    However, all paths that I have a value of 1. How can I prove that the lim is in fact 1? Is there any inequality that i can use to solve this limit for the squeeze theorem?
    Last edited by 1.2.3.pi.4; December 14th 2009 at 07:27 PM.
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  4. #4
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    Quote Originally Posted by 1.2.3.pi.4 View Post
    However, all paths that I have a value of 1. How can I prove that the lim is in fact 1? Is there any inequality that i can use to solve this limit for the squeeze theorem?
    You can use polar coordinates to show that the limit exists and is equal to 1 (the limit as r --> 0 is independent of theta).
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