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Math Help - lim problem with several variables

  1. #1
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    lim problem with several variables

    Prove that lim (x,y->0,0) (xy)/(x^2+2y^2) does not exist.
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Prove that lim (x,y->0,0) (xy)/(x^2+2y^2) does not exist.
    I think you want a more formal proof but if not try this:

    Assume it exists. Now approach the limit with the path x=0 and y--> 0.

    Then approach the path with x=y -->0

    You shall see the limits are not the same.
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  3. #3
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    I'm actually working on the method of proving there exist an E>0, N in the set of natural numbers, then for each k >= N implies |f(x,y)| > E.

    I just don't know how to get there.
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  4. #4
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    I had been trying to plug in the x and y differently, but I just don't really get the limits for each one. I should know how to do this, I think they taught us in Cal III.

    But any hint, please?
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  5. #5
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    Quote Originally Posted by tttcomrader View Post
    I had been trying to plug in the x and y differently, but I just don't really get the limits for each one. I should know how to do this, I think they taught us in Cal III.

    But any hint, please?
    I already did it out for thee in my first post.
    I show you different paths which work.
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