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Math Help - Continuity of a Curve

  1. #1
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    Continuity of a Curve

    I am really having a hard time understanding these concepts in multivariable calculus and just do not know where to begin.

    Here I am trying to find all the values of alpha > 0 such that the curve is continuous at the point (0,0). See the curve below...

    Any help on where to start or suggestions would be greatly appreciated!
    Thanks!
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  2. #2
    MHF Contributor arbolis's Avatar
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    You have to show for which values of \alpha the limit of f as (x,y) tends to 0 is worth 1.
    By the way I think there is a typo error. It shows " xy=0, xy \neq 0" while I believe it should be " (x,y)=(0,0), (x,y)\neq (0,0)" which is different.
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