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Thread: Continuity of a Curve

  1. #1
    Junior Member
    May 2009

    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!
    Attached Thumbnails Attached Thumbnails Continuity of a Curve-picture2.png  
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  2. #2
    MHF Contributor arbolis's Avatar
    Apr 2008
    You have to show for which values of $\displaystyle \alpha$ the limit of $\displaystyle f$ as $\displaystyle (x,y)$ tends to $\displaystyle 0$ is worth $\displaystyle 1$.
    By the way I think there is a typo error. It shows "$\displaystyle xy=0, xy \neq 0$" while I believe it should be "$\displaystyle (x,y)=(0,0), (x,y)\neq (0,0)$" which is different.
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