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Continuity of g(x,y) = (xy)^1/3

  1. Sep 9, 2011 #1
    1. The problem statement, all variables and given/known data

    Show if the function g(x,y) = (xy)1/3 is continuous at the point (0,0)

    2. Relevant equations



    3. The attempt at a solution

    I'm a bit confused. When I take the limit as (x,y)->(0,0) I get that L = 0, and the function is equal to 0 at (0,0), but when I plot the function in maple, it seems as if there is a discontinuity along the line x =0 and y = 0. I am ultimately trying to show if the function is differentiable at (0,0). Any help?
     
  2. jcsd
  3. Sep 9, 2011 #2

    micromass

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    Well, your calculations are correct. The function is continuous.

    Many function graphers cannot handle the cube root well, which is likely the reason that it doesn't show up nice in maple.
     
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