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

[pergradus]

Homework Statement

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

Homework Equations

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?

 

[micromass]

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.