1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook