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Math Help - [SOLVED] Limits with polar corrdinates

  1. #1
    rsmith88
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    [SOLVED] Limits with polar corrdinates

    How would you use polar coordinates to find the limit as (x,y) -> (0,0) of (x^2*y^2)/(x^2+y^2)?

    Thanks.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by rsmith88
    How would you use polar coordinates to find the limit as (x,y) -> (0,0) of (x^2*y^2)/(x^2+y^2)?

    Thanks.
    Start by converting your expression into polar coordinates:
    x=rcos\theta
    y=rsin\theta

    So \frac{x^2y^2}{x^2+y^2}=\frac{r^4sin^2\theta cos^2\theta}{r^2}=r^2sin^2\theta cos^2\theta.

    r goes to 0 as (x,y) goes to (0,0) so the limit should be obvious in this form.

    -Dan
    Last edited by topsquark; February 26th 2006 at 02:59 PM.
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