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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- Feb 26th 2006, 11:49 AMrsmith88[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. - Feb 26th 2006, 02:57 PMtopsquarkQuote:

Originally Posted by**rsmith88**

$\displaystyle x=rcos\theta$

$\displaystyle y=rsin\theta$

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

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

-Dan