# Thread: [SOLVED] Limits with polar corrdinates

1. ## [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.

2. 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