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: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