- #1

quietrain

- 655

- 2

## Homework Statement

find limit if exist, or not then why

f(x,y) = xy / sqrt(x

^{2}+y

^{2})

as (x,y) --> (0,0)

## The Attempt at a Solution

can i change to polar coordinates

x=rcost

y=rsint

so f(r,t) = rcostsint

so as x,y tends to 0, r t will tend to 0 too?but cos(t) at 0 gives me 1?

so i can only rely on r?

so i say since r tends to 0 , rcostsint gives 0 , so the limit exist and is 0? but what about the variable t?

thanks!