Use polar coordinates to find the indicated limit, if it exists. Note that is equivalent to .
A) 0
B) 1
C) -1
D) The limit is undefined.

Question

Use polar coordinates to find the indicated limit, if it exists. Note that  is equivalent to  . 
A) 0 
B) 1 
C) -1 
D) The limit is undefined.

Quizplus · Accepted Answer

Converting to polar coordinates, we have $r\cos	heta\cdot r\sin	heta=\sin	heta \cos	heta \cdot r^2$. Notice that this function is bounded by $-\frac{1}{2}r^2$ and $\frac{1}{2}r^2$, which both approach 0 as $r$ approaches 0. Therefore, by the squeeze theorem, the limit as $(x,y)$ approaches the origin (or as $r$ approaches 0) is $\boxed{	extbf{(A) }0}$.

Use Polar Coordinates to Find the Indicated Limit, If It