Use polar coordinates to find the limit.[Hint: Let and note that implies
A) 1
B) 0
C) 2
E)limit does not exist

Question

Use polar coordinates to find the limit.[Hint: Let  and note that  implies  
A) 1 
B) 0 
C) 2 
E)limit does not exist

Quizplus · Accepted Answer

Converting to polar coordinates, we have $x=r\cos	heta$ and $y=r\sin	heta$. Thus, $\frac{x^2y}{x^2+y^2}=r^2\cos^2	heta\sin	heta/(r^2)=\cos^2	heta\sin	heta$. We now note that this expression is nonnegative and bounded above by $1/\sqrt{2}$, which is achieved when $	heta=\pi/4$ or $3\pi/4$. Hence, by the squeeze theorem, the limit is $\boxed{0}$.

Use Polar Coordinates to Find the Limit