For what values of $a$ and $b$ is the function $\frac{x^ay^b}{x^2+y^2}$ continuous at $(0,0)$? I have the function $$f(x,y)=\begin{cases}\dfrac{x^ay^b}{x^2+y^2} &(x,y)\neq(0,0)\\ 0 &(x,y)=(0,0) \end{cases}$$ I am trying to figure out what constants $a$ and $b$ will make the function continuous at $(0,0)$. I know that the limit has to be $0$ as $(x,y)\to(0,0)$ for it to be continuous. 
Using polar coordinates, I think that $a+b \geq 3$ since $x^2+y^2= r^2$ and the limit of any polar function $r^x$ with $x > 0$ as $r\to0$ is $0$. Am I on the right track or am I missing something?

$\dfrac{x^ay^b}{x^2+y^2} \overset{POLAR \, \, COORD.}{\Longrightarrow} \dfrac{r^a\cos^a(\theta) r^b\sin^b(\theta)}{r^2} \Longleftrightarrow r^{a+b-2}\cos^a(\theta)\sin^b(\theta)$ 
What happens for different values of $a+b-2$ in the limit,
$\lim_{r\rightarrow 0}r^{a+b-2}\cos^a(\theta)\sin^b(\theta)=0$ ?
