Compute $\lim_{ (x,y)\to (0,0)}\frac{x^ny^m}{x^2+y^2}$ 
Compute $\displaystyle\lim_{ (x,y)\to (0,0)}\dfrac{x^ny^m}{x^2+y^2}$

Determine with the conditions on $n$ and $m$ for which this limit exists and conditions for which this limit does not exist. 
I found that when $x$ approaches $0$ the limit approaches $0$ and as $y$ approaches $0$ the limit also approaches $0$. As $x$ and $y$ approaches $x$ it seems like there are no conditions for $m$ and $n$ which will make the limit exist. 

Hint: To get some insight into this expression, consider polar coordinates with $x = r\cos\theta$, $y = r\sin\theta$. Then
$$\frac{x^ny^m}{x^2 + y^2} = \frac{r^{m+n}\cos^n\theta\sin^m\theta}{r^2(\cos^2\theta + \sin^2\theta)} = \ ...$$
