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. 

Try using polar coordinates ($x=r \cos(\theta), y=r\sin(\theta)$, then make $r$ tend to 0).
Try also studying what happens along a straight line (do the substitution $x=ay$)
