$$f(x,y)=\begin{cases}{xy\over(x^2+y^2)^{5\over 2}}[1-\cos (x^2+y^2)] & (x,y)\ne(0,0)\\ k & (x,y)=(0,0)
\end{cases}$$

could anyone give me hints how to solve this one?

I tried to find $\lim \_{(x,y)\to (0,0)}f(x,y)$ but did not proceed much. Thank you.