<s>[INST] Find $\lim_{(x,y)\to(0,0)}\frac{1-\cos(x^2+y^2)}{(x^2+y^2)x^2y^2}$ 
$$\lim_{(x,y)\to(0,0)}\frac{1-\cos(x^2+y^2)}{(x^2+y^2)x^2y^2}$$

how should I approach this?
$$\lim_{(x,y)\to(0,0)}\frac{1-\cos(x^2+y^2)}{(x^2+y^2)}=0$$ but I still have $$\lim_{(x,y)\to(0,0)}\frac{1}{x^2y^2}$$
The answer says there is no limit
 [/INST] Hint :
$$\lim_{(x,y)\to (0,0)}\frac{1-\cos(x^2+y^2)}{(x^2+y^2)}=\lim_{(x,y)\to (0,0)}\frac{2\sin^2\left (\frac{x^2+y^2}{2}\right)}{x^2+y^2} = \lim_{(x,y)\to (0,0)}\frac{x^2+y^2}{2}$$
</s>