prove limit doesn't exist $\lim\limits_{(x,y)\to(0,0)} \frac{1-\cos(x^2+y^2)}{(x^2+y^2)x^2y^2}$ I need to show that limit doesn't exist:
$\lim\limits_{(x,y)\to(0,0)} \frac{1-\cos(x^2+y^2)}{(x^2+y^2)x^2y^2}$
How can I show it? 

Polar coordinates:
$\dfrac{1-\cos (r^2)}{r^6 \cos^2 t \sin^2 t}= 4\dfrac{1- \cos (r^2)}{r^6 \sin^2(2t)}.$
$2t \not = kπ$, $k=0,1,2,3$.
Fix $t$, and consider
$A \dfrac{1-\cos (r^2)}{r^6}$, with $A=\dfrac{4}{\sin^2(2t)}>0$.
$A \lim_{r \rightarrow 0}\dfrac{1-\cos (r^2)}{r^6}=\infty.$
