I'm trying to solve the following limit:
$\lim_{(x,y)\to(2,1)} \frac{xy(x-2)^{5/3}(y^2-1)^{2/3}}{|y|(x-2)^2+x^2(y-1)^2}$
I already know that if it exists the limit is $0$ since approaching $y \to 1$ while fixing $x=2$ yields $0$; but I'm unable to give a $\delta$-$\epsilon$ proof for this. Any ideas?