Does anybody know how to prove that in $D=\{(x,y)\in\mathbb{R}^2:x>0\wedge y>0\}$ the following is true: $ \lim\limits_{(x,y)\to(0,0)}x\cdot y\cdot\ln{(x\cdot y)}=0 $ I have to find a $\delta$ so that if $\|(x,y)\|=\sqrt{x^2+y^2}<\delta$, that $|x\cdot y\cdot\ln{(x\cdot y)}|<\epsilon$ follows. But I don't know what to do, because the $\ln$ goes to minus infinity.
Can anybody solve this? Thank you!