Limit of a the function $f(x,y)=x \log(y-x)$ at $(0,0)$ Let $D=\{(x,y) \in \mathbb{R}^2 :y>x\}$ and $f:D\to \mathbb{R}$ with $f(x,y)=x \log(y-x)$.
Does the limit $\lim_{(x,y)\rightarrow(0,0)} f(x,y)$ exist?
I consider $E=\{(-t,t) : t>0\}$ so $f\vert_{E}=-t\log(2t) \to 0 $ for $t \to 0$. So the limit is null?

Hint: Approach $(0,0)$ along a path with $x$ positive and $y=x+e^{-1/x}$. 
