Let $f(x,y)=\begin{cases}\dfrac{\mathrm{e}^{xy}-1}{x+y} & x\not=-y, \\ 0 & x=-y \end{cases}$ be a two variable function on $\mathbb{R}^2$.
How can I give a proof (Only by definition $\varepsilon , \delta$) for $\displaystyle\lim_{(x,y)\to(0,0)}f(x,y)=0$?