0
$\begingroup$

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 $\displaystyle\lim_{(x,y)\to(0,0)}f(x,y)=0$?

  • 0
    Your expression is undefined in certain points arbitrarily close to $(0,0)$. Therefore the limit cannot exist.2012-12-28
  • 0
    Sorry, You are right. I fixed the problem. Now, Please help me.2012-12-28
  • 0
    In realy, I received to the problem through this excecise: prove that $h(x,y)=\mathrm{e}^{xy}$ is differentiable. (Only by the following definition)2012-12-28

2 Answers 2