Show that the function f is continuous at (0,0) where
$f(x,y) = e^ \frac{-|x-y|}{x^2-2xy+y^2}$, where (x,y)$\not=$(x,x) and f(x,x)=0 using $\epsilon-\delta$ method. I know $e^x$ is continuous but i'm stuck at proving $|e^ \frac{-|x-y|}{x^2-2xy+y^2}| < \epsilon$ whenever $0<\sqrt{x^2+y^2}<\delta$.
HINT
Note that
$$f(x,y) = e^ \frac{-|x-y|}{x^2-2xy+y^2}=f(x,y) = e^ \frac{-|x-y|}{(x-y)^2}= e^ {-\frac1{|x-y|}}$$
than let $t=|x-y|\to 0^+$ and prove that $e^{-1/t} \to 0$.