I'm kind of lost on this problem:
The question says to state whether the limit exists, find its value and prove it:
$\lim_{(x,y) \rightarrow (1,1)} \frac{x^3-y^3}{x^2-y^2}$
So after evaluating several paths (and graphing the contour plot) I know that the limit exists and it's $\frac{3}{2}$. But when it comes to the epsilon delta proof, I'm lost.
I know I have to prove that $\forall \epsilon>0, \exists \delta=\delta(\epsilon) >0$ such that if $\ 0<\left\Vert(x,y) - (1,1)\right\Vert<\epsilon \Rightarrow \left\vert\frac{x^3-y^3}{x^2-y^2} - \frac{3}{2}\right\vert< \epsilon $
I've done other epsilon delta proofs, but the limits were of the form $\lim_{(x,y) \rightarrow (0,0)} f(x,y) = 0$ and now I don't know how to start this one or which inequalities use.