I'm a relative novice to epsilon-delta proofs. My professor assigned this practice problem and I'm having terrible trouble understanding the answer he gave. Moreover, I can't find a good account for a general strategy for how to do these sorts of proofs. I understand the epsilon delta definition, I understand what I'm *supposed* to do, but I need advice on strategy.

The actual problem.

Prove that the limit

$$ \lim\_{x \rightarrow 2} \frac{x^3}{x-2} $$
does not exist.

So far I'm pretty stumped; I know I need to show that there is some $\epsilon$ st. such that x being arbitrarily close to 2 does not guarantee that f(x) is within epsilon of L, but that's all I've got.

Thanks.