Need help with the following proof:
prove that if lim x->c 1/f(x)= 0 then
lim x->c f(x) does not exist.I think i need to use the delta epsilon definition i am not sure how to set it up.
Proof by contradiction. Suppose that the limit exists, and that .
We know that . So for each there exists such that whenever .
Choose . Then .
But that means that whenever x is sufficiently close to c, f(x) differs from L by at least 1. That contradicts the assumption that as . (I'll leave it to you to make that last sentence rigorous in terms of epsilons and deltas.)