Question

Use the definition of limit (epsilon-delta) or (sequentially limit) that if \(\lim_{x\to c}f(x)=L\neq 0\) then \(\lim_{x\to c}\frac{1}{f(x)}=\frac{1}{L}\)

Answer 1

lol go look at the example I just posted in the other question, weird...

Answer 2

This falls out directly from the sequential version, but you need the bounded away from 0 property to prove that. Do you know this property?

Answer 3

if a sequence converges to a non zero number a, then there is an M such that for all n>m we have that |f(x)|> |a|/2

Answer 4

well, it needs proof as well :)