1. Mar 22, 2008

Bigo75

1. The problem statement, all variables and given/known data
Prove: If the Lim as x goes to a of F(x)=infinity, then lim as x goes to a of 1/F(x)=0

2. Relevant equations

We have only gone over limits and continuity using delta epsilion proofs.

2. Mar 22, 2008

ircdan

what have you tried? this is straightforward in the sense that it follows from the definitions

show us what you have tried

3. Mar 22, 2008

Bigo75

Since the limit is equal to infinity I took an M greater than zero such that X>M implies |F(x)-L| is less than epsilon but I get confused with the one over F(x)=0

4. Mar 22, 2008

Bigo75

am I on the right track? I am really confused!

5. Mar 22, 2008

ircdan

this is wrong, lim x->a F(x) = inf means for all M > 0 there is a d > 0 s.t. |x-a| < d implies |F(x)| > M. (you can actually drop the absolute value sign here but i'll leave it)

6. Mar 22, 2008

Bigo75

ok I understand this definition but how does that help me get lim as x goes to a of 1/f(x)=0? This definition will help me prove another one I was having trouble with. thank you.