F:[a,infinity)->R is continuous with f(x) > 0 for all x in [a,infinity),

1. Dec 1, 2008

sdff22

f:[a,infinity)-->R is continuous with f(x) > 0 for all x in [a,infinity),...

Suppose "a" belongs to R, and f:[a,infinity)-->R is continuous with f(x) > 0 for all x in [a,infinity) and limf(x)=1 (as x goes to infinity). Prove that there exists r>0 such that f(x)>r for all x in [a,infinity).

2. Dec 2, 2008

morphism

Re: f:[a,infinity)-->R is continuous with f(x) > 0 for all x in [a,infinity),...

And what have you tried?

3. Dec 2, 2008

sdff22

Re: f:[a,infinity)-->R is continuous with f(x) > 0 for all x in [a,infinity),...

I found it!

Last edited: Dec 2, 2008