# Limit theorems

1. Oct 31, 2007

### javi438

1. The problem statement, all variables and given/known data

prove that if $$lim_{x\rightarrow c}$$ f(x) = L, then there are positive numbers A and B such that if 0 < |x-c|< A, then |f(x)|< B

2. The attempt at a solution

i know it's something to do with the limit definition, where for $$\epsilon$$ > 0, there exists a $$\delta$$ > 0 such that 0 < |x-c| < $$\delta$$, then |f(x)-L| < $$\epsilon$$

i don't know how to get my way through proving it!

2. Oct 31, 2007

### mjsd

yes, precisely, use the definition of a limit. Your task is to identify what delta and epsilon will make it works

3. Oct 31, 2007

### Dick

Pick a B>L. Pick epsilon=B-L. Use the definition of limit to find a delta. Set A=delta.