# Epsilon-Delta Proof

1. Dec 12, 2013

### dainty77

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

For every ε> 0, there is a δ> 0 such that 1- δ< x <1 + implies 2- ε <7-5x <2 + ε

2. Relevant equations

3. The attempt at a solution

My understanding of epsilon-delta proofs is very minimal at this point. Was hoping someone would be able to explain your thought process when attempting these kinds of proofs. Thank you!

2. Dec 12, 2013

### tiny-tim

hi dainty77!
my thought process would be to attempt the simplest possible solution first …

ie try δ = kε first (for a constant k),

then δ = kε2, then δ = k√ε and so on

3. Dec 12, 2013

### HallsofIvy

I would start with $2- \epsilon< 7- 5x$ and see that $-5- \epsilon< -5x$ so that $x< 1+ \epsilon/5$ and $x- 1< \epsilon/5$. Then turn to $7- 5x< 2+ \epsilon$, so that $-5x< -5+ \epsilon$ and $x> 1- \epsilon/5$, $x- 1> -\epsilon/5$. Now do you see what $\delta$ must be?

4. Dec 12, 2013

### dainty77

I see where you are gettiing at! Let me work on it some more. Thank you for your help!