Solving Epsilon-Delta Proof: Homework Statement

[appplejack]

Homework Statement

I just want to make sure I include all the steps in doing this:

lim (6x-7) = 11
x->3

Homework Equations

The Attempt at a Solution

given ε>0, we need to find a δ>0, such that 0< lx-3l < δ then 0 < l (6x-7)-11 l < ε
To prove this I need to make 0 < l (6x-7)-11 l < ε look like 0< lx-3l < δ

1. l 6x-18 l < ε = l x-3 l < ε/6

2. let δ = ε/6

3. lx-3l < δ = > lx-3l < ε/6

This still doesn't feel like I proved something but was there something that I missed?

 

[Dick]

What you have proved is that if δ=ε/6 then lx-3l<δ -> |(6x-7)-11|<ε. That should really be your last line. And, yes, that proves your limit.