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Epsilon Delta Proof

  • Thread starter appplejack
  • Start date
  • #1
43
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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?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
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.
 

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