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Epsilon Delta Proof

  1. Apr 8, 2012 #1
    1. The problem statement, all variables and given/known data
    I just want to make sure I include all the steps in doing this:

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


    2. Relevant equations



    3. 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?
     
  2. jcsd
  3. Apr 8, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    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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