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Finding delta in terms of epsilon-delta definition

  1. Jun 24, 2014 #1
    1. The problem statement, all variables and given/known data

    If f(x) = 3x+1 en assume δ > 0. Assume ε>0.
    Give a δ > 0 with the following property :

    |x-1|< δ => |f(x) - f(1)| < ε

    2. Relevant equations



    3. The attempt at a solution


    |f(x) - f(1)| < ε
    <=> |3x+1-(3*1+1)| < ε
    <=> |3x-3| < ε
    <=> |x-1| < ε/3


    |x-1| < δ
    |x-1| < ε/3


    => δ=ε/3>0


    What am I doing wrong?

    Thanks in advance!
     
  2. jcsd
  3. Jun 24, 2014 #2

    pasmith

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    Homework Helper

    Nothing. Your solution is correct.
     
  4. Jun 24, 2014 #3
    Oh ok. I'm learning this on my own so I assumed it had to be wrong. Self confidence is important in math too apparently..
    Anyway, thanks for checking it! :)
     
  5. Jun 24, 2014 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Then it would have been better to ask "Is this correct" rather than "What am I doing wrong"! You are not going to do very well assuming that you cannot do the work.
     
  6. Jun 24, 2014 #5

    Sorry, you're right. I'm just struggling with a lot in life and I think my lack of self confidence leaked into doing math. Sorry again.
     
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