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Homework Help: Epsilon-Delta proof of zero?

  1. Feb 24, 2012 #1
    Epsilon-Delta proof of zero??

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

    Write an epsilon delta proof for the limx[itex]\rightarrow[/itex]2 0 = 0.

    3. The attempt at a solution

    This is for my discrete math class. I know how to do limit proofs with a variable, like x or x2, but it seems that this is obvious that the limit approaching zero is zero. It is so easy, that it is hard for me to use epsilon and delta to prove. I don't know really where to start for this one. I would appreciate some hints and help!
  2. jcsd
  3. Feb 24, 2012 #2


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    Re: Epsilon-Delta proof of zero??

    It might help to call f(x) = 0. Write down the definition as you would with f(x) and L and replace f(x) and L by 0.
  4. Feb 24, 2012 #3
    Re: Epsilon-Delta proof of zero??

    Start by choosing an epsilon maybe let epsilon equal something really close to 0 like 0.2

    and assume that x-2< alpha . so that you can so that 0<ε .
  5. Feb 24, 2012 #4


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    Re: Epsilon-Delta proof of zero??

    hint: the proof is eactly the same if you replace 0 by c, where c is any constant. that is, if you replace the function f(x) = 0 with g(x) = c, the same argument works for both (the "delta" is really easy to find, for any "epsilon").
  6. Mar 1, 2012 #5
    Re: Epsilon-Delta proof of zero??

    Thank you guys for all of your help! I know I am really late responding back, but all of the feedback really helped!
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