Prove Limits Using Epsilon-delta Definition...5

Discussion in 'Calculus' started by nycmathguy, May 8, 2022.

  1. nycmathguy

    nycmathguy

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    Calculus
    Section 2.4

    I don't need to know this stuff to succeed in Calculus. However, I would like to have your math work reply file away as future study notes and/or reference notes. How about working out 24?

    Screenshot_20220507-174246_Samsung Notes.jpg
     
    nycmathguy, May 8, 2022
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  2. nycmathguy

    MathLover1

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    24. upload_2022-5-8_18-58-14.gif

    Proof:
    Let ϵ> 0 be given, now we need to choose a δ > 0 such that for
    any x, that satisfies |x − a| < δ, the condition |f(x) − c| < ϵ is satisfied.

    Well this one is an easy one to prove because f(x) = c for any x.
    So |f(x) − c| = |c − c| = 0.

    So there is no game here at all, because for any given ϵ> 0, it doesn’t matter what δ I choose, for any x, in any (a−δ, a+δ) interval corresponding |f(x) − c| = |c − c| = 0 < ϵ.

    So in this case upload_2022-5-8_18-57-21.gif .
     
    MathLover1, May 9, 2022
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    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    I yearn for the day this makes sense to me. Your reply is notgoing to waste. The goal is to study your reasoning to prove the limit. This I will do all in good time.
     
    nycmathguy, May 9, 2022
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