# Prove Limits Using Epsilon-delta Definition...5

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

1. ### 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? nycmathguy, May 8, 2022
2. ### MathLover1

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24. 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 .

MathLover1, May 9, 2022
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