Question

2. Prove that f is continuous at c if and only if lim f(c+h) = f(c).
h->0​

Answer 1

Answer:

This is a question from a calculus sample test, and I can't figure out how to prove it. Can I get some help from you guys?

Definition of continuity that we've learned is

limx→af(x)=f(a).

If that holds, then f is continuous at a.

The definition that we learned of a limit is:

For every ϵ>0, there exists δ>0 such that |x−a|<δ implies |f(x)−L|<ϵ.

ϵ and δ, as far as I can tell, are just variables, a is what x is approaching, and L is the limit.

Step-by-step explanation:

hope it helps