Lecture 6 (Calculus) Continuity, Epsilon-Delta Definition of Limit, and One-Sided Limits

A function f is continuous at an interior point a precisely when:

1. A.lim_{x→a} f(x) exists, f(a) is defined, and the two are equal
2. B.lim_{x→a} f(x) exists, even if f(a) is undefined at the point
3. C.f(a) is defined, even if the limit happens to disagree with it
4. D.f is defined on every open interval surrounding the point a