Continuity and Intermediate Value Theorem (Calculus 1)

This Calculus 1 video explains continuity and the Intermediate Value Theorem. We discuss what it means for a function to be continuous, both in general and at a point. We describe the different types of discontinuities (point, jump, and infinite) and classify them as removable and non-removable. We work an example using a graph to determine any discontinuity of a function, and we classify each type of discontinuity as removable or nonremovable. We also work an example using an equation without a graph, and we determine which discontinuity is a hole and which is a vertical asymptote. Finally, we talk about how the idea of continuity is important in calculus for ideas like the Intermediate Value Theorem.
0:00 Continuity and type of discontinuities
2:13 Example using a graph
4:23 Example from an equation
7:16 Criteria for continuity
8:21 Intermediate value theorem