Limits and continuity

This course is a part of AP®︎ Calculus AB, a 10-course Topic series from Khan Academy.

Limits describe the behavior of a function as we approach a certain input value, regardless of the function's actual value there. Continuity requires that the behavior of a function around a point matches the function's value at that point. These simple yet powerful ideas play a major role in all of calculus.

This course contains 16 segments:

Defining limits and using limit notation

Estimating limit values from graphs

Estimating limit values from tables

Determining limits using algebraic properties of limits: limit properties

Determining limits using algebraic properties of limits: direct substitution

Determining limits using algebraic manipulation

Selecting procedures for determining limits

Determining limits using the squeeze theorem

Exploring types of discontinuities

Defining continuity at a point

Confirming continuity over an interval

Removing discontinuities

Connecting infinite limits and vertical asymptotes

Connecting limits at infinity and horizontal asymptotes

Working with the intermediate value theorem

Optional videos

Some things are not explicitly required by the AP Calculus AB course, but many teachers cover them and we also find them useful. We've gathered those optional videos here for your convenience.