If you're seeing this message, it means we're having trouble loading external resources for Khan Academy.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Limits

8 videos
5 skills
Limits are the core tool that we build upon for calculus. Many times, a function can be undefined at a point, but we can think about what the function "approaches" as it gets closer and closer to that point (this is the "limit"). Other times, the function may be defined at a point, but it may approach a different limit. There are many, many times where the function value is the same as the limit at a point. Either way, this is a powerful tool as we start thinking about slope of a tangent line to a curve. If you have a decent background in algebra (graphing and functions in particular), you'll hopefully enjoy this tutorial!

Introduction to limits

VIDEO 11:32 minutes
Introduction to limits

Introduction to limits

VIDEO 7:37 minutes
Introduction to the intuition behind limits

Finding limits numerically

PRACTICE PROBLEMS
Find limits numerically by completing a table of values.

Limit examples (part 1)

VIDEO 8:56 minutes
Some limit exercises

Limit examples (part 2)

VIDEO 6:57 minutes
More limit examples

Limit examples (part 3)

VIDEO 9:58 minutes
More limit examples

Limit examples w/ brain malfunction on first prob (part 4)

VIDEO 15:02 minutes
3 interesting limit examples (correct answer for problem 1 is 3/16 (6/(4*8) NOT 6/(4+8))

More limits

VIDEO 13:09 minutes
More limit examples