If you're seeing this message, it means we're having trouble loading external resources on our website.

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

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Main content

Unit: Limits and continuity

0

Possible mastery points

Limits intro

Learn

Practice

Limits introGet 3 of 4 questions to level up!

Estimating limits from graphs

Learn

Practice

Estimating limit values from graphsGet 3 of 4 questions to level up!
One-sided limits from graphsGet 3 of 4 questions to level up!
Connecting limits and graphical behaviorGet 3 of 4 questions to level up!

Estimating limits from tables

Learn

Practice

Creating tables for approximating limitsGet 3 of 4 questions to level up!
Estimating limits from tablesGet 3 of 4 questions to level up!
One-sided limits from tablesGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 700 Mastery points

Formal definition of limits (epsilon-delta)

Learn

Properties of limits

Learn

Practice

Limits of combined functions: sums and differencesGet 3 of 4 questions to level up!
Limits of combined functions: products and quotientsGet 3 of 4 questions to level up!
Limits of composite functionsGet 3 of 4 questions to level up!

Limits by direct substitution

Learn

Practice

Limits by direct substitutionGet 3 of 4 questions to level up!
Direct substitution with limits that don't existGet 3 of 4 questions to level up!
Limits of trigonometric functionsGet 3 of 4 questions to level up!
Limits of piecewise functionsGet 3 of 4 questions to level up!

Quiz 2

Level up on the above skills and collect up to 700 Mastery points

Limits using algebraic manipulation

Learn

Practice

Limits by factoringGet 3 of 4 questions to level up!
Limits using conjugatesGet 3 of 4 questions to level up!
Limits using trig identitiesGet 3 of 4 questions to level up!

Strategy in finding limits

Learn

Practice

Conclusions from direct substitution (finding limits)Get 3 of 4 questions to level up!
Next steps after indeterminate form (finding limits)Get 3 of 4 questions to level up!
Strategy in finding limitsGet 3 of 4 questions to level up!

Squeeze theorem

Learn

Practice

Squeeze theoremGet 3 of 4 questions to level up!

Quiz 3

Level up on the above skills and collect up to 700 Mastery points

Types of discontinuities

Learn

Types of discontinuities
(Opens a modal)

Practice

Classify discontinuitiesGet 3 of 4 questions to level up!

Continuity at a point

Learn

Practice

Continuity at a point (graphical)Get 3 of 4 questions to level up!
Continuity at a point (algebraic)Get 3 of 4 questions to level up!

Continuity over an interval

Learn

Practice

Continuity over an intervalGet 3 of 4 questions to level up!
Continuity and common functionsGet 3 of 4 questions to level up!

Removing discontinuities

Learn

Practice

Removable discontinuitiesGet 3 of 4 questions to level up!

Quiz 4

Level up on the above skills and collect up to 600 Mastery points

Infinite limits

Learn

Practice

Infinite limits: graphicalGet 3 of 4 questions to level up!
Infinite limits: algebraicGet 3 of 4 questions to level up!

Limits at infinity

Learn

Practice

Limits at infinity: graphicalGet 3 of 4 questions to level up!
Limits at infinity of quotientsGet 5 of 7 questions to level up!
Limits at infinity of quotients with square rootsGet 3 of 4 questions to level up!
Limits at infinity of quotients with trigGet 3 of 4 questions to level up!

Quiz 5

Level up on the above skills and collect up to 600 Mastery points

Intermediate value theorem

Learn

Practice

Using the intermediate value theoremGet 3 of 4 questions to level up!
Justification with the intermediate value theoremGet 3 of 4 questions to level up!

Quiz 6

Level up on the above skills and collect up to 200 Mastery points

Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 3500 Mastery points!

About this unit

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.