Limits and Continuity: Free Course

About this course

A limit describes nearby behavior, which may differ from a function’s value at a point. This course develops that distinction through graphs, tables, algebra, continuity and formal reasoning. Study the complete public source playlist from Khan Academy in English, with all 54 recordings available in the on-site classroom. Lessons retain their original titles and source order, including worked examples, introductions and repeated entries.

Course at a glance

What you’ll learn

• Estimate and compare one-sided limits.
• Choose algebraic or theorem-based limit arguments.
• Check continuity and classify discontinuities.
• Interpret asymptotic behavior and the formal limit definition.

Skills you’ll gain

• Limits
• Continuity
• Asymptotes
• Mathematical justification

Course Overview

Graphical and tabular examples establish one-sided and two-sided limits before limit properties are applied to combined and composite functions. Direct substitution is useful when justified, while factoring, rationalizing and trigonometric identities address examples where substitution alone is inconclusive. The squeeze theorem provides a different kind of argument. Continuity is then checked at points and across intervals, including cases where a definition must be adjusted to remove a discontinuity. Infinite limits and limits at infinity connect local asymptotic behavior with end behavior. The intermediate value theorem introduces conclusions that depend on continuity hypotheses. Finally, the epsilon–delta sequence moves from intuition to a formal definition. Keep these ideas distinct: an undefined function value, a nonexistent limit and an unbounded limit are not interchangeable descriptions.

How to study the course

• Videos 1–13: this part of the source list includes “Introduction to limits” through “Limits of composite functions”. Identify the function, variable and conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 14–27: this part of the source list includes “Limits by direct substitution” through “Types of discontinuities”. Connect the method to the meaning of the problem. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 28–40: this part of the source list includes “Continuity at a point” through “Analyzing unbounded limits: mixed function”. Rework a demonstration with a changed parameter. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 41–54: this part of the source list includes “Introduction to limits at infinity” through “Formal definition of limits Part 4: using the definition”. Check the result and explain its interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits learners with algebra and trigonometry preparation who want the specific calculus topic in the title. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort manipulating algebraic expressions and interpreting functions is important. Review the prerequisite calculus stated by a lesson before using an advanced technique.

Put the lessons into practice

Build a small comparison sheet containing a removable discontinuity, a jump and an asymptote. For each, record the function value when defined and the left- and right-hand behavior. Solve one limit by algebraic simplification and another using a bound or theorem from the course. State the assumptions needed before applying the intermediate value theorem to a chosen interval.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.