Calculus Circus

AP Calculus practice

Limits Practice for AP Calculus

Learn and practice limits the way AP Calculus teaches them: from graphs, tables, and expressions through continuity, algebraic techniques, and limits at infinity. Calculus Circus has 19 free limits skills across 5 topics. Start a skill now, then sign in when you want the circus to remember your progress.

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Sign in to keep completions, track your progress, and make your learning visible to your teacher. Access to limits skills is free and publicly available. Full access to Calculus Circus is a flat annual fee with no automatic renewal.

What you will practice

A limit describes the value a function approaches, which may differ from the value of the function at that point. AP Calculus asks students to read that idea from more than one representation, then connect it to continuity, one-sided limits, infinite limits, and limits at infinity.

If a graph has a hole at x = 2 but the y-values approach 5 from both sides, then the limit as x approaches 2 is 5 even though f(2) is undefined.

The five limits topics

  1. Evaluating Limits From Representations

    8 skills

    Language of limits, tables, graphs, one-sided limits, function expressions, mixed representations, and the Squeeze Theorem.

    Practice evaluating limits from representations

  2. Continuity and Limit Theorems

    5 skills

    Limit properties, continuity at a point, removable discontinuities, continuity on an interval, and the Intermediate Value Theorem.

    Practice continuity and limit theorems

  3. Evaluating Limits With Algebraic Manipulation

    3 skills

    Factoring, rationalizing, and distinguishing holes from vertical asymptotes.

    Practice algebraic limit techniques

  4. Limits at Infinity and End Behavior

    2 skills

    Horizontal asymptotes and limits at infinity, including cases that need algebraic cleanup.

    Practice limits at infinity

  5. Choosing a Limit Procedure

    1 skill

    A mix of questions involving skills from throughout the unit.

    Practice choosing a limit procedure

How practice works

  • Short problem sets with instant feedback.
  • Skills arranged in a pathway.
  • Access to limits skills is free. Sign in to save your progress or join a class created by your teacher.
  • Continue into free precalculus review or differentiation practice. Teachers can see how Calculus Circus works on the About page.

Limits practice FAQ

What limit skills can I practice here?

There are 19 skills across the five topics above: graphs, tables, expressions, continuity, removable discontinuities, the Intermediate Value Theorem, algebraic manipulation, limits at infinity, and mixed procedure practice.

Do I need an account to start?

No. You can begin practicing free without an account. Sign in when you want Calculus Circus to keep your completions.

Why should I sign in?

Signing in saves progress so you can return to the next skill and, if you join a class, so a teacher can see where you are practicing.

Is this aligned with AP Calculus?

Yes — this pathway is organized around AP Calculus AB Unit 1: Limits and Continuity. Calculus Circus is teacher-led practice, not an official College Board product or endorsement.

What comes after limits?

After limits, students typically move into differentiation and then integration.

Ready to try a limits skill?

Open the limits pathway and start with the language of limits, or jump to the topic you need. Sign in if you want Calculus Circus to save your place.

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