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# Limits and continuity

AP Calc: CHA (BI), CHA‑1 (EU), FUN (BI), FUN‑1 (EU), LIM (BI), LIM‑1 (EU), LIM‑2 (EU)

AP Calc: LIM (BI), LIM‑1 (EU), LIM‑1.A (LO), LIM‑1.A.1 (EK), LIM‑1.B (LO), LIM‑1.B.1 (EK)

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Limits introGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑1 (EU), LIM‑1.C (LO), LIM‑1.C.1 (EK), LIM‑1.C.2 (EK), LIM‑1.C.3 (EK), LIM‑1.C.4 (EK)

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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!

AP Calc: LIM (BI), LIM‑1 (EU), LIM‑1.C (LO), LIM‑1.C.5 (EK)

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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!

AP Calc: LIM (BI), LIM‑1 (EU), LIM‑1.D (LO), LIM‑1.D.1 (EK), LIM‑1.D.2 (EK)

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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!

AP Calc: LIM (BI), LIM‑1 (EU), LIM‑1.D (LO), LIM‑1.D.1 (EK), LIM‑1.D.2 (EK)

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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!

AP Calc: LIM (BI), LIM‑1 (EU), LIM‑1.E (LO), LIM‑1.E.1 (EK)

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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!

AP Calc: LIM (BI), LIM‑1 (EU), LIM‑1.E (LO), LIM‑1.E.1 (EK)

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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!

AP Calc: LIM (BI), LIM‑1 (EU), LIM‑1.E (LO), LIM‑1.E.2 (EK)

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Squeeze theoremGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑2 (EU), LIM‑2.A (LO), LIM‑2.A.1 (EK)

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Classify discontinuitiesGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑2 (EU), LIM‑2.A (LO), LIM‑2.A.2 (EK)

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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!

AP Calc: LIM (BI), LIM‑2 (EU), LIM‑2.B (LO), LIM‑2.B.1 (EK), LIM‑2.B.2 (EK)

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

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

AP Calc: LIM (BI), LIM‑2 (EU), LIM‑2.C (LO), LIM‑2.C.1 (EK), LIM‑2.C.2 (EK)

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Removable discontinuitiesGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑2 (EU), LIM‑2.D (LO), LIM‑2.D.1 (EK), LIM‑2.D.2 (EK)

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

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

AP Calc: LIM (BI), LIM‑2 (EU), LIM‑2.D (LO), LIM‑2.D.3 (EK), LIM‑2.D.4 (EK), LIM‑2.D.5 (EK)

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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!

AP Calc: FUN (BI), FUN‑1 (EU), FUN‑1.A (LO), FUN‑1.A.1 (EK)

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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!

### 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.AP® is a registered trademark of the College Board, which has not reviewed this resource.