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# Unit: Limits and continuity

AP Calc:

CHA (BI)

, CHA‑1 (EU)

, FUN (BI)

, FUN‑1 (EU)

, LIM (BI)

, LIM‑1 (EU)

, LIM‑2 (EU)

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### 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 Calc:

LIM (BI)

, LIM‑1 (EU)

, LIM‑1.A (LO)

, LIM‑1.A.1 (EK)

, LIM‑1.B (LO)

, LIM‑1.B.1 (EK)

### Practice

- 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)

### 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!

AP Calc:

LIM (BI)

, LIM‑1 (EU)

, LIM‑1.C (LO)

, LIM‑1.C.5 (EK)

### 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!

Level up on the above skills and collect up to 560 Mastery points

AP Calc:

LIM (BI)

, LIM‑1 (EU)

, LIM‑1.D (LO)

, LIM‑1.D.1 (EK)

, LIM‑1.D.2 (EK)

### 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!

AP Calc:

LIM (BI)

, LIM‑1 (EU)

, LIM‑1.D (LO)

, LIM‑1.D.1 (EK)

### 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!

Level up on the above skills and collect up to 560 Mastery points

AP Calc:

LIM (BI)

, LIM‑1 (EU)

, LIM‑1.E (LO)

, LIM‑1.E.1 (EK)

### 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!

AP Calc:

LIM (BI)

, LIM‑1 (EU)

, LIM‑1.E (LO)

, LIM‑1.E.1 (EK)

### 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!

AP Calc:

LIM (BI)

, LIM‑1 (EU)

, LIM‑1.E (LO)

, LIM‑1.E.2 (EK)

### Learn

### Practice

- Squeeze theoremGet 3 of 4 questions to level up!

Level up on the above skills and collect up to 560 Mastery points

AP Calc:

LIM (BI)

, LIM‑2 (EU)

, LIM‑2.A (LO)

, LIM‑2.A.1 (EK)

### Practice

- 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)

### 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!

AP Calc:

LIM (BI)

, LIM‑2 (EU)

, LIM‑2.B (LO)

, LIM‑2.B.1 (EK)

, LIM‑2.B.2 (EK)

### Learn

### Practice

- 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)

### Learn

### Practice

- Removable discontinuitiesGet 3 of 4 questions to level up!

Level up on the above skills and collect up to 480 Mastery points

AP Calc:

LIM (BI)

, LIM‑2 (EU)

, LIM‑2.D (LO)

, LIM‑2.D.1 (EK)

, LIM‑2.D.2 (EK)

### Learn

### Practice

- 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)

### 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!

Level up on the above skills and collect up to 400 Mastery points

AP Calc:

FUN (BI)

, FUN‑1 (EU)

, FUN‑1.A (LO)

, FUN‑1.A.1 (EK)

### 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!

Level up on the above skills and collect up to 160 Mastery points

Up next for you:

Level up on all the skills in this unit and collect up to 3400 Mastery points!#### Unit test

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