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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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#### 0

Possible 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.

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)

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)

## Estimating limit values from tables

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

### Practice

#### Quiz 1

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)

## Determining limits using algebraic properties of limits: direct substitution

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

### Practice

#### Quiz 2

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)

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

## Determining limits using the squeeze theorem

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

### Practice

#### Quiz 3

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)

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

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

## Removing discontinuities

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

### Practice

#### Quiz 4

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)

## Connecting limits at infinity and horizontal asymptotes

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)

### Practice

#### Quiz 5

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

## Working with the intermediate value theorem

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

### Practice

#### Quiz 6

Level up on the above skills and collect up to 160 Mastery points
Up next for you:

#### Unit test

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