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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

## Defining limits and using limit notation

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!

## Estimating limit values from graphs

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)
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!

## Estimating limit values from tables

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

#### Quiz 1

Level up on the above skills and collect up to 700 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
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!

#### Quiz 2

Level up on the above skills and collect up to 700 Mastery points

## Determining limits using algebraic manipulation

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

## Selecting procedures for determining limits

AP Calc:
LIM (BI)
,
LIM‑1 (EU)
,
LIM‑1.E (LO)
,
LIM‑1.E.1 (EK)
Practice
Strategy in finding limitsGet 3 of 4 questions to level up!

## Determining limits using the squeeze theorem

AP Calc:
LIM (BI)
,
LIM‑1 (EU)
,
LIM‑1.E (LO)
,
LIM‑1.E.2 (EK)
Practice
Squeeze theoremGet 3 of 4 questions to level up!

#### Quiz 3

Level up on the above skills and collect up to 700 Mastery points

## Exploring types of discontinuities

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!

## Defining continuity at a point

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

## Confirming continuity over an interval

AP Calc:
LIM (BI)
,
LIM‑2 (EU)
,
LIM‑2.B (LO)
,
LIM‑2.B.1 (EK)
,
LIM‑2.B.2 (EK)
Practice
Continuity over an intervalGet 3 of 4 questions to level up!
Continuity and common functionsGet 3 of 4 questions to level up!

## Removing discontinuities

AP Calc:
LIM (BI)
,
LIM‑2 (EU)
,
LIM‑2.C (LO)
,
LIM‑2.C.1 (EK)
,
LIM‑2.C.2 (EK)
Practice
Removable discontinuitiesGet 3 of 4 questions to level up!

#### Quiz 4

Level up on the above skills and collect up to 600 Mastery points

## Connecting infinite limits and vertical asymptotes

AP Calc:
LIM (BI)
,
LIM‑2 (EU)
,
LIM‑2.D (LO)
,
LIM‑2.D.1 (EK)
,
LIM‑2.D.2 (EK)
Practice
Infinite limits: graphicalGet 3 of 4 questions to level up!
Infinite limits: algebraicGet 3 of 4 questions to level up!

## 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)

#### Quiz 5

Level up on the above skills and collect up to 500 Mastery points

## Working with the intermediate value theorem

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

#### Quiz 6

Level up on the above skills and collect up to 200 Mastery points
Up next for you:

#### Unit test

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