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Unit: Limits and continuity

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Limits intro

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Limits introGet 3 of 4 questions to level up!

Estimating limits from graphs

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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!

Estimating limits from tables

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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!

Quiz 1

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

Formal definition of limits (epsilon-delta)

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Properties of limits

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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!

Limits by direct substitution

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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!

Quiz 2

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

Limits using algebraic manipulation

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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!

Strategy in finding limits

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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!

Squeeze theorem

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Squeeze theoremGet 3 of 4 questions to level up!

Quiz 3

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Types of discontinuities

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Types of discontinuities
(Opens a modal)

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Classify discontinuitiesGet 3 of 4 questions to level up!

Continuity at a point

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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!

Continuity over an interval

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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!

Removing discontinuities

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Removable discontinuitiesGet 3 of 4 questions to level up!

Quiz 4

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Infinite limits

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

Limits at infinity

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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!
Limits at infinity of quotients with trigGet 3 of 4 questions to level up!

Quiz 5

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Intermediate value theorem

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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!

Quiz 6

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Unit test

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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.