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Unit: Limits and continuity

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About this unit

In this unit, we'll explore the concepts of limits and continuity. We'll start by learning the notation used to express limits, and then we'll practice estimating limits from graphs and tables. We'll also work on determining limits algebraically. From there, we'll move on to understanding continuity and discontinuity, and how the intermediate value theorem can help us reason about functions in these contexts.

Defining limits and using limit notation

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Estimating limit values from graphs

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Practice

Estimating limit values from tables

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Practice

Quiz 1

Identify your areas for growth in these lessons:
Defining limits and using limit notation
Estimating limit values from graphs
Estimating limit values from tables

Determining limits using algebraic properties of limits: limit properties

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Practice

Determining limits using algebraic properties of limits: direct substitution

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Practice

Quiz 2

Identify your areas for growth in these lessons:
Determining limits using algebraic properties of limits: limit properties
Determining limits using algebraic properties of limits: direct substitution

Determining limits using algebraic manipulation

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Practice

Selecting procedures for determining limits

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Practice

Determining limits using the squeeze theorem

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Practice

Quiz 3

Identify your areas for growth in these lessons:
Determining limits using algebraic manipulation
Selecting procedures for determining limits
Determining limits using the squeeze theorem

Exploring types of discontinuities

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Practice

Defining continuity at a point

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Practice

Confirming continuity over an interval

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Removing discontinuities

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Practice

Quiz 4

Identify your areas for growth in these lessons:
Exploring types of discontinuities
Defining continuity at a point
Confirming continuity over an interval
Removing discontinuities

Connecting infinite limits and vertical asymptotes

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Practice

Connecting limits at infinity and horizontal asymptotes

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Practice

Quiz 5

Identify your areas for growth in these lessons:
Connecting infinite limits and vertical asymptotes
Connecting limits at infinity and horizontal asymptotes

Working with the intermediate value theorem

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Practice

Quiz 6

Identify your areas for growth in this lesson:
Working with the intermediate value theorem

Unit test

Test your understanding of Limits and continuity with these 30 questions.