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Ch 4: Overview of Limits of Functions

About This Chapter

Using this chapter, grasp an understanding of the overview of limits of functions. Become familiar with properties of limits, squeeze theorem, and finding asymptotes using limits.

Overview of Limits of Functions - Chapter Summary

Within this chapter, our experts explain the overview of limits and functions. Become familiar with how to use a graph to define limits, properties of limits, and determining if a limit does not exist. Once you finish this chapter, you should be able to:

  • Understand limits using notation
  • Analyze graphs to define limits
  • Become familiar with one-sided limits and continuity
  • Define infinite limit and squeeze theorem
  • Analyze the properties of limits
  • Understand the limits of functions and how to determine if a limit does not exist
  • Define asymptotes and infinity using graphs
  • Detect asymptotes using limits
  • Understand how to compare relative magnitudes of functions

Use the timeline tags within the videos to review a concept you are unfamiliar with. The Dashboard allows you to track your progress and see the overview of the course. Once you have completed a lesson, make sure to complete the self-assessment quiz to make sure you fully understand each concept.

12 Lessons in Chapter 4: Overview of Limits of Functions
Test your knowledge with a 30-question chapter practice test
Understanding Limits: Using Notation

1. Understanding Limits: Using Notation

Limits are the values that a function approaches as the variable approaches a number. Discover the mathematical notation of limits, how to find them, and how to write them as equations.

Symbolic Logic: Definition & Examples

2. Symbolic Logic: Definition & Examples

In this lesson, we'll cover the definition of symbolic logic, introduce some of the common symbols used, and work out some truth tables for a few logical expressions.

Using a Graph to Define Limits

3. Using a Graph to Define Limits

A graph can be sued to define limits of all kinds. Find examples of using a graph to define limits, including speed limits, pendulum limits, and other limits in mathematics.

One-Sided Limits and Continuity

4. One-Sided Limits and Continuity

Learn about the relationship between one-sided limits and continuity. Begin by looking at what makes a path continuous or discontinuous, how a one-sided limit is defined, and how the two concepts are related.

Infinite Limit: Definition & Rules

5. Infinite Limit: Definition & Rules

In this lesson, we learn how to interpret limits whose values are unbounded, or infinite. We'll look at a few examples to show you how to compute these infinite limits.

How to Determine the Limits of Functions

6. How to Determine the Limits of Functions

To find the limit of a continuous function, use substitution. Learn more about this rule and more about the properties of limits and how to determine the limits of functions using examples.

Understanding the Properties of Limits

7. Understanding the Properties of Limits

The properties of limits can be one-sided or two-sided. Understand the reasons why that is true, and learn more about addition and subtraction properties, product properties, and division properties.

Squeeze Theorem: Definition and Examples

8. Squeeze Theorem: Definition and Examples

The squeeze theorem is used to find the limits of functions. Explore a definition of the squeeze theorem and find examples of how it is expressed through mathematical equations.

Graphs and Limits: Defining Asymptotes and Infinity

9. Graphs and Limits: Defining Asymptotes and Infinity

Understand the definition of asymptotes and infinity as applied to graphs and limits. Learn the definition of infinity, the definition of an asymptote, and explore the different types of asymptotes.

How to Determine if a Limit Does Not Exist

10. How to Determine if a Limit Does Not Exist

In this lesson, we'll discuss when a limit does not exist. We'll begin with a description of each type of limit and when that particular type does not exist. Then, we'll use a graph to show how to recognize when a limit does not exist based on the graph of a function ''f.''

Finding Asymptotes Using Limits

11. Finding Asymptotes Using Limits

A function can have a vertical asymptote, a horizontal asymptote and more generally, an asymptote along any given line (e.g., y = x). In this lesson, we learn how to find all asymptotes by evaluating the limits of a function.

Comparing Relative Magnitudes of Functions

12. Comparing Relative Magnitudes of Functions

The magnitude of a function can be thought of as how it behaves when it is graphed. In this lesson, we will investigate five function types and how to compare their magnitudes.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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