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Ch 21: Limits & Continuity in Differential Calculus

About This Chapter

Ensure you fully understand how the binomial theorem is used in math by working through this informative chapter. Use our helpful video lessons and multiple-choice quizzes to get ready for a class project or to prepare to take an important exam.

Limits & Continuity in Differential Calculus - Chapter Summary

In these lessons, our instructors introduce you to the process of defining limits by using a graph and using notation to understand limits. You'll learn about two methods used to find limits: the squeeze theorem and L'Hopital's Rule. Other lessons cover the difference between continuous and discontinuous functions.

Additional topics include the intermediate value theorem and how it's used to decipher whether a problem has an answer. After reviewing this informative chapter, you'll be able to do the following:

  • Describe the relationship between continuity and limits
  • Calculate the limits of complex functions
  • Use a graph to show the relationship between infinity and asymptotes
  • Name some of the commonly seen discontinuities in functions
  • Define regions of continuity in functions

Watch these easy-to-use video lessons to learn about these topics in a fun way. The multiple-choice quizzes help you test yourself on how well you understand these subjects before moving on. If you'd like to skip to a specific section of a video lesson, the video tabs feature in the Timeline allows you to jump ahead. Our instructors can help you if you struggle with any of the topics presented here.

13 Lessons in Chapter 21: Limits & Continuity in Differential Calculus
Test your knowledge with a 30-question chapter practice test
Using a Graph to Define Limits

1. Using a Graph to Define Limits

My mom always said I tested the limits of her patience. Use graphs to learn about limits in math. You won't get grounded as we approach limits in this lesson.

Understanding Limits: Using Notation

2. Understanding Limits: Using Notation

Join me on a road trip as we define the mathematical notation of limits. As time goes by and I traverse hills and highways, the limit of my speed changes. Learn how to write these limits in this lesson.

One-Sided Limits and Continuity

3. One-Sided Limits and Continuity

Over the river and through the woods is only fun on a continuous path. What happens when the path has a discontinuity? In this lesson, learn about the relationship between continuity and limits as we walk up and down this wildlife path.

How to Determine the Limits of Functions

4. How to Determine the Limits of Functions

You know the definition of a limit. You know the properties of limits. You can connect limits and continuity. Now use this knowledge to calculate the limits of complex functions in this lesson.

Understanding the Properties of Limits

5. Understanding the Properties of Limits

Graphically we can see limits, but how do we actually calculate them? Three words: Divide and Conquer. In this lesson, explore some of the properties that we can use to find limits.

Squeeze Theorem: Definition and Examples

6. Squeeze Theorem: Definition and Examples

In the Kingdom of Rimonn there are three rivers. In this lesson, learn how these waterways demonstrate the power of the squeeze theorem for finding the limits of functions.

What is L'Hopital's Rule?

7. What is L'Hopital's Rule?

A Swiss mathematician and a French mathematician walk into a bar ... and they walk out with the famous L'Hopital's rule for finding limits. In this lesson, learn what these two mathematicians came up with and how to use it to avoid the limit of zero divided by zero!

Applying L'Hopital's Rule in Simple Cases

8. Applying L'Hopital's Rule in Simple Cases

L'Hôpital's rule may have disputed origins, but in this lesson you will use it for finding the limits of a range of functions, from trigonometric to polynomials and for limits of infinity/infinity and 0/0.

Graphs and Limits: Defining Asymptotes and Infinity

9. Graphs and Limits: Defining Asymptotes and Infinity

Infinity is a hard concept to understand and the word asymptote is pretty intimidating. But this fun lesson will make both seem like a walk in the park as it defines both and shows their relationship using a graph.

Continuity in a Function

10. Continuity in a Function

Travel to space and explore the difference between continuous and discontinuous functions in this lesson. Learn how determining continuity is as easy as tracing a line.

Discontinuities in Functions and Graphs

11. Discontinuities in Functions and Graphs

In this lesson, we talk about the types of discontinuities that you commonly see in functions. In particular, learn how to identify point, jump and asymptotic discontinuities.

Regions of Continuity in a Function

12. Regions of Continuity in a Function

Can Earth ever compete with extraterrestrial UFOs? In this lesson, you'll learn that not all functions are continuous, but most have regions where they are continuous. Discover how to define regions of continuity for functions that have discontinuities.

Intermediate Value Theorem: Examples and Applications

13. Intermediate Value Theorem: Examples and Applications

Many problems in math don't require an exact solution. Some problems exist simply to find out if any solution exists. In this lesson, we'll learn how to use the intermediate value theorem to answer an age-old question.

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.
Not Taken

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