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Ch 24: MTLE Mathematics: Continuity & Limits

About This Chapter

Let us guide you through the process of studying for the MTLE Mathematics assessment with this in-depth look at continuity and limits. You can boost your knowledge of the subject area by watching short video lessons and taking multiple-choice lesson quizzes.

MTLE Mathematics: Continuity & Limits - Chapter Summary

Get reacquainted with continuity and limits, and improve your ability to succeed on the MTLE Mathematics assessment by reviewing the lessons in this chapter. You can gain greater insight into discontinuities, intermediate value theorem, notation and more to ensure you're able to answer questions on the exam asking you to:

  • Describe continuity in a function and discontinuities in functions and graphs
  • Analyze regions of continuity in a function, and define intermediate value theorem
  • Discuss the properties of limits
  • Display an understanding of the meaning and uses of squeeze theorem
  • Demonstrate how to use a graph to define limits, and understand limits using notation
  • Explain one-sided limits and continuity and how to determine the limits of functions
  • Share the meaning of asymptotes and infinity as they relate to graphs and limits

Select the first lesson you want to watch in this chapter based on your studying needs, then easily navigate others by choosing from the list of lessons along the right-hand sidebar. When you select a lesson, you can choose between watching an entertaining video or reading a full transcript with helpful vocabulary words. Before, during or after reviewing the lessons, test your comprehension of continuity and limits by taking short quizzes and a chapter exam.

11 Lessons in Chapter 24: MTLE Mathematics: Continuity & Limits
Test your knowledge with a 30-question chapter practice test
Continuity in a Function

1. 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

2. 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

3. 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: Definition

4. Intermediate Value Theorem: Definition

A UFO and a jet take off and ascend to 30,000 feet along discontinuous and continuous paths, respectively. In this lesson, learn about the intermediate value theorem and why the jet has to cross 15,000 feet.

Using a Graph to Define Limits

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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.

Graphs and Limits: Defining Asymptotes and Infinity

11. 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.

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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Other Chapters

Other chapters within the MTLE Mathematics: Practice & Study Guide course

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