# Ch 3: CSET Math: Limits & Continuity

### About This Chapter

## CSET Math: Limits & Continuity - Chapter Summary

Our video lessons introduce you to continuities in functions and the definition and properties of a limit. The instructors who teach these lessons break down the individual concepts and teach you how to apply them using examples and step-by-step instructions. The video lessons cover the following topics that you'll see in exam questions:

- Determining sum, difference and constant multiple
- Using graphs to determine continuity of a function
- Identifying discontinuities in graphs
- Using the intermediate value theorem
- Using notation to define limits
- Applying one-sided limits to practical situations
- Determining limits of functions
- Using squeeze theorem to find function limits
- Calculating limits at infinity

### CSET Math: Limits & Continuity Objectives

The CSET Math exam is used to determine your readiness to teach math in California. The math exam has three subtests that test your knowledge of critical math concepts in geometry, algebra, probability and number theory. Limits and continuity are addressed in Subtest III, which focuses on calculus and the history of math. Subtest III has 30 multiple choice questions as well as four constructed response questions.

Use the self-assessment quizzes that accompany each lesson on limits and continuity to make sure you're ready for the exam. These quizzes can also help you get familiar with the style of questions asked on the exam.

### 1. Continuity in a Function

Continuity is the state of an equation or graph where the solutions form a continuous line, with no gaps on the graph. Learn the concept of continuity, opposed by discontinuity, and examples of both types of functions.

### 2. Discontinuities in Functions and Graphs

A discontinuity is where the potential values in an equation 'jump', rather than being continuous as with an un-broken line on a graph. See how discontinuities appear in graphs and equations, including jump discontinuities and asymptotic discontinuities.

### 3. Regions of Continuity in a Function

A region of continuity is where you have a function that is continuous and is a critical understanding in calculus and mathematics. Learn more about regions of continuity as a function and read examples.

### 4. Intermediate Value Theorem: Definition

The intermediate value theorem concerns the properties of continuous functions over a range and finding at least one solution. Learn more about the definition of the intermediate value theorem using the altitudes of a jet airplane as an example.

### 5. Intermediate Value Theorem: Examples and Applications

The intermediate value theorem states that a function, when continuous, can have a solution for all points along the range that it is within. Identify the applications of this theorem in finding roots, and solve some example functions.

### 6. Using a Graph to Define Limits

Limits can be visualized and defined better with the use of graphs. Explore examples of limits defined by graphs such as speed limits and limits of a pendulum, as well as other limits in math.

### 7. Understanding Limits: Using Notation

Limits describe what happens as you get closer to a number. Learn about defining and understanding limits. Then, learn about finding limits, using notation.

### 8. One-Sided Limits and Continuity

When studying mathematics functions and methodology of calculation, a good place to start is understanding the significance of one-sided limits and continuity. Learn more about the properties and functions, and study an example of a formula for finding one-sided limits and continuity.

### 9. How to Determine the Limits of Functions

A limit can tell us the value that a function approaches as that function's inputs get closer and closer to a number. Learn more about how to determine the limits of functions, properties of limits and read examples.

### 10. Understanding the Properties of Limits

The key to understanding the properties of limits is that it requires dividing the function into its individual parts first. Learn more about the properties of limits, including the addition and subtraction property, product property, and division property.

### 11. Squeeze Theorem: Definition and Examples

In calculus, the squeeze theorem is a principle that examines the limit of a function. Explore this concept in theory and in practice through examples.

### 12. Graphs and Limits: Defining Asymptotes and Infinity

In the study of mathematics, it is important to understand the usages and functions of asymptotes and infinity in graphs and equations. Learn more on how to define them, their use in graphs and formula methodology.

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### Other Chapters

Other chapters within the CSET Math Subtest III (213): Practice & Study Guide course

- About the CSET Mathematics Test
- CSET Math: Trigonometry
- CSET Math: Derivatives Overview
- CSET Math: Derivatives and Differentiation
- CSET Math: Derivatives and Theorems
- CSET Math: Derivatives and Graphs
- CSET Math: Applications of Derivatives
- CSET Math: Integrals
- CSET Math: Applications of Integrals
- CSET Math: Integrals in Geometry and Trigonometry
- CSET Math: Sequences & Series
- CSET Math Subtest 3 Flashcards