About This Chapter
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.''
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.
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.
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Other chapters within the AP Calculus AB & BC: Exam Prep course
- Graph Basics
- The Basics of Functions
- How to Graph Functions
- Overview of Function Continuity
- Understanding Exponentials & Logarithms
- Using Exponents and Polynomials
- Parametric, Polar and Vector Functions
- Overview of Properties of Derivatives
- The Derivative at a Point
- The Derivative as a Function
- Second Derivatives
- Derivative Applications
- Finding Derivatives
- Properties of Definite Integrals
- Applications of Integrals
- Using the Fundamental Theorem of Calculus
- Applying Integration Techniques
- Approximation of Definite Integrals
- Understanding Sequences & Series
- Series of Constants
- Taylor Series
- Using a Scientific Calculator for Calculus
- AP Calculus AB & BC Flashcards