## Chapter 2 Limits and Continuity

## Chapter 2 Overview

The concept of a limit is one of the ideas that distinguish calculus from algebra and trigonometry.

In this chapter you will define and calculate limits of function values. Most of the limits we need can be found by substitution, graphical investigation, numerical approximation, algebra, or some combination of these.

One of the uses of limits is to test functions for continuity. Continuous functions arise frequently in scientific work because they model such an enormous range of natural behavior. They also have special mathematical properties, not otherwise guaranteed.

-Finney, Demana, Waits & Kennedy

In this chapter you will define and calculate limits of function values. Most of the limits we need can be found by substitution, graphical investigation, numerical approximation, algebra, or some combination of these.

One of the uses of limits is to test functions for continuity. Continuous functions arise frequently in scientific work because they model such an enormous range of natural behavior. They also have special mathematical properties, not otherwise guaranteed.

-Finney, Demana, Waits & Kennedy

## Key Terms and Properties

Average and Instantaneous Speed

Definition of Limit

Properties of Limits

One-sided and Two-sided Limits

Sandwich Theorem

Finite Limits as x Approaches +/- Infinity

Infinite Limits as x approaches a

End Behavior Models

"Seeing" Limits as x approaches +/- Infinity

Continuity at a Point

Continuous Functions

Algebraic Combinations

Composites

Intermediate Value Theorem for Continuous Functions

Average Rates of Change

Tangent to a Curve

Slope of a Curve

Normal to a Curve

Definition of Limit

Properties of Limits

One-sided and Two-sided Limits

Sandwich Theorem

Finite Limits as x Approaches +/- Infinity

Infinite Limits as x approaches a

End Behavior Models

"Seeing" Limits as x approaches +/- Infinity

Continuity at a Point

Continuous Functions

Algebraic Combinations

Composites

Intermediate Value Theorem for Continuous Functions

Average Rates of Change

Tangent to a Curve

Slope of a Curve

Normal to a Curve

## Downloadable Documents

AP Calc Chapter 2 Assignment Sheet:

Chapter 2 Homework Answers:

ch_2_answers_2014.pdf | |

File Size: | 1208 kb |

File Type: |

Chapter 2 Homework Solutions

The file below shows all of the homework problems worked out. Be aware that some problems may have been added or taken off of the assignment since this packet has been been scanned.

The file below shows all of the homework problems worked out. Be aware that some problems may have been added or taken off of the assignment since this packet has been been scanned.

ap_calc_ch_2_hw_solutions.pdf | |

File Size: | 1805 kb |

File Type: |

Ch 2 Supplemental Note Sheets for Lectures:

note_supplements_for_ch_2___2013.pdf | |

File Size: | 991 kb |

File Type: |

## Screencasts

2.1A Rates of Change Example 1

2.1A Rates of Change Example 2

2.1A Rates of Change Example 3

2.1B Limit Notation Introduction

2.1B The Limit of a Function E1

2.1B The Limit of a Function E2

2.1C Methods of Finding Limits

2.2 Limits Involving Infinity

2.4A The Average Rate of Change

2.1A Rates of Change Example 2

2.1A Rates of Change Example 3

2.1B Limit Notation Introduction

2.1B The Limit of a Function E1

2.1B The Limit of a Function E2

2.1C Methods of Finding Limits

2.2 Limits Involving Infinity

2.4A The Average Rate of Change

## Additional Resources Specific for Limits and Continuity

Paul's Online Math Notes : Limits