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