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Contents
Prerequisite Skills Diagnostic Test
R. Functions, Graphs, and Models
R.1 Graphs and Equations
R.2 Functions and Models
R.3 Finding Domain and Range
R.4 Slope and Linear Functions
R.5 Nonlinear Functions and Models
R.6 Exponential and Logarithmic Functions
R.7 Mathematical Modeling and Curve Fitting
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Average Price of a Movie Ticket
1. Differentiation
1.1 Limits: A Numerical and Graphical Approach
1.2 Algebraic Limits and Continuity
1.3 Average Rates of Change
1.4 Differentiation Using Limits and Difference Quotients
1.5 Leibniz Notation and the Power and Sum—Difference Rules
1.6 The Product and Quotient Rules
1.7 The Chain Rule
1.8 Higher-Order Derivatives
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Path of a Baseball: The Tale of the Tape
2. Exponential and Logarithmic Functions
2.1 Exponential and Logarithmic Functions of the Natural Base, e
2.2 Derivatives of Exponential (Base-e) Functions
2.3 Derivatives of Natural Logarithmic Functions
2.4 Applications: Uninhibited and Limited Growth Models
2.5 Applications: Exponential Decay231
2.6 The Derivatives of ax and loga x
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: The Business of Motion Picture Revenue and DVD Release
3. Applications of Differentiation
3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
3.3 Graph Sketching: Asymptotes and Rational Functions
3.4 Optimization: Finding Absolute Maximum and Minimum Values
3.5 Optimization: Business, Economics, and General Applications
3.6 Marginals, Differentials, and Linearization
3.7 Elasticity of Demand
3.8 Implicit Differentiation and Logarithmic Differentiation
3.9 Related Rates
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Maximum Sustainable Harvest
4. Integration
4.1 Antidifferentiation
4.2 Antiderivatives as Areas
4.3 Area and Definite Integrals
4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average
4.5 Integration Techniques: Substitution
4.6 Integration Techniques: Integration by Parts
4.7 Numerical Integration
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Business and Economics: Distribution of Wealth
5. Applications of Integration
5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss
5.2 Integrating Growth and Decay Models
5.3 Improper Integrals
5.4 Probability
5.5 Probability: Expected Value; the Normal Distribution
5.6 Volume
5.7 Differential Equations
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Curve Fitting and Volumes of Containers
6. Functions of Several Variables
6.1 Functions of Several Variables
6.2 Partial Derivatives
6.3 Maximum—Minimum Problems
6.4 An Application: The Least-Squares Technique
6.5 Constrained Optimization: Lagrange Multipliers and the Extreme-Value Theorem
6.6 Double Integrals
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Minimizing Employees' Travel Time in a Building
7. Trigonometric Functions
7.1 Basics of Trigonometry
7.2 Derivatives of Trigonometric Functions
7.3 Integration of Trigonometric Functions
7.4 Inverse Trigonometric Functions and Applications
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
8. Differential Equations
8.1 Direction Fields, Autonomic Forms, and Population Models
8.2 Applications: Inhibited Growth Models
8.3 First-Order Linear Differential Equations
8.4 Higher-Order Differential Equations and a Trigonometry Connection
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
9. Sequences and Series
9.1 Arithmetic Sequences and Series
9.2 Geometric Sequences and Series
9.3 Simple and Compound Interest
9.4 Annuities and Amortization
9.5 Power Series and Linearization
9.6 Taylor Series and a Trigonometry Connection
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
10. Probability Distributions
10.1 A Review of Sets
10.2 Theoretical Probability
10.3 Discrete Probability Distributions
10.4 Continuous Probability Distributions: Mean, Variance, and Standard Deviation
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
11. Systems and Matrices (online only)
11.1 Systems of Linear Equations
11.2 Gaussian Elimination
11.3 Matrices and Row Operations
11.4 Matrix Arithmetic: Equality, Addition, and Scalar Multiples
11.5 Matrix Multiplication, Multiplicative Identities, and Inverses
11.6 Determinants and Cramer's Rule
11.7 Systems of Linear Inequalities and Linear Programming
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
12. Combinatorics and Probability (online only)
12.1 Compound Events and Odds
12.2 Combinatorics: The Multiplication Principle and Factorial Notation
12.3 Permutations and Distinguishable Arrangements
12.4 Combinations and the Binomial Theorem
12.5 Conditional Probability and the Hypergeometric Probability Distribution Model
12.6 Independent Events, Bernoulli Trials, and the Binomial Probability Model
12.7 Bayes Theorem
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
Cumulative Review
APPENDICES
A. Review of Basic Algebra
B. Indeterminate Forms and l'Hôpital's Rule
C. Regression and Microsoft Excel
D. Areas for a Standard Normal Distribution
E. Using Tables of Integration Formulas
Answers Index of Applications Index
