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 Decay
- 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
- Review of Basic Algebra
- Indeterminate Forms and l’Hôpital’s Rule
- Regression and Microsoft Excel
- Areas for a Standard Normal Distribution
- Using Tables of Integration Formulas
Answers
Index of Applications
Index
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