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 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 of Difference Quotients
1.5 The Power and SumDifference 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 ApplicationPath of a Baseball: The Tale of the Tape
2. Applications of Differentiation
2.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
2.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
2.3 Graph Sketching: Asymptotes and Rational Functions
2.4 Using Derivatives to Find Absolute Maximum and Minimum Values
2.5 MaximumMinimum Problems; Business, Economics, and General Applications
2.6 Marginals and Differentials
2.7 Elasticity of Demand
2.8 Implicit Differentiation and Related Rates
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology ApplicationMaximum Sustainable Harvest
3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Applications: Uninhibited and Limited Growth Models
3.4 Applications: Decay
3.5 The Derivatives of ax and loga x
3.6 A Business Application: Amortization
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology ApplicationThe Business of Motion Picture Revenue and DVD Release
4. Integration
4.1 Antidifferentiation
4.2 Antiderivatives as Areas
4.3 Area and Definite Integrals
4.4 Properties of Definite Integrals
4.5 Integration Techniques: Substitution
4.6 Integration Techniques: Integration by Parts
4.7 Integration Techniques: Tables
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology ApplicationBusiness: Distribution of Wealth
5. Applications of Integration
5.1 Consumer Surplus and Producer Surplus
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 ApplicationCurve Fitting and Volumes of Containers
6. Functions of Several Variables
6.1 Functions of Several Variables
6.2 Partial Derivatives
6.3 MaximumMinimum Problems
6.4 An Application: The Least-Squares Technique
6.5 Constrained Optimization
6.6 Double Integrals
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology ApplicationMinimizing Employees Travel Time in a Building
Cumulative Revi
