Description
Book SynopsisTable of ContentsPreface 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 logax
- 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
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
