Calculus and its Applications

For one-semester courses in applied calculus. Anticipating and meeting student needs Calculus and Its Applications, Eleventh Edition, remains a best-selling text because of its accessible presentation that anticipates student needs. The writing style is ideal for today's students, providing intuitive explanations that work with the carefully crafted artwork to help them visualize new calculus concepts. Additionally, the text's numerous and up-to-date applications from business, economics, life sciences, and social sciences help motivate students. Algebra diagnostic and review material is available for those who need to strengthen basic skills. Every aspect of this revision is designed to motivate and help students to more readily understand and apply the mathematics. MyMathLab not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information. MyMathLab is an online homework, tutorial, and assessment product designed to personalize learning and improve results. With a wide range of interactive, engaging, and assignable activities, students are encouraged to actively learn and retain tough course concepts.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 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. 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 Maximum-Minimum 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 Application-Maximum 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 Application-The 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 Application-Business: 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 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 6.6 Double Integrals Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application-Minimizing Employees' Travel Time in a Building Cumulative Review Appendix A: Review of Basic Algebra Appendix B: Regression and Microsoft Excel Table A: Areas for a Standard Normal Distribution Answers Index of Applications Index Additional Instructor's Answers Calculus and Its Applications: Expanded Version (ISBN: 978-0-321-83820-9) contains these additional chapters: 7. Trigonometric Functions 8. Differential Equations 9. Sequences and Series 10. Probability Distributions