A Word from the Authors (Preface) 

ix  
Index of Applications 

xxxi  


1  (54) 


3  (8) 

Linear Models and Rates of Change 


11  (9) 

Functions and Their Graphs 


20  (11) 


31  (6) 


37  (11) 

Exponential and Logarithmic Functions 


48  (7) 

Limits and Their Properties 


55  (52) 


57  (6) 

Finding Limits Graphically and Numerically 


63  (9) 

Evaluating Limits Analytically 


72  (12) 

Continuity and OneSided Limits 


84  (12) 


96  (11) 


104  (3) 


107  (86) 

The Derivative and the Tangent Line Problem 


109  (11) 

Basic Differentiation Rules and Rates of Change 


120  (13) 

The Product and Quotient Rules and HigherOrder Derivatives 


133  (10) 


143  (15) 


158  (8) 

Derivatives of Inverse Functions 


166  (7) 


173  (9) 


182  (11) 


188  (5) 

Applications of Differentiation 


193  (82) 


195  (8) 

Rolle's Theorem and the Mean Value Theorem 


203  (6) 

Increasing and Decreasing Functions and the First Derivative Test 


209  (10) 

Concavity and the Second Derivative Test 


219  (8) 


227  (9) 

A Summary of Curve Sketching 


236  (10) 


246  (11) 


257  (7) 

Business and Economics Applications 


264  (11) 


271  (4) 


275  (96) 

Antiderivatives and Indefinite Integration 


277  (11) 


288  (12) 

Riemann Sums and Definite Integrals 


300  (10) 

The Fundamental Theorem of Calculus 


310  (13) 

Integration by Substitution 


323  (12) 


335  (7) 

The Natural Logarithmic Function and Integration 


342  (8) 

Inverse Trigonometric Functions and Integration 


350  (7) 


357  (14) 


367  (4) 


371  (34) 

Differential Equations: Growth and Decay 


373  (8) 

Differential Equations: Separation of Variables 


381  (13) 

FirstOrder Linear Differential Equations 


394  (11) 


403  (2) 

Applications of Integration 


405  (68) 

Area of a Region Between Two Curves 


407  (9) 


416  (11) 


427  (8) 

Arc Length and Surfaces of Revolution 


435  (10) 


445  (9) 

Moments, Centers of Mass, and Centroids 


454  (11) 

Fluid Pressure and Fluid Force 


465  (8) 


471  (2) 

Integration Techniques, L'Hopital's Rule, and Improper Integrals 


473  (72) 


475  (6) 


481  (9) 


490  (9) 

Trigonometric Substitution 


499  (9) 


508  (9) 

Integration by Tables and Other Integration Techniques 


517  (6) 

Indeterminate Forms and L'Hopital's Rule 


523  (10) 


533  (12) 


542  (3) 


545  (90) 


547  (11) 


558  (10) 

The Integral Test and pSeries 


568  (6) 


574  (7) 


581  (7) 


588  (8) 

Taylor Polynomials and Approximations 


596  (10) 


606  (9) 

Representation of Functions by Power Series 


615  (7) 

Taylor and Maclaurin Series 


622  (13) 


632  (3) 

Conics, Parametric Equations, and Polar Coordinates 


635  (2) 


637  (15) 

Plane Curves and Parametric Equations 


652  (10) 

Parametric Equations and Calculus 


662  (9) 

Polar Coordinates and Polar Graphs 


671  (10) 

Area and Arc Length in Polar Coordinates 


681  (8) 

Polar Equations of Conics and Kepler's Laws 


689  (7) 


696  
Appendix A Precalculus Review 

A1  

A.1 Real Numbers and the Real Line 


A1  


A10  

A.3 Review of Trigonometric Functions 


A17  
Appendix B Proofs of Selected Theorems 

A28  
Appendix C Basic Differentiation Rules for Elementary Functions 

A44  
Appendix D Integration Tables 

A45  
Appendix E Rotation and the General SecondDegree Equation 

A51  
Answers to OddNumbered Exercises 

A57  
Index 

A145  