A Word from the Authors (Preface) 

xi  
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  (64) 


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  (10) 


696  (3) 

Vectors and the Geometry of Space 


699  (68) 


701  (11) 

Space Coordinates and Vectors in Space 


712  (8) 

The Dot Product of Two Vectors 


720  (9) 

The Cross Product of Two Vectors in Space 


729  (8) 

Lines and Planes in Space 


737  (11) 


748  (10) 

Cylindrical and Spherical Coordinates 


758  (9) 


765  (2) 


767  (50) 


769  (8) 

Differentiation and Integration of VectorValued Functions 


777  (8) 

Velocity and Acceleration 


785  (9) 

Tangent Vectors and Normal Vectors 


794  (9) 


803  (14) 


815  (2) 

Functions of Several Variables 


817  (96) 

Introduction to Functions of Several Variables 


819  (12) 


831  (9) 


840  (9) 


849  (8) 

Chain Rules for Functions of Several Variables 


857  (8) 

Directional Derivatives and Gradients 


865  (12) 

Tangent Planes and Normal Lines 


877  (9) 

Extrema of Functions of Two Variables 


886  (8) 

Applications of Extrema of Functions of Two Variables 


894  (8) 


902  (11) 


910  (3) 


913  (70) 

Iterated Integrals and Area in the Plane 


915  (8) 

Double Integrals and Volume 


923  (11) 

Change of Variables: Polar Coordinates 


934  (8) 

Center of Mass and Moments of Inertia 


942  (8) 


950  (7) 

Triple Integrals and Applications 


957  (10) 

Triple Integrals in Cylindrical and Spherical Coordinates 


967  (7) 

Change of Variables: Jacobians 


974  (9) 


980  (3) 


983  


985  (11) 


996  (13) 

Conservative Vector Fields and Independence of Path 


1009  (10) 


1019  (9) 


1028  (10) 


1038  (12) 


1050  (8) 


1058  


1064  
Appendix A Precalculus Review 

A1  (1) 

A.1 Real Numbers and the Real Line 


A1  (1) 


A10  (1) 

A.3 Review of Trigonometric Functions 


A17  (1) 
Appendix B Proofs of Selected Theorems 

A28  (1) 
Appendix C Basic Differentiation Rules for Elementary Functions 

A44  (1) 
Appendix D Integration Tables 

A45  (1) 
Appendix E Rotation and the General SecondDegree Equation 

A51  (1) 
Answers to OddNumbered Exercises 

A57  (1) 
Index 

A179  