Preface 

xi  
Acknowledgments 

xvi  
Ancillaries 

xx  
For the Student 

xxiii  
Precalculus Review 

2  (2) 


4  (16) 

Functions and Their Graphs 


20  (16) 


36  (17) 

Exponentials and Logarithms 


53  (10) 


63  (19) 


82  (60) 


84  (13) 


97  (9) 

Techniques for Finding Limits 


106  (10) 

Limits Involving Infinity 


116  (11) 


127  (15) 

Chapter 1 Review Exercises 


139  (1) 

Extended Problems and Group Projects 


140  (2) 


142  (104) 

Tangent Lines and Rates of Change 


144  (13) 


157  (16) 

Techniques of Differentiation 


173  (11) 

Derivatives of the Trigonometric Functions 


184  (11) 


195  (11) 


206  (8) 


214  (10) 

Linear Approximations and Differentials 


224  (13) 


237  (9) 

Chapter 2 Review Exercises 


242  (3) 

Extended Problems and Group Projects 


245  (1) 

Applications of the Derivative 


246  (96) 


248  (13) 


261  (8) 

The First Derivative Test 


269  (10) 

Concavity and the Second Derivative Test 


279  (12) 

Summary of Graphical Methods 


291  (11) 


302  (16) 

Velocity and Acceleration 


318  (10) 

Applications to Economics, Social Sciences, and Life Sciences 


328  (14) 

Chapter 3 Review Exercises 


337  (3) 

Extended Problems and Group Projects 


340  (2) 


342  (88) 

Antiderivatives, Indefinite Integrals, and Simple Differential Equations 


344  (13) 

Change of Variables in Indefinite Integrals 


357  (8) 

Summation Notation and Area 


365  (12) 


377  (11) 

Properties of the Definite Integral 


388  (8) 

The Fundamental Theorem of Calculus 


396  (13) 


409  (21) 

Chapter 4 Review Exercises 


427  (2) 

Extended Problems and Group Projects 


429  (1) 

Applications of the Definite Integral 


430  (84) 


432  (13) 


445  (12) 

Volumes by Cylindrical Shells 


457  (6) 

Volumes by Cross Sections 


463  (5) 

Arc Length and Surfaces of Revolution 


468  (12) 


480  (8) 

Moments and Centers of Mass 


488  (9) 


497  (17) 

Chapter 5 Review Exercises 


511  (2) 

Extended Problems and Group Projects 


513  (1) 


514  (114) 

The Derivative of the Inverse Function 


516  (11) 

The Natural Logarithm Function 


527  (12) 


539  (9) 

Integration Using Natural Logarithm and Exponential Functions 


548  (9) 

General Exponential and Logarithmic Functions 


557  (11) 

Separable Differential Equations and Laws of Growth and Decay 


568  (8) 

Inverse Trigonometric Functions 


576  (15) 

Hyperbolic and Inverse Hyperbolic Functions 


591  (19) 

Indeterminate Forms and I'Hopital's Rule 


610  (18) 

Chapter 6 Review Exercises 


623  (3) 

Extended Problems and Group Projects 


626  (2) 

Techniques of Integration 


628  (64) 


630  (9) 


639  (5) 

Trigonometric Substitutions 


644  (6) 

Integrals of Rational Functions 


650  (10) 

Quadratic Expressions and Miscellaneous Substitutions 


660  (8) 

Tables of Integrals and Computer Algebra Systems 


668  (6) 


674  (18) 

Chapter 7 Review Exercises 


689  (2) 

Extended Problems and Group Projects 


691  (1) 


692  (92) 


694  (15) 

Convergent or Divergent Series 


709  (14) 


723  (11) 


734  (5) 

Alternating Series and Absolute Convergence 


739  (8) 


747  (8) 

Power Series Representations of Functions 


755  (9) 

Maclaurin and Taylor Series 


764  (12) 

Applications of Taylor Polynomials 


776  (8) 

Chapter 8 Review Exercises 


782  (1) 

Extended Problems and Group Projects 


783  (1) 

Parametric Equations and Polar Coordinates 


784  (60) 


786  (17) 

Arc Length and Surface Area 


803  (8) 


811  (11) 

Integrals in Polar Coordinates 


822  (10) 

Translation and Rotation of Axes 


832  (12) 

Chapter 9 Review Exercises 


840  (1) 

Extended Problems and Group Projects 


841  (3) 


844  (76) 

Vectors in Two Dimensions 


846  (11) 

Vectors in Three Dimensions 


857  (9) 


866  (10) 


876  (9) 


885  (13) 


898  (22) 

Chapter 10 Review Exercises 


918  (1) 

Extended Problems and Group Projects 


919  (1) 


920  (52) 

VectorValued Functions and Space Curves 


922  (7) 

Limits, Derivatives, and Integrals 


929  (8) 


937  (10) 


947  (12) 

Tangential and Normal Components of Acceleration 


959  (6) 


965  (7) 

Chapter 11 Review Exercises 


970  (1) 

Extended Problems and Group Projects 


971  (1) 


972  (104) 

Functions of Several Variables 


974  (12) 


986  (12) 


998  (9) 

Increments and Differentials 


1007  (14) 


1021  (9) 


1030  (12) 

Tangent Planes and Normal Lines 


1042  (8) 

Extrema of Functions of Several Variables 


1050  (12) 


1062  (14) 

Chapter 12 Review Exercises 


1071  (3) 

Extended Problems and Group Projects 


1074  (2) 


1076  (90) 


1078  (12) 


1090  (13) 

Double Integrals in Polar Coordinates 


1103  (8) 


1111  (4) 


1115  (12) 

Moments and Center of Mass 


1127  (9) 


1136  (8) 


1144  (8) 

Change of Variables and Jacobians 


1152  (14) 

Chapter 13 Review Exercises 


1163  (2) 

Extended Problems and Group Projects 


1165  (1) 


1166  (68) 


1168  (8) 


1176  (12) 


1188  (11) 


1199  (7) 


1206  (10) 


1216  (7) 


1223  (11) 

Chapter 14 Review Exercises 


1232  (1) 

Extended Problems and Group Projects 


1233  (1) 


1234  

Separable Differential Equations 


1236  

FirstOrder Linear Differential Equations 


1245  

SecondOrder Linear Differential Equations 


1257  

Nonhomogeneous Linear Differential Equations 


1262  


1268  

Chapter 15 Review Exercises 


1277  

Extended Problems and Group Projects 


1278  
Appendices 


I Theorems on Limits and Integrals 


A1  


A14  


A19  
Answers to Selected Exercises 

A24  
Index 

A97  