A Word from the Authors (Preface) 

vii  
Features 

xii  
A Plan for You as a Student (Study Strategies) 

xx  


1  (1) 

The Real Number Line and Order 


2  (6) 

Absolute Value and Distance on the Real Number Line 


8  (5) 


13  (6) 


19  (6) 

Fractions and Rationalization 


25  

Functions, Graphs, and Limits 


1  (80) 

The Cartesian Plane and the Distance Formula 


2  (9) 


11  (13) 

Lines in the Plane and Slope 


24  (12) 


36  (13) 


49  (12) 


61  (20) 


72  (2) 

Chapter Summary and Study Strategies 


74  (2) 


76  (4) 

Sample PostGraduation Exam Questions 


80  (1) 


81  (90) 

The Derivative and the Slope of a Graph 


82  (11) 

Some Rules for Differentiation 


93  (12) 

Rates of Change: Velocity and Marginals 


105  (15) 

The Product and Quotient Rules 


120  (11) 


131  (9) 


140  (7) 


147  (7) 


154  (17) 


162  (2) 

Chapter Summary and Study Strategies 


164  (2) 


166  (4) 

Sample PostGraduation Exam Questions 


170  (1) 

Applications of the Derivative 


171  (86) 

Increasing and Decreasing Functions 


172  (9) 

Extrema and the FirstDerivative Test 


181  (10) 

Concavity and the SecondDerivative Test 


191  (10) 


201  (9) 

Business and Economics Applications 


210  (10) 


220  (11) 

Curve Sketching: A Summary 


231  (9) 

Differentials and Marginal Analysis 


240  (17) 


248  (2) 

Chapter Summary and Study Strategies 


250  (2) 


252  (4) 

Sample PostGraduation Exam Questions 


256  (1) 

Exponential and Logarithmic Functions 


257  (60) 


258  (6) 

Natural Exponential Functions 


264  (9) 

Derivatives of Exponential Functions 


273  (8) 


281  (9) 

Derivatives of Logarithmic Functions 


290  (9) 

Exponential Growth and Decay 


299  (18) 


308  (2) 

Chapter Summary and Study Strategies 


310  (2) 


312  (4) 

Sample PostGraduation Exam Questions 


316  (1) 

Integration and Its Applications 


317  (70) 

Antiderivatives and Indefinite Integrals 


318  (11) 


329  (8) 

Exponential and Logarithmic Integrals 


337  (7) 

Area and the Fundamental Theorem of Calculus 


344  (12) 

The Area of a Region Bounded by Two Graphs 


356  (9) 

The Definite Integral as the Limit of a Sum 


365  (6) 

Volumes of Solids of Revolution 


371  (16) 


378  (2) 

Chapter Summary and Study Strategies 


380  (2) 


382  (4) 

Sample PostGraduation Exam Questions 


386  (1) 

Techniques of Integration 


387  (68) 

Integration by Substitution 


388  (8) 

Integration by Parts and Present Value 


396  (10) 

Partial Fractions and Logistic Growth 


406  (10) 

Integration Tables and Completing the Square 


416  (10) 


426  (10) 


436  (19) 


446  (2) 

Chapter Summary and Study Strategies 


448  (2) 


450  (4) 

Sample PostGraduation Exam Questions 


454  (1) 

Functions of Several Variables 


455  

The ThreeDimensional Coordinate System 


456  (8) 


464  (10) 

Functions of Several Variables 


474  (9) 


483  (11) 

Extrema of Functions of Two Variables 


494  (10) 


504  (10) 

Least Squares Regression Analysis 


514  (10) 

Double Integrals and Area in the Plane 


524  (8) 

Applications of Double Integrals 


532  


540  (2) 

Chapter Summary and Study Strategies 


542  (2) 


544  (4) 

Sample PostGraduation Exam Questions 


548  


1  (20) 

Appendix A: Alternate Introduction to the Fundamental Theorem of Calculus 


2  (10) 


12  (9) 

Appendix C: Differential Equations 



Solutions of Differential Equations 





FirstOrder Linear Differential Equations 



Applications of Differential Equations 



Appendix D: Properties and Measurement 



Review of Algebra, Geometry, and Trigonometry 





Appendix E: Graphing Utility Programs 



Graphing Utility Programs 


Answers to Selected Exercises 

21  (64) 
Answers to Try Its 

85  (12) 
Index 

97  