Preface 

ix  
CHAPTER 1 Preliminaries 

2  (47) 


3  (9) 

1.2 Precalculus Review II 


12  (12) 

1.3 The Cartesian Coordinate System 


24  (8) 


32  (15) 

Chapter 1 Summary of Principal Formulas and Terms 


47  (1) 

Chapter 1 Review Exercises 


47  (2) 
CHAPTER 2 Functions, Limits, and the Derivative 

49  (111) 

2.1 Functions and Their Graphs 


50  (19) 

Using Technology: Graphing a Function 


64  (5) 

2.2 The Algebra of Functions 


69  (5) 

PORTFOLIO: Michael Marchlik 


74  (86) 

2.3 Functions and Mathematical Models 


78  (19) 

Using Technology: Finding the Points of Intersection of Two Graphs and Modeling 


92  (5) 


97  (21) 

Using Technology: Finding the Limit of a Function 


114  (4) 

2.5 OneSided Limits and Continuity 


118  (18) 

Using Technology: Finding the Points of Discontinuity of a Function 


132  (4) 


136  (25) 

Using Technology: Graphing a Function and Its Tangent Line 


152  (5) 

Chapter 2 Summary of Principal Formulas and Terms 


157  (1) 

Chapter 2 Review Exercises 


158  (2) 
CHAPTER 3 Differentiation 

160  (90) 

3.1 Basic Rules of Differentiation 


161  (14) 

Using Technology: Finding the Rate of Change of a Function 


170  (5) 

3.2 The Product and Quotient Rules 


175  (13) 

Using Technology: The Product and Quotient Rules 


184  (4) 


188  (13) 

Using Technology: Finding the Derivative of a Composite Function 


196  (5) 

3.4 Marginal Functions in Economics 


201  (14) 

3.5 HigherOrder Derivatives 


215  (9) 

Using Technology: Finding the Second Derivative of a Function at a Given Point 


222  (2) 

3.6 Implicit Differentiation and Related Rates 


224  (10) 


234  (2) 


236  (96) 

Using Technology: Finding the Differential of a Function 


242  (4) 

Chapter 3 Summary of Principal Formula and Terms 


246  (1) 

Chapter 3 Review Exercises 


247  (3) 
CHAPTER 4 Applications of the Derivative 

250  (82) 

4.1 Applications of the First Derivative 


251  (20) 

Using Technology: Using the First Derivative to Analyze a Function 


266  (5) 

4.2 Applications of the Second Derivative 


271  (17) 

Using Technology: Finding the Inflection Points of a Function 


284  (4) 


288  (15) 

Using Technology: Analyzing the Properties of a Function 


300  (3) 


303  (15) 

Using Technology: Finding the Absolute Extrema of a Function 


314  (4) 


318  (11) 

Chapter 4 Summary of Principal Terms 


329  (1) 

Chapter 4 Review Exercises 


330  (2) 
CHAPTER 5 Exponential and Logarithmic Functions 

332  (65) 

5.1 Exponential Functions 


333  (8) 


338  (3) 

5.2 Logarithmic Functions 


341  (8) 


349  (12) 

PORTFOLIO: Misato Nakazaki 


361  (132) 

5.4 Differentiation of Exponential Functions 


363  (11) 


370  (4) 

5.5 Differentiation of Logarithmic Functions 


374  (7) 

5.6 Exponential Functions as Mathematical Models 


381  (17) 

Using Technology: Analyzing Mathematical Models 


390  (5) 

Chapter 5 Summary of Principal Formulas and Terms 


395  (1) 

Chapter 5 Review Exercises 


395  (2) 
CHAPTER 6 Integration 

397  (96) 

6.1 Antiderivatives and the Rules of Integration 


398  (14) 

6.2 Integration by Substitution 


412  (10) 

6.3 Area and the Definite Integral 


422  (10) 

6.4 The Fundamental Theorem of Calculus 


432  (10) 

Using Technology: Evaluating Definite Integrals 


441  (1) 

6.5 Evaluating Definite Integrals 


442  (12) 

Using Technology: Evaluating Definite Integrals for PiecewiseDefined Functions 


450  (4) 

6.6 Area between Two Curves 


454  (14) 

Using Technology: Finding the Area between Two Curves 


464  (4) 

6.7 Applications of the Definite Integral to Business and Economics 


468  (14) 

Using Technology: Business and Economic Applications/Technology Exercises 


481  (1) 

6.8 Volumes of Solids of Revolution 


482  (7) 

Chapter 6 Summary of Principal Formulas and Terms 


489  (1) 

Chapter 6 Review Exercises 


490  (3) 
CHAPTER 7 Additional Topics in Integration 

493  (43) 


494  (7) 

7.2 Integration Using Tables of Integrals 


501  (7) 

7.3 Numerical Integration 


508  (14) 

PORTFOLIO: James H. Chesebro. M.D. 


522  (131) 


524  (9) 

Chapter 7 Summary of Principal Formulas and Terms 


533  (1) 

Chapter 7 Review Exercises 


534  (2) 
CHAPTER 8 Calculus of Several Variables 

536  (85) 

8.1 Functions of Several Variables 


537  (10) 


547  (15) 

Using Technology: Finding Partial Derivatives at a Given Point 


560  (2) 

8.3 Maxima and Minima of Functions of Several Variables 


562  (11) 

8.4 The Method of Least Squares 


573  (12) 

Using Technology: Finding an Equation of a LeastSquares Line 


580  (5) 

8.5 Constrained Maxima and Minima and the Method of Lagrange Multipliers 


585  (11) 


596  (6) 


602  (7) 

8.8 Applications of Double Integrals 


609  (8) 

Chapter 8 Summary of Principal Terms 


617  (1) 

Chapter 8 Review Exercises 


618  (3) 
CHAPTER 9 Differential Equations 

621  (32) 

9.1 Differential Equations 


622  (7) 

9.2 Separation of Variables 


629  (5) 

9.3 Applications of Separable Differential Equations 


634  (10) 

9.4 Approximate Solutions of Differential Equations 


644  (7) 

Chapter 9 Summary of Principal Terms 


651  (1) 

Chapter 9 Review Exercises 


651  (2) 
CHAPTER 10 Probability and Calculus 

653  (44) 

10.1 Probability Distributions of Random Variables 


654  (14) 

Using Technology: Graphing a Histogram 


664  (4) 

10.2 Expected Value and Standard Deviation 


668  (15) 

Using Technology: Finding the Mean and Standard Deviation 


680  (3) 

PORTFOLIO: Lilli Meiselman 


683  (14) 

10.3 Normal Distributions 


684  (11) 

Chapter 10 Summary of Principal Formulas and Terms 


695  (1) 

Chapter 10 Review Exercises 


695  (2) 
CHAPTER 11 Taylor Polynomials and Infinite Series 

697  (72) 


698  (12) 


710  (8) 


718  (11) 

11.4 series with Positive Terms 


729  (11) 

11.5 Power Series and Taylor Series 


740  (9) 

11.6 More on Taylor Series 


749  (8) 

11.7 The NewtonRaphson Method 


757  (9) 

Chapter 11 Summary of Principal Formulas and Terms 


766  (1) 

Chapter 11 Review Exercises 


767  (2) 
CHAPTER 12 Trigonometric Functions 

769  (42) 

12.1 Measurement of Angles 


770  (6) 

12.2 The Trigonometric Functions 


776  (9) 

12.3 Differentiation of Trigonometric Functions 


785  (14) 

Using Technology: Analyzing Trigonometric Functions 


796  (3) 

12.4 Integration of Trigonometric Functions 


799  (8) 

Using Technology: Evaluating Integrals of Trigonometric Functions 


804  (3) 

Chapter 12 Summary of Principal Formulas and Terms 


807  (1) 

Chapter 12 Review Exercises 


808  (3) 
APPENDIX A Inverse Functions 

811  (6) 

A.1 The Inverse of a Function 


811  (2) 

A.2 The Graphs of Inverse Functions 


813  (1) 

A.3 Functions That Have Inverses 


813  (1) 

A.4 Finding the Inverse of a Function 


814  (3) 
APPENDIX B Table 

817  

The Standard Normal Distribution 


817  