Preface 

ix  
PART ONE A LIBRARY OF ELEMENTARY FUNCTIONS 

1  (126) 

Chapter 1 A Beginning Library of Elementary Functions 


3  (74) 


3  (20) 

12 Elementary Functions: Graphs and Transformations 


23  (13) 

13 Linear Functions and Straight Lines 


36  (16) 


52  (15) 

Important Terms and Symbols 


67  (1) 


68  (4) 

Group Activity 1: Introduction to Regression Analysis 


72  (2) 

Group Activity 2: Mathematical Modeling in Business 


74  (3) 

Chapter 2 Additional Elementary Functions 


77  (50) 

21 Polynomial and Rational Functions 


77  (16) 

22 Exponential Functions 


93  (14) 

23 Logarithmic Functions 


107  (13) 

Important Terms and Symbols 


120  (1) 


120  (3) 

Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions 


123  (1) 

Group Activity 2: Comparing Regression Models 


124  (3) 
PART TWO CALCULUS 

127  (604) 


129  (92) 

31 Rate of Change and Slope 


130  (13) 


143  (17) 


160  (13) 

34 Derivatives of Constants, Power Forms, and Sums 


173  (13) 

35 Derivatives of Products and Quotients 


186  (8) 

36 Chain Rule: Power Form 


194  (8) 

37 Marginal Analysis in Business and Economics 


202  (11) 

Important Terms and Symbols 


213  (1) 

Summary of Rules of Differentiation 


214  (1) 


214  (5) 

Group Activity 1: Minimal Average Cost 


219  (1) 

Group Activity 2: Numerical Differentiation on a Graphing Utility 


220  (1) 

Chapter 4 Graphing and Optimization 


221  (90) 

41 Continuity and Graphs 


222  (16) 

42 First Derivative and Graphs 


238  (17) 

43 Second Derivative and Graphs 


255  (16) 

44 Curve Sketching Techniques: Unified and Extended 


271  (16) 

45 Optimization; Absolute Maxima and Minima 


287  (16) 

Important Terms and Symbols 


303  (1) 


304  (4) 

Group Activity 1: Maximizing Profit 


308  (1) 

Group Activity 2: Minimizing Construction Costs 


308  (3) 

Chapter 5 Additional Derivative Topics 


311  (50) 

51 The Constant e and Continuous Compound Interest 


311  (8) 

52 Derivatives of Logarithmic and Exponential Functions 


319  (12) 

53 Chain Rule: General Form 


331  (12) 

54 Implicit Differentiation 


343  (7) 


350  (6) 

Important Terms and Symbols 


356  (1) 

Additional Rules of Differentiation 


356  (1) 


357  (2) 

Group Activity 1: Elasticity of Demand 


359  (1) 

Group Activity 2: Point of Diminishing Returns 


360  (1) 


361  (84) 

61 Antiderivatives and Indefinite Integrals 


361  (15) 

62 Integration by Substitution 


376  (12) 

63 Differential EquationsGrowth and Decay 


388  (12) 

64 A GeometricNumeric Introduction to the Definite Integral 


400  (16) 

65 Definite Integral as a Limit of a Sum; Fundamental Theorem of Calculus 


416  (19) 

Important Terms and Symbols 


435  (1) 

Integration Formulas and Properties 


435  (1) 


435  (5) 

Group Activity 1: Simpson's Rule 


440  (3) 

Group Activity 2: BellShaped Curves 


443  (2) 

Chapter 7 Additional Integration Topics 


445  (46) 


445  (12) 

72 Applications in Business and Economics 


457  (13) 


470  (7) 

74 Integration Using Tables 


477  (8) 

Important Terms and Symbols 


485  (1) 


485  (2) 

Group Activity 1: Analysis of Income Concentration from Raw Data 


487  (2) 

Group Activity 2: Grain Exchange 


489  (2) 

Chapter 8 Multivariable Calculus 


491  (68) 

81 Functions of Several Variables 


491  (10) 


501  (10) 


511  (9) 

84 Maxima and Minima Using Lagrange Multipliers 


520  (10) 

85 Method of Least Squares 


530  (11) 

86 Double Integrals Over Rectangular Regions 


541  (11) 

Important Terms and Symbols 


552  (1) 


552  (3) 

Group Activity 1: City Planning 


555  (1) 

Group Activity 2: Numerical Integration of Multivariable Functions 


556  (3) 

Chapter 9 Differential Equations 


559  (46) 


559  (12) 

92 Separation of Variables 


571  (12) 

93 FirstOrder Linear Differential Equations 


583  (12) 

Important Terms and Symbols 


595  (1) 


595  (2) 

Group Activity 1: Torricelli's Law 


597  (2) 

Group Activity 2: Euler's Method 


599  (6) 

Chapter 10 Taylor Polynomials and Infinite Series 


605  (52) 


605  (15) 


620  (11) 

103 Operations on Taylor Series 


631  (9) 

104 Approximations Using Taylor Series 


640  (11) 

Important Terms and Symbols 


651  (1) 


651  (2) 

Group Activity 1: L'Hopital's Rule 


653  (2) 

Group Activity 2: Taylor Series Solutions to Differential Equations 


655  (2) 

Chapter 11 Probability and Calculus 


657  (48) 


657  (8) 

112 Continuous Random Variables 


665  (13) 

113 Expected Value, Standard Deviation, and Median 


678  (10) 

114 Special Probability Distributions 


688  (12) 

Important Terms and Symbols 


700  (1) 


700  (3) 

Group Activity 1: Beta Distributions 


703  (1) 

Group Activity 2: ChiSquare Distributions 


704  (1) 

Chapter 12 Trigonometric Functions 


705  (26) 

121 Trigonometric Functions Review 


706  (9) 

122 Derivatives of Trigonometric Functions 


715  (6) 

123 Integration of Trigonometric Functions 


721  (5) 

Important Terms and Symbols 


726  (1) 


727  (1) 

Group Activity 1: Seasonal Business Cycles 


728  (1) 

Group Activity 2: Heating Degree Days 


729  (2) 

Appendix A Basic Algebra Review 


731  (68) 

SelfTest on Basic Algebra 


731  (2) 


733  (6) 

A2 Algebra and Real Numbers 


739  (7) 

A3 Operations on Polynomials 


746  (7) 

A4 Factoring Polynomials 


753  (6) 

A5 Operations on Rational Expressions 


759  (7) 

A6 Integer Exponents and Scientific Notation 


766  (6) 

A7 Rational Exponents and Radicals 


772  (7) 

A8 Linear Equations and Inequalities in One Variable 


779  (10) 


789  (10) 

Appendix B Special Topics 


799  (48) 

B1 Sequences, Series, and Summation Notation 


799  (6) 

B2 Arithmetic and Geometric Sequences 


805  (8) 


813  (4) 

B4 Increments and Differentials 


817  (8) 


825  (11) 

B6 Double Integrals Over More General Regions 


836  (11) 


847  

Table I Basic Geometric Formulas 


847  (2) 

Table II Integration Formulas 


849  (4) 

Table III Area Under the Standard Normal Curve 


853  
Answers 

A1  
Index 

I1  
Library of Elementary Functions 

Inside front cover  
Applications Index 

Inside back cover  