Preface 

xiii  
Part One A Library of Elementary Functions 

1  (128) 

A Beginning Library of Elementary Functions 


3  (76) 


3  (20) 

Elementary Functions: Graphs and Transformations 


23  (13) 

Linear Functions and Straight Lines 


36  (17) 


53  (26) 

Important Terms and Symbols 


68  (1) 


69  (5) 

Group Activity 1: Introduction to Regression Analysis 


74  (1) 

Group Activity 2: Mathematical Modeling in Business 


75  (4) 

Additional Elementary Functions 


79  (50) 

Polynomial and Rational Functions 


79  (17) 


96  (14) 


110  (19) 

Important Terms and Symbols 


122  (1) 


122  (3) 

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


125  (1) 

Group Activity 2: Comparing Regression Models 


125  (4) 
Part Two Calculus 

129  (452) 


131  (94) 


132  (12) 


144  (18) 


162  (13) 

Derivatives of Constants, Power Forms, and Sums 


175  (14) 

Derivatives of Products and Quotients 


189  (8) 


197  (7) 

Marginal Analysis in Business and Economics 


204  (21) 

Important Terms and Symbols 


216  (1) 

Summary of Rules of Differentiation 


216  (1) 


217  (4) 

Group Activity 1: Minimal Average Cost 


221  (1) 

Group Activity 2: Numerical Differentiation on a Graphing Utility 


222  (3) 

Graphing and Optimization 


225  (90) 


226  (16) 

First Derivative and Graphs 


242  (17) 

Second Derivative and Graphs 


259  (16) 

Curve Sketching Techniques: Unified and Extended 


275  (17) 

Optimization: Absolute Maxima and Minima 


292  (23) 

Important Terms and Symbols 


308  (1) 


309  (4) 

Group Activity 1: Maximizing Profit 


313  (1) 

Group Activity 2: Minimizing Construction Costs 


313  (2) 

Additional Derivative Topics 


315  (48) 

The Constant e and Continuous Compound Interest 


315  (7) 

Derivatives of Logarithmic and Exponential Functions 


322  (12) 


334  (11) 


345  (7) 


352  (11) 

Important Terms and Symbols 


358  (1) 

Additional Rules of Differentiation 


358  (1) 


358  (2) 

Group Activity 1: Elasticity of Demand 


360  (1) 

Group Activity 2: Point of Diminishing Returns 


361  (2) 


363  (82) 

Antiderivatives and Indefinite Integrals 


363  (15) 

Integration by Substitution 


378  (12) 

Differential Equations; Growth and Decay 


390  (11) 

GeometricNumeric Introduction to the Definite Integral 


401  (16) 

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


417  (28) 

Important Terms and Symbols 


435  (1) 

Integration Formulas and Properties 


436  (1) 


436  (4) 

Group Activity 1: Simpson's Rule 


440  (3) 

Group Activity 2: BellShaped Curves 


443  (2) 

Additional Integration Topics 


445  (44) 


445  (11) 

Applications in Business and Economics 


456  (13) 


469  (8) 


477  (12) 

Important Terms and Symbols 


484  (1) 


485  (2) 

Group Activity 1: Analysis of Income Concentration from Raw Data 


487  (1) 

Group Activity 2: Grain Exchange 


488  (1) 


489  (68) 

Functions of Several Variables 


489  (11) 


500  (9) 


509  (9) 

Maxima and Minima Using Lagrange Multipliers 


518  (10) 


528  (11) 

Double Integrals over Rectangular Regions 


539  (18) 

Important Terms and Symbols 


549  (1) 


550  (3) 

Group Activity 1: City Planning 


553  (1) 

Group Activity 2: Numerical Integration of Multivariable Functions 


554  (3) 


557  (24) 

Trigonometric Functions Review 


558  (8) 

Derivatives of Trigonometric Functions 


566  (6) 

Integration of Trigonometric Functions 


572  (9) 

Important Terms and Symbols 


577  (1) 


578  (1) 

Group Activity 1: Seasonal Business Cycles 


579  (1) 

Group Activity 2: Heating Degree Days 


580  (1) 
APPENDIX A Basic Algebra Review 

581  (68) 

SelfTest on Basic Algebra 


581  (2) 


583  (6) 

A2 Algebra and Real Numbers 


589  (7) 

A3 Operations on Polynomials 


596  (7) 

A4 Factoring Polynomials 


603  (6) 

A5 Operations on Rational Expressions 


609  (6) 

A6 Integer Exponents and Scientific Notation 


615  (6) 

A7 Rational Exponents and Radicals 


621  (7) 

A8 Linear Equations and Inequalities in One Variable 


628  (10) 


638  (11) 
APPENDIX B Special Topics 

649  (20) 

B1 Sequences, Series, and Summation Notation 


649  (7) 

B2 Arithmetic and Geometric Sequences 


656  (8) 


664  (5) 
APPENDIX C Tables 

669  (1) 

Table I Basic Geometric Formulas 


669  (2) 

Table II Integration Formulas 


671  
Answers 

A1  
Index 

I1  