Preface 

ix  
Index of Applications 

xv  


xix  


xx  


xxiii  


xxv  


xxix  


xxxv  


xl  


xlv  


1  (48) 

Slopes and Equations of Lines 


2  (18) 

Linear Functions and Applications 


20  (10) 


30  (19) 


44  (3) 

Extended Application: Using Extrapolation to Predict Life Expectancy 


47  (2) 


49  (90) 


50  (14) 

Quadratic Functions; Translation and Reflection 


64  (12) 

Polynomials and Rational Functions 


76  (14) 


90  (13) 


103  (14) 

Applications: Growth and Decay; Mathematics of Finance 


117  (22) 


129  (8) 

Extended Application: Characteristics of the Monkeyface Prickleback 


137  (2) 


139  (72) 


140  (18) 


158  (8) 


166  (12) 

Definition of the Derivative 


178  (19) 

Graphical Differentiation 


197  (14) 


205  (6) 

Calculating the Derivative 


211  (58) 

Techniques for Finding Derivatives 


212  (16) 

Derivatives of Products and Quotients 


228  (8) 


236  (11) 

Derivatives of Exponential Functions 


247  (8) 

Derivatives of Logarithmic Functions 


255  (14) 


265  (4) 

Graphs and the Derivative 


269  (56) 

Increasing and Decreasing Functions 


270  (12) 


282  (13) 

Higher Derivatives, Concavity, and the Second Derivative Test 


295  (15) 


310  (15) 


320  (5) 

Applications of the Derivative 


325  (56) 


326  (9) 


335  (11) 

Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand 


346  (9) 


355  (7) 


362  (7) 

Differentials: Linear Approximation 


369  (12) 


376  (3) 

Extended Application: A Total Cost Model for a Training Program 


379  (2) 


381  (78) 


382  (12) 


394  (9) 

Area and the Definite Integral 


403  (14) 

The Fundamental Theorem of Calculus 


417  (11) 

The Area Between Two Curves 


428  (10) 


438  (21) 


450  (6) 

Extended Application: Estimating Depletion Dates for Minerals 


456  (3) 

Further Techniques and Applications of Integration 


459  (38) 


460  (9) 


469  (7) 


476  (8) 


484  (13) 


492  (3) 

Extended Application: Estimating Learning Curves in Manufacturing with Integrals 


495  (2) 


497  (71) 

Functions of Several Variables 


498  (12) 


510  (12) 


522  (10) 


532  (8) 

Total Differentials and Approximations 


540  (6) 


546  (22) 


559  (5) 

Extended Application: Using Multivariable Fitting to Create a Response Surface Design 


564  (4) 


568  (44) 

Solutions of Elementary and Separable Differential Equations 


569  (13) 

Linear FirstOrder Differential Equations 


582  (6) 


588  (8) 

Applications of Differential Equations 


596  (16) 


606  (4) 

Extended Application: Pollution of the Great Lakes 


610  (2) 


612  (41) 

Continuous Probability Models 


613  (10) 

Expected Value and Variance of Continuous Random Variables 


623  (9) 

Special Probability Density Functions 


632  (21) 


645  (5) 

Extended Application: Exponential Waiting Times 


650  (3) 


653  (56) 


654  (4) 

Annuities: An Application of Sequences 


658  (12) 


670  (9) 


679  (7) 


686  (10) 


696  (5) 


701  (8) 


706  (3) 

The Trigonometric Functions 


709  

Definitions of the Trigonometric Functions 


710  (16) 

Derivatives of Trigonometric Functions 


726  (12) 

Integrals of Trigonometric Functions 


738  


745  (4) 

Extended Application: The Shortest Time and the Cheapest Path 


749  



Table 1 Formulas of Geometry 


1  (1) 

Table 2 Area Under a Normal Curve 


2  (2) 


4  (1) 

Table 4 Integrals Involving Trigonometric Functions 


5  (2) 
Answers to Selected Exercises 

7  (44) 
Photo Acknowledgments 

51  
Index 

1  