Preface 

ix  
Index of Applications 

xv  
Algebra Reference 

Polynomials 

xx  
Factoring 

xxiii  
Rational Expressions 

xxv  
Equations 

xxix  
Inequalities 

xxxv  
Exponents 

xl  
Radicals 

xliv  



Slope and Equations of a Line 


2  (13) 


15  (12) 

Linear Mathematical Models 


27  (10) 

Constructing a Mathematical Model 


37  (17) 


49  (3) 

Extended Application: Using Marginal Cost to Estimate the Cost of Educating Immigrants 


52  (2) 




54  (13) 


67  (8) 

Translations and Reflections of Functions 


75  (7) 

Polynomial and Rational Functions 


82  (14) 


96  (11) 


107  (14) 

Applications: Growth and Decay; Mathematics of Finance 


121  (23) 


134  (8) 

Extended Application: Characteristics of the Monkeyface Prickleback 


142  (2) 




144  (17) 


161  (7) 


168  (14) 

Definition of the Derivative 


182  (18) 

Graphical Differentiation 


200  (12) 


206  (6) 

Calculating the Derivative 



Techniques for Finding Derivatives 


212  (13) 

Derivatives of Products and Quotients 


225  (7) 


232  (10) 

Derivatives of Exponential Functions 


242  (6) 

Derivatives of Logarithmic Functions 


248  (10) 


254  (4) 

Graphs and the Derivative 



Increasing and Decreasing Functions 


258  (10) 


268  (13) 

Higher Derivatives, Concavity, and the Second Derivative Test 


281  (14) 


295  (13) 


303  (5) 

Applications of the Derivative 




308  (8) 


316  (11) 

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


327  (9) 


336  (5) 


341  (6) 

Differentials: Linear Approximation 


347  (13) 


353  (3) 

Extended Application: A Total Cost Model for a Training Program 


356  (1) 

Extended Application: The Effect of Oil Price on the Optimal Speed of Ships 


357  (3) 




360  (11) 


371  (8) 

Area and the Definite Integral 


379  (13) 

The Fundamental Theorem of Calculus 


392  (10) 

The Area Between Two Curves 


402  (9) 


411  (17) 


421  (4) 

Extended Application: Estimating Depletion Dates for Minerals 


425  (3) 

Further Techniques and Applications of Integration 



Integration by Parts; Tables of Integrals 


428  (8) 


436  (6) 


442  (8) 


450  (12) 


455  (3) 

Extended Application: How Much Does a Warranty Cost? 


458  (4) 



Functions of Several Variables 


462  (11) 


473  (10) 


483  (9) 


492  (7) 

Total Differentials and Approximations 


499  (5) 


504  (20) 


516  (5) 

Extended Application: Lagrange Multipliers for a Predator 


521  (3) 



Solutions of Elementary and Separable Differential Equations 


524  (12) 

Linear FirstOrder Differential Equations 


536  (5) 


541  (7) 

Applications of Differential Equations 


548  (16) 


558  (3) 

Extended Application: Pollution of the Great Lakes 


561  (3) 



Continuous Probability Models 


564  (7) 

Expected Value and Variance of Continuous Random Variables 


571  (6) 

Special Probability Density Functions 


577  (19) 


589  (3) 

Extended Application: A CropPlanting Model 


592  (4) 

The Trigonometric Functions 



Definitions of the Trigonometric Functions 


596  (12) 

Derivatives of Trigonometric Functions 


608  (6) 

Integrals of Trigonometric Functions 


614  (5) 


619  (4) 


623  (3) 

Extended Application: Light Intensity in Water 


626  
Tables 


Table 1: Formulas from Geometry 


A1  

Table 2: Area Under a Normal Curve 


A2  


A4  

Table 4: Integrals Involving Trigonometric Functions 


A5  
Answers to Selected Exercises 

A7  
Index 

I1  