

2  (56) 


4  (10) 


14  (14) 

The Cartesian Coordinate System 


28  (9) 


37  (21) 

Summary of Principal Formulas and Terms 


55  (1) 


56  (2) 

Functions, Limits, and the Derivative 


58  (124) 

Functions and Their Graphs 


60  (21) 

Using Technology: Graphing a Function 


76  (5) 


81  (9) 

Portfolio: Michael Marchlik 


86  (4) 

Functions and Mathematical Models 


90  (20) 

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


104  (6) 


110  (25) 

Using Technology: Finding the Limit of a Function 


130  (5) 

OneSided Limits and Continuity 


135  (20) 

Using Technology: Finding the Points of Discontinuity of a Function 


150  (5) 


155  (27) 

Using Technology: Graphing a Function and Its Tangent Lines 


176  (3) 

Summary of Principal Formulas and Terms 


179  (1) 


179  (3) 


182  (94) 

Basic Rules of Differentiation 


184  (14) 

Using Technology: Finding the Rate of Change of a Function 


192  (6) 

The Product and Quotient Rules 


198  (13) 

Using Technology: The Product and Quotient Rules 


208  (3) 


211  (13) 

Using Technology: Finding the Derivative of a Composite Function 


218  (6) 

Marginal Functions in Economics 


224  (16) 


240  (9) 

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


246  (3) 

Implicit Differentiation and Related Rates 


249  (12) 


261  (15) 


262  (8) 

Using Technology: Finding the Differential of a Function 


270  (3) 

Summary of Principal Formulas and Terms 


273  (1) 


274  (2) 

Applications of the Derivative 


276  (96) 

Applications of the First Derivative 


278  (23) 

Using Technology: Using the First Derivative to Analyze a Function 


296  (5) 

Applications of the Second Derivative 


301  (20) 

Using Technology: Finding the Inflection Points of a Function 


318  (3) 


321  (20) 

Using Technology: Analyzing the Properties of a Function 


334  (7) 


341  (16) 

Using Technology: Finding the Absolute Extrema of a Function 


354  (3) 


357  (15) 

Summary of Principal Terms 


369  (1) 


369  (3) 

Exponential and Logarithmic Functions 


372  (66) 


374  (9) 


380  (3) 


383  (8) 


391  (14) 

Portfolio: Misato Nakazaki 


403  (2) 

Differentiation of Exponential Functions 


405  (12) 


414  (3) 

Differentiation of Logarithmic Functions 


417  (8) 

Exponential Functions as Mathematical Models 


425  (13) 

Summary of Principal Formulas and Terms 


436  (1) 


437  (1) 


438  (110) 

Antiderivatives and the Rules of Integration 


440  (15) 

Integration by Substitution 


455  (11) 

Area and the Definite Integral 


466  (11) 

The Fundamental Theorem of Calculus 


477  (14) 

Using Technology: Evaluating Definite Integrals 


488  (3) 

Evaluating Definite Integrals 


491  (12) 

Using Technology: Evaluating Definite Integrals for PiecewiseDefined Functions 


500  (3) 


503  (16) 

Using Technology: Finding the Area Between Two Curves 


516  (3) 

Applications of the Definite Integral to Business and Economics 


519  (16) 

Using Technology: Consumers' Surplus and Producers' Surplus 


533  (2) 

Volumes of Solids of Revolution 


535  (13) 

Summary of Principal Formulas and Terms 


543  (1) 


544  (4) 

Additional Topics in Integration 


548  (48) 


550  (7) 

Integration Using Tables of Integrals 


557  (8) 


565  (17) 

Portfolio: James H. Chesebro 


580  (2) 


582  (14) 

Summary of Principal Formulas and Terms 


593  (1) 


594  (2) 

Calculus of Several Variables 


596  (94) 

Functions of Several Variables 


598  (10) 


608  (18) 

Using Technology: Finding Partial Derivatives at a Given Point 


622  (4) 

Maxima and Minima of Functions of Several Variables 


626  (11) 

The Method of Least Squares 


637  (13) 

Using Technology: Finding an Equation of a LeastSquares Line 


646  (4) 

Constrained Maxima and Minima and the Method of Lagrange Multipliers 


650  (13) 


663  (6) 


669  (8) 

Applications of Double Integrals 


677  (13) 

Summary of Principal Terms 


687  (1) 


687  (3) 


690  (36) 


692  (7) 


699  (7) 

Applications of Separable Differential Equations 


706  (10) 

Approximate Solutions of Differential Equations 


716  (10) 

Summary of Principal Terms 


724  (1) 


724  (2) 


726  (46) 

Probability Distributions of Random Variables 


728  (11) 

Using Technology: Graphing a Histogram 


736  (3) 

Expected Value and Standard Deviation 


739  (17) 

Using Technology: Finding the Mean and Standard Deviation 


754  (2) 


756  (16) 

Summary of Principal Formulas and Terms 


769  (1) 


770  (2) 

Taylor Polynomials and Infinite Series 


772  (80) 


774  (13) 


787  (9) 


796  (12) 

Series with Positive Terms 


808  (11) 

Power Series and Taylor Series 


819  (10) 


829  (10) 

The NewtonRaphson Method 


839  (13) 

Summary of Principal Formulas and Terms 


849  (1) 


850  (2) 


852  (47) 


854  (6) 

The Trigonometric Functions 


860  (11) 

Differentiation of Trigonometric Functions 


871  (16) 

Using Technology: Analyzing Trigonometric Functions 


884  (3) 

Integration of Trigonometric Functions 


887  (12) 

Using Technology: Evaluating Integrals of Trigonometric Functions 


892  (4) 

Summary of Principal Formulas and Terms 


896  (1) 


897  (2) 
Table 

899  (4) 

The Standard Normal Distribution 


900  (3) 
Answers to OddNumbered Exercises 

903  (42) 
Index 

945  