A Word from the Authors (Preface) 

ix  
Features 

xi  


1  (39) 

Eruptions of Old Faithful 


1  (1) 


2  (8) 

Linear Models and Rates of Change 


10  (9) 

Functions and Their Graphs 


19  (11) 


30  (10) 


36  (2) 


38  (2) 

Limits and Their Properties 


40  (52) 

Swimming Speed: Taking It to the Limit 


40  (2) 


42  (6) 

Finding Limits Graphically and Numerically 


48  (9) 

Evaluating Limits Analytically 


57  (11) 

Continuity and OneSided Limits 


68  (12) 


80  (12) 

Section Project: Graphs and Limits of Trigonometric Functions 


87  (1) 


88  (2) 


90  (2) 


92  (66) 

Gravity: Finding It Experimentally 


92  (2) 

The Derivative and the Tangent Line Problem 


94  (11) 

Basic Differentiation Rules and Rates of Change 


105  (12) 

The Product and Quotient Rules and HigherOrder Derivatives 


117  (10) 


127  (10) 


137  (7) 

Section Project: Optical Illusions 


143  (1) 


144  (14) 


153  (3) 


156  (2) 

Applications of Differentiation 


158  (82) 

Packaging: The Optimal Form 


158  (2) 


160  (8) 

Rolle's Theorem and the Mean Value Theorem 


168  (6) 

Increasing and Decreasing Functions and the First Derivative Test 


174  (10) 

Section Project: Rainbows 


183  (1) 

Concavity and the Second Derivative Test 


184  (8) 


192  (10) 

A Summary of Curve Sketching 


202  (9) 


211  (11) 

Section Project: Connecticut River 


211  (11) 


222  (6) 


228  (12) 


235  (3) 


238  (2) 


240  (72) 

The Wankel Rotary Engine and Area 


240  (2) 

Antiderivatives and Indefinite Integration 


242  (11) 


253  (12) 

Reimann Sums and Definite Integrals 


265  (10) 

The Fundamental Theorem of Calculus 


275  (13) 

Section Project: Demonstrating the Fundamental Theorem 


287  (1) 

Integration by Substitution 


288  (12) 


300  (12) 


307  (3) 


310  (2) 

Logarithmic, Exponential, and Other Transcendental Functions 


312  (98) 


312  (2) 

The Natural Logarithmic Function: Differentiation 


314  (10) 

The Natural Logarithmic Function: Integration 


324  (8) 


332  (9) 

Exponential Functions: Differentiation and Integration 


341  (10) 

Bases Other Than e and Applications 


351  (10) 

Section Project: Using Graphing Utilities to Estimate Slope 


360  (1) 

Differential Equations: Growth and Decay 


361  (8) 

Differential Equations: Separation of Variables 


369  (11) 

Inverse Trigonometric Functions: Differentiation 


380  (8) 

Inverse Trigonometric Functions: Integration 


388  (7) 


395  (15) 

Section Project: St. Louis Arch 


405  (1) 


405  (3) 


408  (2) 

Applications of Integration 


410  (70) 


410  (2) 

Area of a Region Between Two Curves 


412  (9) 


421  (11) 


432  (8) 


439  (1) 

Arc Length and Surfaces of Revolution 


440  (10) 


450  (9) 

Section Project: Tidal Energy 


458  (1) 

Moments, Centers of Mass, and Centroids 


459  (11) 

Fluid Pressure and Fluid Force 


470  (10) 


476  (2) 


478  (2) 

Integration Techniques, L'Hopital's Rule, and Improper Integrals 


480  (74) 


480  (2) 


482  (6) 


488  (9) 


497  (9) 

Section Project: Power Lines 


505  (1) 

Trigonometric Substitution 


506  (9) 


515  (9) 

Integration by Tables and Other Integration Techniques 


524  (6) 

Indeterminate Forms and L'Hopital's Rule 


530  (10) 


540  (14) 


550  (2) 


552  (2) 


554  (94) 

The Koch Snowflake: Infinite Perimeter? 


554  (2) 


556  (11) 


567  (10) 

Section Project: Cantor's Disappearing Table 


576  (1) 

The Integral Test and pSeries 


577  (6) 

Section Project: The Harmonic Series 


582  (1) 


583  (7) 

Section Project: Solera Method 


589  (1) 


590  (7) 


597  (8) 

Taylor Polynomials and Approximations 


605  (11) 


616  (9) 

Representation of Functions by Power Series 


625  (7) 

Taylor and Maclaurin Series 


632  (16) 


643  (3) 


646  (2) 

Conics, Parametric Equations, and Polar Coordinates 


648  (1) 


648  (2) 


650  (15) 

Plane Curves and Parametric Equations 


665  (9) 

Section Project: Cycloids 


674  (1) 

Parametric Equations and Calculus 


675  (9) 

Polar Coordinates and Polar Graphs 


684  (9) 

Section Project: Anamorphic Art 


693  (1) 

Area and Arc Length in Polar Coordinates 


694  (8) 

Polar Equations of Conics and Kepler's Laws 


702  (7) 


709  (3) 


712  
Appendices 

1  (1) 

Appendix A Additional Topics in Differential Equations 


2  (7) 

Appendix B Proofs of Selected Theorems 


9  (18) 

Appendix C Integration Tables 


27  (6) 

Appendix D Precalculus Review 



Appendix E Rotation and the General SecondDegree Equation 



Appendix F Complex Numbers 



Appendix G Business and Economic Applications 


Answers to OddNumbered Exercises 

33  (96) 
Index of Applications 

129  (4) 
Index 

133  