# Calculus, Ninth Edition PDF by James Stewart, Daniel Clegg and Saleem Watson

## Calculus, Ninth Edition

By James Stewart, Daniel Clegg and Saleem Watson

Contents:

Preface x

A Tribute to James Stewart xxii

Technology in the Ninth Edition xxiv

To the Student xxv

Diagnostic Tests xxvi

A Preview of Calculus 1

1 Functions and Limits 7

1.1 Four Ways to Represent a Function 8

1.2 Mathematical Models: A Catalog of Essential Functions 21

1.3 New Functions from Old Functions 36

1.4 The Tangent and Velocity Problems 45

1.5 The Limit of a Function 51

1.6 Calculating Limits Using the Limit Laws 62

1.7 The Precise Definition of a Limit 73

1.8 Continuity 83

Review 95

Principles of Problem Solving 99

2 Derivatives 107

2.1 Derivatives and Rates of Change 108

writing project • Early Methods for Finding Tangents 120

2.2 The Derivative as a Function 120

2.3 Differentiation Formulas 133

applied project • Building a Better Roller Coaster 147

2.4 Derivatives of Trigonometric Functions 148

2.5 The Chain Rule 156

applied project • Where Should a Pilot Start Descent? 164

2.6 Implicit Differentiation 164

discovery project • Families of Implicit Curves 172

2.7 Rates of Change in the Natural and Social Sciences 172

2.8 Related Rates 185

2.9 Linear Approximations and Differentials 192

discovery project • Polynomial Approximations 198

Review 199

Problems Plus 204

3 Applications of Differentiation 209

3.1 Maximum and Minimum Values 210

applied project • The Calculus of Rainbows 219

3.2 The Mean Value Theorem 220

3.3 What Derivatives Tell Us about the Shape of a Graph 226

3.4 Limits at Infinity; Horizontal Asymptotes 237

3.5 Summary of Curve Sketching 250

3.6 Graphing with Calculus and Technology 258

3.7 Optimization Problems 265

applied project • The Shape of a Can 278

applied project • Planes and Birds: Minimizing Energy 279

3.8 Newton’s Method 280

3.9 Antiderivatives 285

Review 292

Problems Plus 297

4 Integrals 301

4.1 The Area and Distance Problems 302

4.2 The Definite Integral 314

discovery project • Area Functions 328

4.3 The Fundamental Theorem of Calculus 329

4.4 Indefinite Integrals and the Net Change Theorem 339

writing project • Newton, Leibniz, and the Invention of Calculus 348

4.5 The Substitution Rule 349

Review 357

Problems Plus 361

5 Applications of Integration 363

5.1 Areas Between Curves 364

applied project • The Gini Index 373

5.2 Volumes 374

5.3 Volumes by Cylindrical Shells 388

5.4 Work 395

5.5 Average Value of a Function 401

applied project • Calculus and Baseball 404

Review 405

Problems Plus 408

6 Inverse Functions: 411

Exponential, Logarithmic, and Inverse Trigonometric Functions

6.1 Inverse Functions and Their Derivatives 412

Instructors may cover either Sections 6.2–6.4 or Sections 6.2*–6.4*. See the Preface.

6.2 Exponential Functions and

Their Derivatives 420

6.2* The Natural Logarithmic

Function 451

6.3 Logarithmic

Functions 433

6.3* The Natural Exponential

Function 460

6.4 Derivatives of Logarithmic

Functions 440

6.4* General Logarithmic and

Exponential Functions 468

6.5 Exponential Growth and Decay 478

applied project • Controlling Red Blood Cell Loss During Surgery 486

6.6 Inverse Trigonometric Functions 486

applied project • Where to Sit at the Movies 495

6.7 Hyperbolic Functions 495

6.8 Indeterminate Forms and l’Hospital’s Rule 503

writing project • The Origins of l’Hospital’s Rule 515

Review 516

Problems Plus 520

7 Techniques of Integration 523

7.1 Integration by Parts 524

7.2 Trigonometric Integrals 531

7.3 Trigonometric Substitution 538

7.4 Integration of Rational Functions by Partial Fractions 545

7.5 Strategy for Integration 555

7.6 Integration Using Tables and Technology 561

discovery project • Patterns in Integrals 566

7.7 Approximate Integration 567

7.8 Improper Integrals 580

Review 590

Problems Plus 594

8 Further Applications of Integration 597

8.1 Arc Length 598

discovery project • Arc Length Contest 605

8.2 Area of a Surface of Revolution 605

discovery project • Rotating on a Slant 613

8.3 Applications to Physics and Engineering 614

discovery project • Complementary Coffee Cups 625

8.4 Applications to Economics and Biology 625

8.5 Probability 630

Review 638

Problems Plus 640

9 Differential Equations 643

9.1 Modeling with Differential Equations 644

9.2 Direction Fields and Euler’s Method 650

9.3 Separable Equations 659

applied project • How Fast Does a Tank Drain? 668

9.4 Models for Population Growth 669

9.5 Linear Equations 679

applied project • Which Is Faster, Going Up or Coming Down? 686

9.6 Predator-Prey Systems 687

Review 694

Problems Plus 697

10 Parametric Equations and Polar Coordinates 699

10.1 Curves Defined by Parametric Equations 700

discovery project • Running Circles Around Circles 710

10.2 Calculus with Parametric Curves 711

discovery project • Bézier Curves 722

10.3 Polar Coordinates 722

discovery project • Families of Polar Curves 732

10.4 Calculus in Polar Coordinates 732

10.5 Conic Sections 740

10.6 Conic Sections in Polar Coordinates 749

Review 757

Problems Plus 760

11 Sequences, Series, and Power Series 761

11.1 Sequences 762

discovery project • Logistic Sequences 776

11.2 Series 776

11.3 The Integral Test and Estimates of Sums 789

11.4 The Comparison Tests 798

11.5 Alternating Series and Absolute Convergence 803

11.6 The Ratio and Root Tests 812

11.7 Strategy for Testing Series 817

11.8 Power Series 819

11.9 Representations of Functions as Power Series 825

11.10 Taylor and Maclaurin Series 833

discovery project • An Elusive Limit 848

writing project • How Newton Discovered the Binomial Series 849

11.11 Applications of Taylor Polynomials 849

applied project • Radiation from the Stars 858

Review 859

Problems Plus 863

12 Vectors and the Geometry of Space 867

12.1 Three-Dimensional Coordinate Systems 868

12.2 Vectors 874

discovery project • The Shape of a Hanging Chain 884

12.3 The Dot Product 885

12.4 The Cross Product 893

discovery project • The Geometry of a Tetrahedron 902

12.5 Equations of Lines and Planes 902

discovery project • Putting 3D in Perspective 912

12.6 Cylinders and Quadric Surfaces 913

Review 921

Problems Plus 925

13 Vector Functions 927

13.1 Vector Functions and Space Curves 928

13.2 Derivatives and Integrals of Vector Functions 936

13.3 Arc Length and Curvature 942

13.4 Motion in Space: Velocity and Acceleration 954

applied project • Kepler’s Laws 963

Review 965

Problems Plus 968

14 Partial Derivatives 971

14.1 Functions of Several Variables 972

14.2 Limits and Continuity 989

14.3 Partial Derivatives 999

discovery project • Deriving the Cobb-Douglas Production Function 1011

14.4 Tangent Planes and Linear Approximations 1012

applied project • The Speedo LZR Racer 1022

14.5 The Chain Rule 1023

14.6 Directional Derivatives and the Gradient Vector 1032

14.7 Maximum and Minimum Values 1046

discovery project • Quadratic Approximations and Critical Points 1057

14.8 Lagrange Multipliers 1058

applied project • Rocket Science 1066

applied project • Hydro-Turbine Optimization 1068

Review 1069

Problems Plus 1073

15 Multiple Integrals 1075

15.1 Double Integrals over Rectangles 1076

15.2 Double Integrals over General Regions 1089

15.3 Double Integrals in Polar Coordinates 1100

15.4 Applications of Double Integrals 1107

15.5 Surface Area 1117

15.6 Triple Integrals 1120

discovery project • Volumes of Hyperspheres 1133

15.7 Triple Integrals in Cylindrical Coordinates 1133

discovery project • The Intersection of Three Cylinders 1139

15.8 Triple Integrals in Spherical Coordinates 1140

applied project • Roller Derby 1146

15.9 Change of Variables in Multiple Integrals 1147

Review 1155

Problems Plus 1159

16 Vector Calculus 1161

16.1 Vector Fields 1162

16.2 Line Integrals 1169

16.3 The Fundamental Theorem for Line Integrals 1182

16.4 Green’s Theorem 1192

16.5 Curl and Divergence 1199

16.6 Parametric Surfaces and Their Areas 1208

16.7 Surface Integrals 1220

16.8 Stokes’ Theorem 1233

16.9 The Divergence Theorem 1239

16.10 Summary 1246

Review 1247

Problems Plus 1251

Appendixes A1

A Numbers, Inequalities, and Absolute Values A2

B Coordinate Geometry and Lines A10

C Graphs of Second-Degree Equations A16

D Trigonometry A24

E Sigma Notation A36

F Proofs of Theorems A41

G Answers to Odd-Numbered Exercises A51

Index A135

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