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Calculus 6th Ed. By James Stewart
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Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, Seventh Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!
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CALCULUS
EARLY TRANSCENDENTALS
SIXTH EDITION
JAMES STEWART
McMASTER UNIVERSITY
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K05T07
Calculus Early Transcendentals, 6e
James Stewart
iii
Preface xi
To the Student xxiii
Diagnostic Tests xxiv
A PREVIEW OF CALCULUS 2
FUNCTIONS AND MODELS 10
1.1 Four Ways to Represent a Function 11
1.2 Mathematical Models: A Catalog of Essential Functions 24
1.3 New Functions from Old Functions 37
1.4 Graphing Calculators and Computers 46
1.5 Exponential Functions 52
1.6 Inverse Functions and Logarithms 59
Review 73
Principles of Problem Solving 76
LIMITS AND DERIVATIVES 82
2.1 The Tangent and Velocity Problems 83
2.2 The Limit of a Function 88
2.3 Calculating Limits Using the Limit Laws 99
2.4 The Precise Definition of a Limit 109
2.5 Continuity 119
2.6 Limits at Infinity; Horizontal Asymptotes 130
2.7 Derivatives and Rates of Change 143
Writing Project
N
Early Methods for Finding Tangents 153
2.8 The Derivative as a Function 154
Review 165
Problems Plus 170
2
1
CONTENTS
DIFFERENTIATION RULES 172
3.1 Derivatives of Polynomials and Exponential Functions 173
Applied Project
N
Building a Better Roller Coaster 182
3.2 The Product and Quotient Rules 183
3.3 Derivatives of Trigonometric Functions 189
3.4 The Chain Rule 197
Applied Project
N
Where Should a Pilot Start Descent? 206
3.5 Implicit Differentiation 207
3.6 Derivatives of Logarithmic Functions 215
3.7 Rates of Change in the Natural and Social Sciences 221
3.8 Exponential Growth and Decay 233
3.9 Related Rates 241
3.10 Linear Approximations and Differentials 247
Laboratory Project
N
Taylor Polynomials 253
3.11 Hyperbolic Functions 254
Review 261
Problems Plus 265
APPLICATIONS OF DIFFERENTIATION 270
4.1 Maximum and Minimum Values 271
Applied Project
N
The Calculus of Rainbows 279
4.2 The Mean Value Theorem 280
4.3 How Derivatives Affect the Shape of a Graph 287
4.4 Indeterminate Forms and L’Hospital’s Rule 298
Writing Project
N
The Origins of L’Hospital’s Rule 307
4.5 Summary of Curve Sketching 307
4.6 Graphing with Calculus and Calculators 315
4.7 Optimization Problems 322
Applied Project
N
The Shape of a Can 333
4.8 Newton’s Method 334
4.9 Antiderivatives 340
Review 347
Problems Plus 351
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CONTENTS
CONTENTS
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v
INTEGRALS 354
5.1 Areas and Distances 355
5.2 The Definite Integral 366
Discovery Project
N
Area Functions 379
5.3 The Fundamental Theorem of Calculus 379
5.4 Indefinite Integrals and the Net Change Theorem 391
Writing Project
N
Newton, Leibniz, and the Invention of Calculus 399
5.5 The Substitution Rule 400
Review 408
Problems Plus 412
INTEGRALS 414
6.1 Areas between Curves 415
6.2 Volumes 422
6.3 Volumes by Cylindrical Shells 433
6.4 Work 438
6.5 Average Value of a Function 442
Applied Project
N
Where to Sit at the Movies 446
Review 446
Problems Plus 448.
TECHNIQUES OF INTEGRATION 452
7.1 Integration by Parts 453
7.2 Trigonometric Integrals 460
7.3 Trigonometric Substitution 467
7.4 Integration of Rational Functions by Partial Fractions 473
7.5 Strategy for Integration 483
7.6 Integration Using Tables and Computer Algebra Systems 489
Discovery Project
N
Patterns in Integrals 494
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