Calculus, 10th edition By Ron Larson.pdf

Calculus, 10th edition By Ron Larson 

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Preparation for Calculus 1
P.1 Graphs and Models 2
P.2 Linear Models and Rates of Change 10
P.3 Functions and Their Graphs 19
P.4 Fitting Models to Data 31
Review Exercises 37
P.S. Problem Solving 39
Limits and Their Properties 41
1.1 A Preview of Calculus 42
1.2 Finding Limits Graphically and Numerically 48
1.3 Evaluating Limits Analytically 59
1.4 Continuity and One-Sided Limits 70
1.5 Infinite Limits 83
Section Project: Graphs and Limits of
Trigonometric Functions 90
Review Exercises 91
P.S. Problem Solving 93
Differentiation 95
2.1 The Derivative and the Tangent Line Problem 96
2.2 Basic Differentiation Rules and Rates of Change 106
2.3 Product and Quotient Rules and Higher-Order
Derivatives 118
2.4 The Chain Rule 129
2.5 Implicit Differentiation 140
Section Project: Optical Illusions 147
2.6 Related Rates 148
Review Exercises 157
P.S. Problem Solving 159
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Applications of Differentiation 161
3.1 Extrema on an Interval 162
3.2 Rolle’s Theorem and the Mean Value Theorem 170
3.3 Increasing and Decreasing Functions and
the First Derivative Test 177
Section Project: Rainbows 186
3.4 Concavity and the Second Derivative Test 187
3.5 Limits at Infinity 195
3.6 A Summary of Curve Sketching 206
3.7 Optimization Problems 215
Section Project: Connecticut River 224
3.8 Newton’s Method 225
3.9 Differentials 231
Review Exercises 238
P.S. Problem Solving 241
Integration 243
4.1 Antiderivatives and Indefinite Integration 244
4.2 Area 254
4.3 Riemann Sums and Definite Integrals 266
4.4 The Fundamental Theorem of Calculus 277
Section Project: Demonstrating the
Fundamental Theorem 291
4.5 Integration by Substitution 292
4.6 Numerical Integration 305
Review Exercises 312
P.S. Problem Solving 315
Logarithmic, Exponential, and
Other Transcendental Functions 317
5.1 The Natural Logarithmic Function: Differentiation 318
5.2 The Natural Logarithmic Function: Integration 328
5.3 Inverse Functions 337
5.4 Exponential Functions: Differentiation and Integration 346
5.5 Bases Other than e and Applications 356
Section Project: Using Graphing Utilities to
Estimate Slope 365
5.6 Inverse Trigonometric Functions: Differentiation 366
5.7 Inverse Trigonometric Functions: Integration 375
5.8 Hyperbolic Functions 383
Section Project: St. Louis Arch 392
Review Exercises 393
P.S. Problem Solving 395
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Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Differential Equations 397
6.1 Slope Fields and Euler’s Method 398
6.2 Differential Equations: Growth and Decay 407
6.3 Separation of Variables and the Logistic Equation 415
6.4 First-Order Linear Differential Equations 424
Section Project: Weight Loss 430
Review Exercises 431
P.S. Problem Solving 433
Applications of Integration 435
7.1 Area of a Region Between Two Curves 436
7.2 Volume: The Disk Method 446
7.3 Volume: The Shell Method 457
Section Project: Saturn 465
7.4 Arc Length and Surfaces of Revolution 466
7.5 Work 477
Section Project:Tidal Energy 485
7.6 Moments, Centers of Mass, and Centroids 486
7.7 Fluid Pressure and Fluid Force 497
Review Exercises 503
P.S. Problem Solving 505
Integration Techniques, L’Hopital’s Rule,
and Improper Integrals 507
8.1 Basic Integration Rules 508
8.2 Integration by Parts 515
8.3 Trigonometric Integrals 524
Section Project: Power Lines 532
8.4 Trigonometric Substitution 533
8.5 Partial Fractions 542
8.6 Integration by Tables and Other Integration Techniques 551
8.7 Indeterminate Forms and L’Hopital’s Rule 557
8.8 Improper Integrals 568
Review Exercises 579
P.S. Problem Solving 581
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Infinite Series 583
9.1 Sequences 584
9.2 Series and Convergence 595
Section Project: Cantor’s Disappearing Table 604
9.3 The Integral Test and p-Series 605
Section Project:The Harmonic Series 611
9.4 Comparisons of Series 612
Section Project: Solera Method 618
9.5 Alternating Series 619
9.6 The Ratio and Root Tests 627
9.7 Taylor Polynomials and Approximations 636
9.8 Power Series 647
9.9 Representation of Functions by Power Series 657
9.10 Taylor and Maclaurin Series 664
Review Exercises 676
P.S. Problem Solving 679
Conics, Parametric Equations, and
Polar Coordinates 681
10.1 Conics and Calculus 682
10.2 Plane Curves and Parametric Equations 696
Section Project: Cycloids 705
10.3 Parametric Equations and Calculus 706
10.4 Polar Coordinates and Polar Graphs 715
Section Project: Anamorphic Art 724
10.5 Area and Arc Length in Polar Coordinates 725
10.6 Polar Equations of Conics and Kepler’s Laws 734
Review Exercises 742
P.S. Problem Solving 745
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Appendices
Appendix A: Proofs of Selected Theorems A2
Appendix B: Integration Tables A3
Appendix C: Precalculus Review (Web)*
C.1 Real Numbers and the Real Number Line
C.2 The Cartesian Plane
C.3 Review of Trigonometric Functions
Appendix D: Rotation and the General Second-Degree Equation (Web)*
Appendix E: Complex Numbers (Web)*
Appendix F: Business and Economic Applications (Web)*
Answers to All Odd-Numbered Exercises and Tests A7