Thomas' Calculus 15th Edition By Joel Hass, Christopher Heil, Maurice Weir, Przemyslaw Bogacki (Solutions Manual)

SOLUTIONS MANUAL
JENNIFER A. BLUE



THOMAS ’ CALCULUS
L ATE T RANSCENDENTALS
FIFTEENTH EDITION

Based on the original work by

George B. Thomas, Jr

as revised by
Joel Hass

Christopher Heil

Maurice D. Weir


All Chapters Arranged Reverse: Chapter 11-1

, TABLE OF CONTENTS
1 Functions 1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 9
1.3 Trigonometric Functions 19
1.4 Graphing with Software 27
Practice Exercises 32
Additional and Advanced Exercises 40


2 Limits and Continuity 43
2.1 Rates of Change and Tangents to Curves 43
2.2 Limit of a Function and Limit Laws 47
2.3 The Precise Definition of a Limit 57
2.4 One-Sided Limits 65
2.5 Continuity 70
2.6 Limits Involving Infinity; Asymptotes of Graphs 75
Practice Exercises 86
Additional and Advanced Exercises 92


3 Derivatives 99
3.1 Tangents and the Derivative at a Point 99
3.2 The Derivative as a Function 105
3.3 Differentiation Rules 116
3.4 The Derivative as a Rate of Change 121
3.5 Derivatives of Trigonometric Functions 127
3.6 The Chain Rule 134
3.7 Implicit Differentiation 146
3.8 Related Rates 155
3.9 Linearization and Differentials 160
Practice Exercises 167
Additional and Advanced Exercises 180




Copyright  2023 Pearson Education, Inc.
iii

,4 Applications of Derivatives 187
4.1 Extreme Values of Functions on Closed Intervals 187
4.2 The Mean Value Theorem 195
4.3 Monotonic Functions and the First Derivative Test 201
4.4 Concavity and Curve Sketching 213
4.5 Applied Optimization 236
4.6 Newton's Method 251
4.7 Antiderivatives 255
Practice Exercises 263
Additional and Advanced Exercises 277


5 Integrals 285
5.1 Area and Estimating with Finite Sums 285
5.2 Sigma Notation and Limits of Finite Sums 290
5.3 The Definite Integral 296
5.4 The Fundamental Theorem of Calculus 312
5.5 Indefinite Integrals and the Substitution Method 322
5.6 Definite Integral Substitutions and the Area Between Curves 328
Practice Exercises 345
Additional and Advanced Exercises 355


6 Applications of Definite Integrals 361
6.1 Volumes Using Cross-Sections 361
6.2 Volumes Using Cylindrical Shells 373
6.3 Arc Length 384
6.4 Areas of Surfaces of Revolution 391
6.5 Work and Fluid Forces 397
6.6 Moments and Centers of Mass 408
Practice Exercises 422
Additional and Advanced Exercises 432




Copyright  2023 Pearson Education, Inc.
iv

, 7 Transcendental Functions 439
7.1 Inverse Functions and Their Derivatives 439
7.2 Natural Logarithms 449
7.3 Exponential Functions 457
7.4 Exponential Change and Separable Differential Equations 472
7.5 Indeterminate Forms and L’Hôpital’s Rule 478
7.6 Inverse Trigonometric Functions 487
7.7 Hyperbolic Functions 501
7.8 Relative Rates of Growth 510
Practice Exercises 515
Additional and Advanced Exercises 529


8 Techniques of Integration 533
8.1 Using Basic Integration Formulas 533
8.2 Integration by Parts 544
8.3 Trigonometric Integrals 558
8.4 Trigonometric Substitutions 567
8.5 Integration of Rational Functions by Partial Fractions 577
8.6 Integral Tables and Computer Algebra Systems 588
8.7 Numerical Integration 599
8.8 Improper Integrals 612
8.9 Probability 626
Practice Exercises 634
Additional and Advanced Exercises 648


9 First-Order Differential Equations 657
9.1 Solutions, Slope Fields, and Euler's Method 657
9.2 First-Order Linear Equations 667
9.3 Applications 671
9.4 Graphical Solutions of Autonomous Equations 675
9.5 Systems of Equations and Phase Planes 683
Practice Exercises 688
Additional and Advanced Exercises 696




Copyright  2023 Pearson Education, Inc.
v