Instructor's Solutions Manual to Thomas' Calculus, 12th Edition

Title: Instructor\'s Solutions Manual, Single Variable, 12/E......Page 1
ISBN-13: 978-0-321-60807-9......Page 2
PREFACE TO THE INSTRUCTOR......Page 3
Table of Contents......Page 4
1.1 FUNCTIONS AND THEIR GRAPHS......Page 7
1.2 COMBINING FUNCTIONS; SHIFTING AND SCALING GRAPHS......Page 14
1.3 TRIGONOMETRIC FUNCTIONS......Page 25
1.4 GRAPHING WITH CALCULATORS AND COMPUTERS......Page 32
CHAPTER 1 PRACTICE EXERCISES......Page 36
CHAPTER 1 ADDITIONAL AND ADVANCED EXERCISES......Page 44
2.1 RATES OF CHANGE AND TANGENTS TO CURVES......Page 49
2.2 LIMIT OF A FUNCTION AND LIMIT LAWS......Page 52
2.3 THE PRECISE DEFINITION OF A LIMIT......Page 61
2.4 ONE-SIDED LIMITS......Page 69
2.5 CONTINUITY......Page 73
2.6 LIMITS INVOLVING INFINITY; ASMYPTOTES OF GRAPHS......Page 79
CHAPTER 2 PRACTICE EXERCISES......Page 88
CHAPTER 2 ADDITIONAL AND ADVANCED EXERCISES......Page 92
3.1 TANGENTS AND THE DERIVATIVE AT A POINT......Page 99
3.2 THE DERIVATIVE AS A FUNCTION......Page 105
3.3 DIFFERENTIATION RULES......Page 115
3.4 THE DERIVATIVE AS A RATE OF CHANGE......Page 120
3.5 DERIVATIVES OF TRIGONOMETRIC FUNCTIONS......Page 126
3.6 THE CHAIN RULE......Page 133
3.7 IMPLICIT DIFFERENTIATION......Page 141
3.8 RELATED RATES......Page 148
3.9 LINEARIZATION AND DIFFERENTIALS......Page 152
CHAPTER 3 PRACTICE EXERCISES......Page 157
CHAPTER 3 ADDITIONAL AND ADVANCED EXERCISES......Page 168
4.1 EXTREME VALUES OF FUNCTIONS......Page 173
4.2 THE MEAN VALUE THEOREM......Page 185
4.3 MONOTONIC FUNCTIONS AND THE FIRST DERIVATIVE TEST......Page 190
4.4 CONCAVITY AND CURVE SKETCHING......Page 202
4.5 APPLIED OPTIMIZATION......Page 222
4 6 NEWTON\'S METHOD......Page 235
4.7 ANTIDERIVATIVES......Page 239
CHAPTER 4 PRACTICE EXERCISES......Page 245
CHAPTER 4 ADDITIONAL AND ADVANCED EXERCISES......Page 257
5.1 AREA AND ESTIMATING WITH FINITE SUMS......Page 263
5.2 SIGMA NOTATION AND LIMITS OF FINITE SUMS......Page 268
5.3 THE DEFINITE INTEGRAL......Page 274
5.4 THE FUNDAMENTAL THEOREM OF CALCULUS......Page 288
5.5 INDEFINTE INTEGRALS AND THE SUBSTITUTION RULE......Page 296
5.6 SUBSTITUTION AND AREA BETWEEN CURVES......Page 302
CHAPTER 5 PRACTICE EXERCISES......Page 316
CHAPTER 5 ADDITIONAL AND ADVANCED EXERCISES......Page 326
6.1 VOLUMES USING CROSS-SECTIONS......Page 333
6.2 VOLUME USING CYLINDRICAL SHELLS......Page 343
6.3 ARC LENGTHS......Page 353
6.4 AREAS OF SURFACES OF REVOLUTION......Page 359
6.5 WORK AND FLUID FORCES......Page 364
6.6 MOMENTS AND CENTERS OF MASS......Page 371
CHAPTER 6 PRACTICE EXERCISES......Page 382
CHAPTER 6 ADDITIONAL AND ADVANCED EXERCISES......Page 390
7.1 INVERSE FUNCTIONS AND THEIR DERIVATIVES......Page 395
7.2 NATURAL LOGARITHMS......Page 402
7.3 EXPONENTIAL FUNCTIONS......Page 409
7.4 EXPONENTIAL CHANGE AND SEPARABLE DIFFERENTIAL EQUATIONS......Page 420
7.5 INDETERMINATE FORMS AND L\'HO^PITAL\'S RULE......Page 424
7.6 INVERSE TRIGONOMETRIC FUNCTIONS......Page 431
7.7 HYPERBOLIC FUNCTIONS......Page 442
7.8 RELATIVE RATES OF GROWTH......Page 449
CHAPTER 7 PRACTICE EXERCISES......Page 453
CHAPTER 7 ADDITIONAL AND ADVANCED EXERCISES......Page 464
8.1 INTEGRATION BY PARTS......Page 467
8.2 TRIGONOMETRIC INTEGRALS......Page 477
8.3 TRIGONOMETRIC SUBSTITUTIONS......Page 484
8.4 INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS......Page 490
8.5 INTEGRAL TABLES AND COMPUTER ALGEBRA SYSTEMS......Page 497
8.6 NUMERICAL INTEGRATION......Page 508
8.7 IMPROPER INTEGRALS......Page 516
CHAPTER 8 PRACTICE EXERCISES......Page 524
CHAPTER 8 ADDITIONAL AND ADVANCED EXERCISES......Page 534
9.1 SOLUTIONS, SLOPE FIELDS AND EULER\'S METHOD......Page 543
9.2 FIRST-ORDER LINEAR DIFFERENTIAL EQUATIONS......Page 549
9.3 APPLICATIONS......Page 552
9.4 GRAPHICAL SOUTIONS OF AUTONOMOUS EQUATIONS......Page 555
9.5 SYSTEMS OF EQUATIONS AND PHASE PLANES......Page 563
CHAPTER 9 PRACTICE EXERCISES......Page 568
CHAPTER 9 ADDITIONAL AND ADVANCED EXERCISES......Page 573
10.1 SEQUENCES......Page 575
10.2 INFINITE SERIES......Page 583
10.3 THE INTEGRAL TEST......Page 589
10.4 COMPARISON TESTS......Page 596
10.5 THE RATIO AND ROOT TESTS......Page 603
10.6 ALTERNATING SERIES, ABSOLUTE AND CONDITIONAL CONVERGENCE......Page 608
10.7 POWER SERIES......Page 614
10.8 TAYLOR AND MACLAURIN SERIES......Page 623
10.9 CONVERGENCE OF TAYLOR SERIES......Page 627
10.10 THE BINOMIAL SERIES......Page 633
CHAPTER 10 PRACTICE EXERCISES......Page 640
CHAPTER 10 ADDITIONAL AND ADVANCED EXERCISES......Page 648
11.1 PARAMETRIZATIONS OF PLANE CURVES......Page 653
11.2 CALCULUS WITH PARAMETRIC CURVES......Page 660
11.3 POLAR COORDINATES......Page 668
11.4 GRAPHING IN POLAR COORDINATES......Page 673
11.5 AREA AND LENGTHS IN POLAR COORDINATES......Page 680
11.6 CONIC SECTIONS......Page 685
11.7 CONICS IN POLAR COORDINATES......Page 695
CHAPTER 11 PRACTICE EXERCISES......Page 705
CHAPTER 11 ADDITIONAL AND ADVANCED EXERCISES......Page 715