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Introductory Inorganic And Physical Chemistry (MTHS111) Thomas Calculus

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Sandra Watson
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North-West University

Thomas Calculus 12Th Edition Instructor’S Solutions Manual

TABLE OF CONTENTS
1 Functions 1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 8
1.3 Trigonometric Functions 19
1.4 Graphing with Calculators and Computers 26
Practice Exercises 30
Additional and Advanced Exercises 38
2 Limits and Continuity 43
2.1 Rates of Change and Tangents to Curves 43
2.2 Limit of a Function and Limit Laws 46
2.3 The Precise Definition of a Limit 55
2.4 One-Sided Limits 63
2.5 Continuity 67
2.6 Limits Involving Infinity; Asymptotes of Graphs 73
Practice Exercises 82
Additional and Advanced Exercises 86
3 Differentiation 93
3.1 Tangents and the Derivative at a Point 93
3.2 The Derivative as a Function 99
3.3 Differentiation Rules 109
3.4 The Derivative as a Rate of Change 114
3.5 Derivatives of Trigonometric Functions 120
3.6 The Chain Rule 127
3.7 Implicit Differentiation 135
3.8 Related Rates 142
3.9 Linearizations and Differentials 146
Practice Exercises 151
Additional and Advanced Exercises 162
4 Applications of Derivatives 167
4.1 Extreme Values of Functions 167
4.2 The Mean Value Theorem 179
4.3 Monotonic Functions and the First Derivative Test 188
4.4 Concavity and Curve Sketching 196
4.5 Applied Optimization 216
4.6 Newton’s Method 229
4.7 Antiderivatives 233
Practice Exercises 239
Additional and Advanced Exercises 251
5 Integration 257
5.1 Area and Estimating with Finite Sums 257
5.2 Sigma Notation and Limits of Finite Sums 262
5.3 The Definite Integral 268
5.4 The Fundamental Theorem of Calculus 282
5.5 Indefinite Integrals and the Substitution Rule 290
5.6 Substitution and Area Between Curves 296
Practice Exercises 310
Additional and Advanced Exercises 320

6 Applications of Definite Integrals 327
6.1 Volumes Using Cross-Sections 327
6.2 Volumes Using Cylindrical Shells 337
6.3 Arc Lengths 347
6.4 Areas of Surfaces of Revolution 353
6.5 Work and Fluid Forces 358
6.6 Moments and Centers of Mass 365
Practice Exercises 376
Additional and Advanced Exercises 384
7 Transcendental Functions 389
7.1 Inverse Functions and Their Derivatives 389
7.2 Natural Logarithms 396
7.3 Exponential Functions 403
7.4 Exponential Change and Separable Differential Equations 414
7.5 Indeterminate Forms and L’Ho^pital’s Rule 418
7.6 Inverse Trigonometric Functions 425
7.7 Hyperbolic Functions 436
7.8 Relative Rates of Growth 443
Practice Exercises 447
Additional and Advanced Exercises 458
8 Techniques of Integration 461
8.1 Integration by Parts 461
8.2 Trigonometric Integrals 471
8.3 Trigonometric Substitutions 478
8.4 Integration of Rational Functions by Partial Fractions 484
8.5 Integral Tables and Computer Algebra Systems 491
8.6 Numerical Integration 502
8.7 Improper Integrals 510
Practice Exercises 518
Additional and Advanced Exercises 528
9 First-Order Differential Equations 537
9.1 Solutions, Slope Fields and Euler’s Method 537
9.2 First-Order Linear Equations 543
9.3 Applications 546
9.4 Graphical Solutions of Autonomous Equations 549
9.5 Systems of Equations and Phase Planes 557
Practice Exercises 562
Additional and Advanced Exercises 567
10 Infinite Sequences and Series 569
10.1 Sequences 569
10.2 Infinite Series 577
10.3 The Integral Test 583
10.4 Comparison Tests 590
10.5 The Ratio and Root Tests 597
10.6 Alternating Series, Absolute and Conditional Convergence 602
10.7 Power Series 608
10.8 Taylor and Maclaurin Series 617
10.9 Convergence of Taylor Series 621
10.10 The Binomial Series and Applications of Taylor Series 627
Practice Exercises 634
Additional and Advanced Exercises 642

TABLE OF CONTENTS
10 Infinite Sequences and Series 569
10.1 Sequences 569
10.2 Infinite Series 577
10.3 The Integral Test 583
10.4 Comparison Tests 590
10.5 The Ratio and Root Tests 597
10.6 Alternating Series, Absolute and Conditional Convergence 602
10.7 Power Series 608
10.8 Taylor and Maclaurin Series 617
10.9 Convergence of Taylor Series 621
10.10 The Binomial Series and Applications of Taylor Series 627
Practice Exercises 634
Additional and Advanced Exercises 642
11 Parametric Equations and Polar Coordinates 647
11.1 Parametrizations of Plane Curves 647
11.2 Calculus with Parametric Curves 654
11.3 Polar Coordinates 662
11.4 Graphing in Polar Coordinates 667
11.5 Areas and Lengths in Polar Coordinates 674
11.6 Conic Sections 679
11.7 Conics in Polar Coordinates 689
Practice Exercises 699
Additional and Advanced Exercises 709
12 Vectors and the Geometry of Space 715
12.1 Three-Dimensional Coordinate Systems 715
12.2 Vectors 718
12.3 The Dot Product 723
12.4 The Cross Product 728
12.5 Lines and Planes in Space 734
12.6 Cylinders and Quadric Surfaces 741
Practice Exercises 746
Additional Exercises 754
13 Vector-Valued Functions and Motion in Space 759
13.1 Curves in Space and Their Tangents 759
13.2 Integrals of Vector Functions; Projectile Motion 764
13.3 Arc Length in Space 770
13.4 Curvature and Normal Vectors of a Curve 773
13.5 Tangential and Normal Components of Acceleration 778
13.6 Velocity and Acceleration in Polar Coordinates 784
Practice Exercises 785
Additional Exercises 791

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Introductory Inorganic And Physical Chemistry (MTHS111) Thomas Calculus

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