Technical Mathematics With Calculus

Cover Page......Page 1
Title Page......Page 5
Dedication & Copyright Page......Page 6
Preface......Page 7
About the Authors......Page 11
CONTENTS......Page 13
 OBJECTIVES......Page 19
  Real and Imaginary Numbers......Page 20
  Signed Numbers......Page 21
  Symbols of Grouping......Page 22
  Significant Digits and Accuracy......Page 23
  Rounding......Page 24
  Changing the Calculator Display......Page 27
  Adding Signed Numbers......Page 28
  Subtracting Negative Numbers by Calculator......Page 29
  Adding and Subtracting Approximate Numbers......Page 30
  Combining Exact and Approximate Numbers......Page 31
  Loss of Significant Digits During Subtraction......Page 32
  Multiplying Signed Numbers......Page 33
  Multiplying Negative Numbers by Calculator......Page 34
  Multiplication of Approximate Numbers......Page 35
  Multiplying Exact and Approximate Numbers......Page 36
  Dividing by Calculator......Page 37
  Dividing Signed Numbers......Page 38
  Zero......Page 39
  Reciprocals by Calculator......Page 40
  Powers......Page 41
  Negative Base......Page 42
  Principal Root......Page 43
  Odd Roots of Negative Numbers by Calculator......Page 44
  Parentheses......Page 47
  Combined Operations with Approximate Numbers......Page 48
 1-7 Scientific Notation and Engineering Notation......Page 50
  Converting Numbers to Scientific Notation......Page 51
  Converting Numbers to Engineering Notation......Page 52
  Addition and Subtraction......Page 53
  Division......Page 54
  Scientific and Engineering Notation on the Calculator......Page 55
  Conversion of Units......Page 59
  Converting Areas and Volumes......Page 60
  Using More Than One Conversion Factor......Page 61
  Metric Prefixes......Page 62
  Angle Conversions......Page 63
  Substituting into Formulas......Page 65
  Converting to Percent......Page 69
  Finding the Amount When the Base and the Rate Are Known......Page 70
  Finding the Base When a Percent of It Is Known......Page 71
  Percent Change......Page 72
  Percent Efficiency......Page 73
  Percent Concentration......Page 74
 CHAPTER 1 REVIEW PROBLEMS......Page 77
 OBJECTIVES......Page 80
  Constants and Variables......Page 81
  Symbols of Grouping......Page 82
  Monomials, Multinomials, and Polynomials......Page 83
  Combining Like Terms......Page 85
  Commutative Law of Addition......Page 86
  Instructions Given Verbally......Page 87
  Multiplying Powers......Page 90
  Dividing Powers......Page 91
  Product Raised to a Power......Page 92
  Zero Exponent......Page 93
  Negative Exponent......Page 94
  Exponents on the Calculator......Page 95
  Rules of Signs......Page 98
  Multiplying Monomials......Page 99
 2-5 Multiplying a Monomial and a Multinomial......Page 101
  Multiplication by Calculator......Page 102
 2-6 Multiplying a Binomial by a Binomial......Page 104
  FOIL Rule......Page 105
 2-7 Multiplying a Multinomial by a Multinomial......Page 106
 2-8 Raising a Multinomial to a Power......Page 108
  Rules of Signs......Page 110
  Dividing a Monomial by a Monomial......Page 111
 2-10 Dividing a Polynomial by a Monomial......Page 113
 2-11 Dividing a Polynomial by a Polynomial......Page 116
 CHAPTER 2 REVIEW PROBLEMS......Page 119
 OBJECTIVES......Page 121
  The Solution of an Equation......Page 122
  Solving an Equation......Page 123
  Simple Fractional Equations......Page 124
  Equations with Approximate Numbers......Page 125
  Strategy......Page 126
  Solving an Equation Using a Calculator’s Equation Solver......Page 127
  Implicit or Literal Equations......Page 128
  Picture the Problem......Page 131
  Estimate the Answer......Page 132
  Don’t Give Up......Page 133
  Number Puzzles......Page 134
  Define Other Unknowns......Page 135
 3-3 Uniform Motion Applications......Page 136
 3-4 Money Problems......Page 139
  Basic Relationships......Page 141
  A Typical Mixture Problem......Page 142
  Equations of Equilibrium......Page 145
  Solving Rate Problems......Page 147
  Work......Page 148
  Fluid Flow and Energy Flow......Page 149
 CHAPTER 3 REVIEW PROBLEMS......Page 151
 OBJECTIVES......Page 154
  Domain and Range......Page 155
  Implicit and Explicit Forms......Page 156
  Functional Notation......Page 157
  Changing from Implicit to Explicit Form......Page 158
  Functions by Calculator......Page 159
  A Function as a Set of Point Pairs......Page 162
  A Function as a Verbal Statement......Page 163
  Substituting into a Function......Page 164
  Composite Functions......Page 165
  Inverse of a Function......Page 166
  Finding Domain and Range......Page 168
 CHAPTER 4 REVIEW PROBLEMS......Page 172
 OBJECTIVES......Page 174
  Graphing Point Pairs......Page 175
  Applications: Graphing Empirical Data......Page 176
  Graphing an Equation Given in Implicit Form......Page 179
  Graphing a Relation......Page 180
  Graphing an Equation Given in Implicit Form......Page 182
  Exploring Your Graph: Special Operations on the Calculator......Page 183
  Table of Point Pairs and Split Screen Display......Page 184
  Slope......Page 185
  Equation of a Straight Line......Page 186
  Writing the Equation Given Two Points on the Line......Page 187
 5-5 Solving an Equation Graphically......Page 190
 CHAPTER 5 REVIEW PROBLEMS......Page 191
 OBJECTIVES......Page 193
  Angles......Page 194
  Families of Lines and Transversals......Page 195
  Triangles......Page 198
  Area of a Triangle......Page 199
  Congruent and Similar Triangles......Page 200
  Right Triangles......Page 201
  Special Right Triangles......Page 202
 6-3 Quadrilaterals......Page 205
  Sum of the Interior Angles......Page 206
  Circumference and Pi (p)......Page 208
  Area of a Circle......Page 209
  Tangent, Secant, and Chord......Page 210
  Semicircle......Page 211
  Polyhedra......Page 214
  Rectangular Parallelepiped and Cube......Page 215
  The Pyramid......Page 216
  The Cylinder......Page 219
  The Cone......Page 220
  The Sphere......Page 221
 CHAPTER 6 REVIEW PROBLEMS......Page 223
 OBJECTIVES......Page 225
  Sine, Cosine, and Tangent......Page 226
  Finding the Angle......Page 227
  Solving a Right Triangle When One Side and One Angle Are Known......Page 230
  Solving a Right Triangle When Two Sides Are Known......Page 232
 7-3 Applications of the Right Triangle......Page 234
 7-4 An Angle in Standard Position......Page 239
  Representation of a Vector......Page 240
  Components of a Vector......Page 241
  Rectangular Components by Calculator......Page 242
  Resultants by Calculator......Page 243
  Force Vectors......Page 244
  Impedance Vectors......Page 245
 CHAPTER 7 REVIEW PROBLEMS......Page 247
 OBJECTIVES......Page 249
 8-1 Trigonometric Functions of Any Angle......Page 250
  Trigonometric Functions of Any Angle by Calculator......Page 251
  Reciprocal Relationships......Page 252
  Cofunctions......Page 253
 8-2 Finding the Angle When the Trigonometric Function Is Known......Page 254
  Algebraic Signs of the Trigonometric Functions......Page 255
  Finding the Angle by Calculator......Page 256
  Inverse of the Cotangent, Secant, and Cosecant......Page 257
  Derivation......Page 258
  Solving a Triangle When Two Angles and One Side Are Known (AAS or ASA)......Page 259
  Solving a Triangle When Two Sides and One Angle Are Given (SSA): The Ambiguous Case......Page 260
  Derivation......Page 264
  When to Use the Law of Sines or the Law of Cosines......Page 265
  Using the Law of Cosines When Two Sides and the Included Angle Are Known......Page 266
  Using the Law of Cosines When Three Sides Are Known......Page 267
 8-5 Applications......Page 269
  Finding x and y Components of a Vector......Page 273
  Resultant of Two Vectors at Any Angle......Page 274
  Resultants by Calculator......Page 275
 CHAPTER 8 REVIEW PROBLEMS......Page 278
 OBJECTIVES......Page 281
  Solution to a System of Equations......Page 282
  Approximate Graphical Solution to a System of Two Equations......Page 283
  Solving a Pair of Linear Equations by the Addition-Subtraction Method......Page 284
  Systems Having No Solution......Page 286
  Solving Sets of Equations Symbolically by Calculator......Page 287
 9-2 Applications......Page 288
  Money Applications......Page 289
  Applications Involving Mixtures......Page 290
  Statics Applications......Page 291
  Applications to Work, Fluid Flow, and Energy Flow......Page 292
  Electrical Applications......Page 293
  A System with Fractional Coefficients......Page 297
  Fractional Equations with Unknowns in the Denominator......Page 298
  Literal Equations......Page 299
  Addition-Subtraction Method......Page 302
  Substitution Method......Page 303
  Fractional Equations......Page 304
  Literal Equations......Page 305
 CHAPTER 9 REVIEW PROBLEMS......Page 308
 OBJECTIVES......Page 310
  Dimensions......Page 311
  The Unit Matrix and the Null Matrix......Page 312
  Entering a Matrix into a Calculator......Page 313
 10-2 Solving Systems of Equations by the Unit Matrix Method......Page 315
  Value of a Determinant......Page 320
  Determinants by Calculator......Page 321
  Solving a System of Two Linear Equations by Determinants......Page 322
  Evaluating a Higher-Order Determinant by Calculator......Page 326
  Development by Minors......Page 327
  Solving a System of Equations by Determinants......Page 329
  Systems of More than Three Equations......Page 332
 CHAPTER 10 REVIEW PROBLEMS......Page 334
 OBJECTIVES......Page 337
  Common Factors......Page 338
  Checking......Page 339
  Factoring by Calculator......Page 340
 11-2 Difference of Two Squares......Page 341
  Factoring the Difference of Two Squares......Page 342
  Factoring Completely......Page 343
 11-3 Factoring Trinomials......Page 344
  Factoring by Trial and Error......Page 345
  Using the Signs to Aid Factoring......Page 346
  Grouping Method......Page 347
  The Perfect Square Trinomial......Page 348
  Sum or Difference of Two Cubes......Page 351
  Division by Zero......Page 353
  Mixed Form......Page 354
  Simplifying a Fraction by Reducing to Lowest Terms......Page 355
  Simplifying a Fraction by Manipulating Signs......Page 356
  Multiplying Fractions......Page 358
  Dividing Fractions......Page 359
  Multiplying and Dividing Fractions by Calculator......Page 360
  Least Common Denominator......Page 362
  Combining Fractions with Different Denominators......Page 363
  An Application......Page 365
 11–8 Complex Fractions......Page 367
  Solving a Fractional Equation by Calculator......Page 370
  Equations with the Unknown in the Denominator......Page 371
 11–10 Literal Equations and Formulas......Page 373
  Solving Literal Equations and Formulas......Page 374
  Literal Fractional Equations......Page 376
  Formulas......Page 377
 CHAPTER 11 REVIEW PROBLEMS......Page 378
 OBJECTIVES......Page 381
  Solving a Quadratic Graphically......Page 382
  Solving a Quadratic Using a Calculator’s Equation Solver......Page 383
  Implicit Functions......Page 384
  An Application......Page 385
  General Form of a Quadratic......Page 386
  The Quadratic Formula......Page 387
  Completing the Square......Page 388
  Derivation of the Quadratic Formula......Page 389
 12-3 Applications......Page 390
 CHAPTER 12 REVIEW PROBLEMS......Page 395
 OBJECTIVES......Page 397
  Zero Exponents......Page 398
  Products......Page 399
  Quotients......Page 400
  Relation between Fractional Exponents and Radicals......Page 403
  Root of a Product......Page 404
  Root of a Quotient......Page 405
  Reducing the Radicand......Page 406
  Removing Radicals from the Denominator......Page 407
  Reducing the Index......Page 408
  Adding and Subtracting Radicals......Page 410
  Multiplying Radicals......Page 411
  Dividing Radicals......Page 412
  Solving a Radical Equation Using a Calculator’s Equation Solver......Page 416
  Solving a Radical Equation Algebraically......Page 417
 CHAPTER 13 REVIEW PROBLEMS......Page 421
 OBJECTIVES......Page 423
  Angle Conversion......Page 424
  Angle Conversion by Calculator......Page 425
  Trigonometric Functions of Angles in Radians......Page 426
  The Inverse Trigonometric Functions......Page 427
  Areas of Sectors and Segments......Page 428
 14-2 Arc Length......Page 431
  Angular Displacement......Page 434
  Applications......Page 435
 CHAPTER 14 REVIEW PROBLEMS......Page 438
 OBJECTIVES......Page 440
  Periodic Functions......Page 441
  The Sine Wave: Period and Frequency......Page 442
  Amplitude and Phase Shift Related......Page 443
  Zeros and Instantaneous Value......Page 444
  An Application......Page 445
  Quick Manual Graph of the Sine Wave......Page 448
  Writing the Equation When the Amplitude, Period, and Phase Shift Are Given......Page 450
  Writing the Equation When the Curve Is Given......Page 451
  Period......Page 453
  Frequency......Page 454
  Alternating Current......Page 456
  Phase Shift......Page 457
  The Cosine Wave......Page 459
  Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions......Page 460
  The Inverse Trigonometric Functions......Page 461
  Arc Cosine and Arc Tangent......Page 462
  Graphing an Inverse Trigonometric Function by Calculator......Page 463
  Graphing Parametric Equations by Calculator......Page 466
  Graphing a Trigonometric Equation in Parametric Form......Page 467
  Graphing an Equation in Polar Coordinates by Calculator......Page 470
  Graphing an Equation in Polar Coordinates Manually......Page 471
  Transforming Between Rectangular and Polar Coordinates by Calculator......Page 473
  Transforming an Equation......Page 474
 CHAPTER 15 REVIEW PROBLEMS......Page 477
 OBJECTIVES......Page 479
  Quotient Relations......Page 480
  Pythagorean Relations......Page 481
  Simplifying a Trigonometric Expression......Page 482
  Simplifying a Trigonometric Expression by Calculator......Page 483
  Proving a Trigonometric Identity......Page 484
 16-2 Sum or Difference of Two Angles......Page 487
  Difference of Two Angles......Page 488
  Tangent of the Sum or Difference of Two Angles......Page 489
  Sine of Twice an Angle......Page 492
  Cosine of Twice an Angle......Page 493
  Sine of Half an Angle......Page 494
  Tangent of Half an Angle......Page 496
 16-4 Evaluating a Trigonometric Expression......Page 499
  An Application: Compound cuts:......Page 500
 16-5 Solving a Trigonometric Equation......Page 502
  Equations Containing a Single Trigonometric Function and a Single Angle......Page 503
  Equations with One Angle But More Than One Function......Page 505
 CHAPTER 16 REVIEW PROBLEMS......Page 507
 OBJECTIVES......Page 509
  Dimensionless Ratios......Page 510
  Finding a Missing Term......Page 511
  Mean Proportional......Page 512
  Applications......Page 513
 17-2 Similar Figures......Page 515
  Areas of Similar Figures......Page 516
  Volumes of Similar Solids......Page 517
 17-3 Direct Variation......Page 519
  Solving Variation Problems......Page 520
  Applications......Page 521
  Graph of the Power Function......Page 523
  Solving Power Function Problems......Page 524
  An Application......Page 525
 17-5 Inverse Variation......Page 527
  An Application......Page 529
  Joint Variation......Page 531
  Combined Variation......Page 532
  An Application......Page 533
 CHAPTER 17 REVIEW PROBLEMS......Page 536
 OBJECTIVES......Page 539
  Graph of the Exponential Function......Page 540
  Compound Interest......Page 541
  Exponential Growth......Page 542
  Exponential Growth to an Upper Limit......Page 544
  Time Constant......Page 545
  Universal Growth and Decay Curves......Page 546
  Definition of a Logarithm......Page 550
  Converting between Logarithmic and Exponential Forms......Page 551
  Common Logarithms......Page 552
  Antilogarithms......Page 553
  Natural Antilogarithms......Page 554
  Products......Page 557
  Quotients......Page 558
  Powers......Page 559
  Log of 1......Page 561
  Base Raised to a Logarithm of the Same Base......Page 562
  Change of Base......Page 563
  Solution by Calculator......Page 565
  Algebraic Solution......Page 566
  Solving an Exponential Equation with Base e......Page 567
  Half-Life......Page 568
  Doubling Time......Page 569
  Algebraic Solution......Page 572
  An Application......Page 573
 CHAPTER 18 REVIEW PROBLEMS......Page 578
 OBJECTIVES......Page 580
  Addition and Subtraction of Complex Numbers......Page 581
  Multiplying by Imaginary Numbers......Page 582
  Multiplying Complex Numbers......Page 583
  Dividing Complex Numbers......Page 584
 19-2 Complex Numbers in Polar Form......Page 586
  Arithmetic Operations in Polar Form......Page 587
  Quotients......Page 588
  Powers......Page 589
  Entering and Converting Complex Numbers on the Calculator......Page 590
  Arithmetic Operations on Complex Numbers by Calculator......Page 591
  Components of a Vector......Page 593
  Resultants of Several Vectors......Page 594
  Rotating Vectors in the Complex Plane......Page 596
  Effective or Root Mean Square (rms) Values......Page 597
  Alternating Current and Voltage in Complex Form......Page 598
  Ohm’s Law for Alternating Current......Page 599
 CHAPTER 19 REVIEW PROBLEMS......Page 602
 OBJECTIVES......Page 604
  General Term......Page 605
  Generating a Sequence or Series Using the General Term......Page 606
  Graphing a Sequence or Series Using a Recursion Formula......Page 607
  Sequences and Series by Computer......Page 608
  Convergence or Divergence of an Infinite Series......Page 609
  General Term......Page 611
  AP: Sum of n Terms......Page 612
  Sums by Calculator......Page 613
  Harmonic Progressions......Page 614
  Harmonic Means......Page 615
  General Term......Page 618
  GP: Sum of n Terms......Page 619
  Geometric Means......Page 620
  Sum of an Infinite Geometric Progression......Page 622
  Limit Notation......Page 623
  A Formula for the Sum of an Infinite, Decreasing Geometric Progression......Page 624
  Powers of a Binomial......Page 625
  Factorial Notation......Page 626
  Pascal’s Triangle......Page 627
  General Term......Page 628
  Fractional and Negative Exponents......Page 629
 CHAPTER 20 REVIEW PROBLEMS......Page 632
 OBJECTIVES......Page 635
  Variables......Page 636
  Ways to Display Data......Page 637
  Displaying Statistical Data on the Calculator......Page 638
  Graphical Representation of Data......Page 639
  Frequency Distribution......Page 640
  Frequency Polygon......Page 642
  Stem and Leaf Plot......Page 643
  Graphing Frequency Distributions on the Calculator......Page 644
  Measures of Central Tendency: The Mean......Page 646
  Weighted Mean......Page 647
  Median......Page 648
  Range......Page 649
  Quartiles, Deciles, and Percentiles......Page 650
  Variance......Page 651
  Standard Deviation......Page 652
  Numerical Description of Data on the Calculator......Page 654
 21-4 Introduction to Probability......Page 656
  Probability of a Single Event Occurring......Page 657
  Probability of Two Events Both Occurring......Page 658
  Probability of Two Mutually Exclusive Events Occurring......Page 659
  Probability Distributions......Page 660
  Probabilities as Areas on a Probability Distribution......Page 661
  Binomial Experiments......Page 662
  Binomial Distribution......Page 663
  Binomial Distribution Obtained by Binomial Theorem......Page 664
  Continuous Probability Distributions......Page 666
  Normal Distribution......Page 667
  Using the Normal Curve on the Calculator......Page 671
 21-6 Standard Errors......Page 672
  Frequency Distribution of a Statistic......Page 673
  Standard Error of the Mean......Page 674
  Predicting μ from a Single Sample......Page 675
  Confidence Intervals......Page 676
  Standard Error of a Proportion......Page 677
  Control Charts......Page 679
  The p Chart......Page 680
  The – and Charts......Page 682
  Curve Fitting......Page 687
  Correlation Coefficient......Page 688
  Method of Least Squares......Page 689
  Linear Regression on the Calculator......Page 691
 CHAPTER 21 REVIEW PROBLEMS......Page 692
 OBJECTIVES......Page 697
  Directed Distance......Page 698
  Distance Formula......Page 699
  Slopes of Horizontal and Vertical Lines......Page 700
  Angle of Inclination......Page 701
  Angle of Intersection Between Two Lines......Page 702
  Applications......Page 704
  Slope-Intercept Form......Page 705
  Point-Slope Form......Page 706
  Two-Point Form......Page 707
  Equation of a Straight Line in General Form......Page 708
  Definition of a Circle......Page 712
  Standard Equation of a Circle: Center at Origin......Page 713
  Standard Equation of a Circle: Center Not at the Origin......Page 714
  Translation of Axes......Page 715
  Changing from General to Standard Form......Page 716
  An Application......Page 717
  Standard Equation of a Parabola: Vertex at the Origin......Page 720
  Standard Equation of a Parabola with Vertical Axis......Page 721
  Standard Equation of a Parabola: Vertex Not at the Origin......Page 723
  General Equation of a Parabola......Page 724
  Completing the Square......Page 725
  Definition of the Ellipse......Page 731
  Distance to Focus......Page 732
  Standard Equation of Ellipse: Center at Origin, Major Axis Horizontal......Page 733
  Graphing an Ellipse with a Graphics Utility......Page 735
  Standard Equation of Ellipse: Center at Origin, Major Axis Vertical......Page 736
  Standard Equation of Ellipse: Center Not at Origin......Page 737
  General Equation of an Ellipse......Page 738
  Completing the Square......Page 739
  Focal Width of an Ellipse......Page 740
  Standard Equations of a Hyperbola with Center at Origin......Page 743
  Asymptotes of a Hyperbola......Page 744
  Manually Graphing a Hyperbola......Page 746
  Standard Equation of Hyperbola: Center Not at Origin......Page 747
  Hyperbola Whose Asymptotes Are the Coordinate Axes......Page 749
 CHAPTER 22 REVIEW PROBLEMS......Page 751
 OBJECTIVES......Page 755
  Limit Notation......Page 756
  Limits Found Numerically......Page 757
  Limits by Computer Algebra System......Page 758
  Limits Involving Zero or Infinity......Page 759
  Limits of the Form 0/0......Page 761
  When the Limit Is an Expression......Page 762
  Tangent to a Curve......Page 764
  Finding the Slope of the Tangent......Page 765
 23-3 The Derivative......Page 768
  Another Symbol for the Derivative......Page 769
  Derivatives by the Delta Method......Page 770
  More Symbols for the Derivative......Page 772
  Approximate Derivatives by Calculator......Page 773
  Graph of a Derivative......Page 774
  Symbolic Differentiation by Calculator or Computer......Page 775
  Derivative of a Constant Times a Power Function......Page 777
  Power Function with Negative Exponent......Page 778
  Derivative of a Sum......Page 779
  Functions with Other Variables......Page 781
  The Chain Rule......Page 784
  The Power Rule......Page 785
  Derivative of a Product......Page 788
  Products with More Than Two Factors......Page 790
  Derivative of a Quotient......Page 792
  Derivatives with Respect to Other Variables......Page 795
  Derivatives of Implicit Relations......Page 796
  Differentials......Page 798
 23-8 Higher-Order Derivatives......Page 801
  Higher Derivatives by Calculator......Page 802
 CHAPTER 23: REVIEW PROBLEMS......Page 803
 OBJECTIVES......Page 805
 24-1 Equations of Tangents and Normals......Page 806
  Implicit Relations......Page 807
  Angle of Intersection of Two Curves......Page 809
  Increasing and Decreasing Functions......Page 810
  Concavity......Page 811
  Maximum and Minimum Points......Page 812
  Testing for Maximum or Minimum......Page 814
  Implicit Relations......Page 816
  Inflection Points......Page 817
  Summary......Page 818
 24-3 Sketching, Verifying, and Interpreting Graphs......Page 820
  Graphing Regions......Page 824
 CHAPTER 24 REVIEW PROBLEMS......Page 825
 OBJECTIVES......Page 827
  Rate of Change with Respect to Time......Page 828
  Current in a Capacitor......Page 829
  Voltage Across an Inductor......Page 830
  Beam Deflection......Page 831
  Displacement and Velocity in Straight-Line Motion......Page 833
  Acceleration in Straight-Line Motion......Page 834
  Velocity in Curvilinear Motion......Page 835
  Displacement Given by Parametric Equations......Page 836
  Trajectories......Page 837
  Rotation......Page 838
 25–3 Related Rates......Page 841
  Two Moving Objects......Page 843
 25–4 Optimization......Page 847
 CHAPTER 25 REVIEW PROBLEMS......Page 857
 OBJECTIVES......Page 859
  The Integral Sign......Page 860
  Some Rules for Finding Integrals......Page 861
  Checking an Integral by Differentiating......Page 865
  Checking an Integral by Calculator......Page 866
  Symbolic Integration by Calculator......Page 867
  Integral of a Power Function......Page 869
  Other Variables......Page 872
  Miscellaneous Rules from a Table of Integrals......Page 874
  Finding the Constant of Integration......Page 877
  Solving a Simple Second-Order Differential Equation......Page 878
  Another Application......Page 879
  The Fundamental Theorem of Calculus......Page 881
  Evaluating a Definite Integral......Page 882
  Finding a Definite Integral by Calculator......Page 883
  Estimating Areas......Page 885
  A Numerical Technique: The Midpoint Method......Page 886
  Exact Area by Integration......Page 889
  Area Under a Curve by Calculator......Page 892
 CHAPTER 26 REVIEW PROBLEMS......Page 893
 OBJECTIVES......Page 895
 27–1 Applications to Motion......Page 896
 27–2 Applications to Electric Circuits......Page 902
 27–3 Finding Areas by Integration......Page 904
 27–4 Volumes by Integration......Page 916
 REVIEW PROBLEMS......Page 925
 OBJECTIVES......Page 927
 28–1 Length of Arc......Page 928
 28–2 Area of Surface of Revolution......Page 932
 28–3 Centroids......Page 936
 28–4 Fluid Pressure......Page 944
 28–5 Work......Page 946
 28–6 Moment of Inertia......Page 950
 Review Problems......Page 956
 OBJECTIVES......Page 958
 29–1 Derivatives of the Sine and Cosine Functions......Page 959
 29–2 Derivatives of the Other Trigonometric Functions......Page 967
 29–3 Derivatives of the Inverse Trigonometric Functions......Page 971
 29–4 Derivatives of Logarithmic Functions......Page 973
 29–5 Derivative of the Exponential Function......Page 979
 29–6 Integral of the Exponential and Logarithmic Functions......Page 985
 29–7 Integrals of the Trigonometric Functions......Page 989
 29–8 Average and Root Mean Square Values......Page 993
 REVIEW PROBLEMS......Page 995
 OBJECTIVES......Page 998
 30–1 Definitions......Page 999
 30–2 Solving a DE by Calculator, Graphically, and Numerically......Page 1001
 30–3 First-Order DE: Variables Separable......Page 1006
 30–4 Exact First-Order DE......Page 1010
 30–5 First-Order Homogeneous DE......Page 1012
 30–6 First-Order Linear DE......Page 1014
 30–7 Geometric Applications of First-Order DEs......Page 1019
 30–8 Exponential Growth and Decay......Page 1022
 30–9 Series RL and RC Circuits......Page 1025
 REVIEW PROBLEMS......Page 1030
 OBJECTIVES......Page 1031
 31–1 Second-Order DE......Page 1032
 31–2 Constant Coefficients and Right Side Zero......Page 1033
 31–3 Right Side Not Zero......Page 1039
 31–4 Mechanical Vibrations......Page 1045
 31–5 RLC Circuits......Page 1050
 REVIEW PROBLEMS......Page 1057
 A: Summary of Facts and Formulas......Page 1059
 B: Conversion Factors......Page 1086
 C: Table of Integrals......Page 1090
 D: Answers to Selected Problems......Page 1094
Applications Index......Page 1135
Index to Writing Questions......Page 1139
Index to Projects......Page 1140
SUBJECT INDEX......Page 1141
Info Sheets......Page 1149