Larson r , hodgkins a college algebra and calculus an applied approach 1ed 2010

Applications Biology and Life Sciences Agriculture, 495, 767, 777, 995, 1020 Air sacs in the lungs, 28 Alligator length, 360 Animal shelter, 986 Antler spread of an elk, 399 Aquaculture, 742 Average recycling cost, 333, 339 Bacteria count, 233, 236, 237, 254 Bacteria growth, 351, 372, 390, 392, 400, 401, 402 Bacterial culture, 616, 759, 832, 889, 986 Biorhythms, 1047, 1050 Blue oak, height of, 103 Body mass index (BMI), 414 Botany, 525, 1231 Calories burned by exercise, 495 Carbon dioxide, 99, 426 Cardiovascular device sales, 1107 Carnivorous plants, 531 Cat cadavers, 200 Cell division, 759 Clinical trial, 19 Comparing calories, 88 Cricket chirps, 1224 Crop spraying mixture, 437 Diet supplement, 450 Dissections, 1168 E coli bacterium, length, 65 Ecology, fencing a study plot, 743 Endangered species population, 393, 800, 889 Environment contour map of the ozone hole, 950 oxygen level in a pond, 606, 686 pollutant level, 616 pollutant removal, 546, 718, 890 recycling, 621, 1179 size of an oil slick, 648 smokestack emissions, 328, 339, 715 Environmental cost, pollutant removal, 557 Erosion, 38 Farming, 697 Fertility rates, 668 Fishing quotas, 845 Forest yield, 381 Forestry, 624, 795, 1150 Fruit tree maximum yield, 696, 740 Galloping speeds of animals, 370 Gardening, 825 Genders of children, 1181, 1194, 1229 Genetically modified soybeans, 438 Genetics, 1229 Gestation period of rabbits, 557 Growth of a red oak tree, 686 Gypsy moths, 525 Hardy-Weinberg Law, 976, 985 Health AIDS cases, 1194 blood oxygen level, 108, 113 blood pressure, 1050 body temperature, 137, 595 epidemic, 854, 889 exposure to a carcinogen and mortality, 1021 exposure to sun, 742 infant mortality, 995 U.S HIV/AIDS epidemic, 640 and wellness, 481 velocity of air flow into and out of the lungs, 1050, 1070 Heart rate, 450 Human height, 78, 137, 188 Hydroflourocarbon emissions, 103 Kidney donation, 1164 Lab practical, 1169 Litter of kittens, 1230 Liver transplants, 268 Lung volume, 217 Medical science drug concentration, 803 length of pregnancy, 1206 surface area of a human body, 1019 velocity of air during coughing, 668 volume of air in the lungs, 867 Medicine amount of drug in bloodstream, 594, 622 bone graft procedures, 379 days until recovery after a medical procedure, 1206, 1231 drug absorption, 910 drug concentration in bloodstream, 300, 333, 583, 686, 736, 910, 1150 duration of an infection, 976 effectiveness of a pain-killing drug, 594 healing rate of a wound, 353 heart transplants, 1232 multiple births, twins, 685 Poiseuille’s Law, 686 spread of a virus, 388, 678, 801 temperature of a patient, 1041 treatment of a bacterial infection, 1019 Metabolic rate, 113 Nutrition, 447, 986 Optimal area of an archaeological dig site, 336 Orthopedic implant sales, 1107 Oxygen level, 61 Peregrine falcons, 450 Pest management in a forest, 191 Physiology blood flow, 845 body surface area, 736 Plant biology lab, 1169 Plant growth, 1060 Population of bees, 901 of bears, 402 of deer, 191, 332, 390, 887 of elk, 332 of fish, 339, 390, 801 of ring-necked pheasants, 926 of sparrows, 263 of trout, 832 Population growth, 596, 606, 752, 789, 794, 890, 900 Predator-prey cycle, 1046, 1050, 1051 Psychology Ebbinghaus Model, 767 human memory model, 332, 333, 339, 360, 362, 381, 399, 400, 402, 880 intelligence quotient (IQ), 1233 IQ scores, 136, 403 learning curve, 392, 401, 718, 795 learning theory, 759, 767, 777, 781, 786, 1195, 1205 memory experiment, 898, 900, 927 migraine prevalence, 580 skill retention model, 363 sleep patterns, 868 Stanford-Binet Test, (IQ test), 967 Ratio of reptiles, 1089 Research study, 19 Respiratory diseases, 1174 Stocking a lake with fish, 392, 976 Suburban wildlife, 381 Systolic blood pressure, 604 Tree growth, 816 Water pollution, 332 Weight of a puppy, 182, 189 Weights of adult male rhesus monkeys, 1203 Wheelchair ramp, 181 Wildlife management, 401, 718, 736 Zebrafish embryos, 1229 Business and Economics Advertising, 192 expenses, 278, 297, 301, 303, 648, 986, 1150 Annual operating cost, 136 payroll of new car dealerships, 1089 sales, 78, 251, 338, 352, 414, 450, 1107 Average cost, 205, 206, 332, 339, 677, 705, 714, 716, 718, 840, 1150 Average cost and profit, 742 Average monthly retail sales, 155 Average production, 1012 Average profit, 718, 1010 Average revenue, 1012 Average weekly demand, 1197 Average weekly profit, 1012 Book value per share, 205, 217 Break-even analysis, 136, 152, 410, 411, 414, 440, 462 Budget analysis, 1116 Budget deficit, 853 Budget variance, 7, Cable television companies, 496 Capital accumulation, 845 Capital campaign, 880 Capitalized cost, 921, 928 Cash flow, 825 Cash flow per share, Harley-Davidson, 791 Charter bus fares, 206 Cobb-Douglas production function, 640, 952, 955, 966, 980, 1012 Compact disc shipments, 685 Company profits, 146, 153 Comparing profits, 235 Comparing sales, 236, 254 Competing restaurants, 1169 Complementary and substitute products, 966 Construction, 986 Consumer and producer surplus, 446, 449, 464, 850, 853, 854, 868, 869, 900 Contract bonuses, 495 Cost, 188, 235, 247, 552, 580, 607, 658, 668, 707, 718, 728, 813, 815, 816, 825, 845, 865, 866, 976, 985, 1070, 1150, 1206 Cost-benefit model, 328 Cost equation, 111 Cost, revenue, and profit, 204, 236, 624, 647, 649, 854 Daily morning newspapers, number of, 993 Defective units, 1178, 1181, 1196 Demand, 589, 590, 595, 596, 606, 607, 638, 640, 707, 736, 742, 758, 776, 785, 800, 815, 832, 879, 995, 1195, 1205, 1206 Demand function, 302, 351, 372, 381, 400, 825, 961 Depreciation, 37, 616, 750, 767, 803, 845, 1155 Diminishing returns, 675, 677 Dividends for Coca-Cola, 206 Dollar value, 251 Dow Jones Industrial Average, 596, 678 Earnings-dividend ratio, Wal-Mart Stores, 247 Earnings per share, 170, 929, 956 Earnings per share, sales, and shareholder equity, PepsiCo, 996 Economics, 595 equation of exchange, 1018 gross domestic product, 736 investment, 1195 marginal benefits and costs, 816 present value, 926 revenue, 740 Elasticity of demand, 706, 719, 741 Elasticity and revenue, 703 Equimarginal Rule, 985 Expected sales, 1185 Factory production, 494, 530 Federal cost of food stamps, 207 debt, 438 financial aid awarded, 254 government expenses, 19 Pell Grants, 47, 414 Perkins Loans, 414 student aid, 47 Finance, cyclical stocks, 1051 Flour production, 125 Fuel cost, 851 Furniture production, 449 Gold prices, 169, 217, 267 Hotel pricing, 494 Increasing production, 646 Increasing profit, 143 Insurance, 1194 Inventory cost, 677, 741 of digital cameras, 1230 of kayaks, 449 levels, 494, 530, 533 of liquefied petroleum gases, 1069 management, 557, 596 of movie players, 464 replenishment, 607 Job applicants, 1168, 1170, 1229 Labor/wage requirements, 495, 507, 530 Least-Cost Rule, 985 Lifetime of a product, 1191 Making a sale, 1179, 1181, 1182 Managing a store, 607 Manufacturing, 1206 Marginal analysis, 731, 732, 736, 742, 845, 909 Marginal cost, 594, 595, 596, 624, 705, 716, 833, 966, 1019 Marginal productivity, 966 Marginal profit, 588, 592, 594, 595, 596, 624, 705 Marginal revenue, 591, 594, 595, 624, 705, 966, 1019 Market analysis, 1195 Market research, 122, 125, 152 Market stabilization, 1114 Marketing, 889 Maximum production level, 980, 981, 1019, 1021 Maximum profit, 218, 666, 701, 705, 706, 719, 972, 982 Maximum revenue, 698, 700, 705, 706, 764 Mean and median useful lifetimes of a product, 1200 Media selection for advertising, 459 Minimum average cost, 699, 705, 719, 785, 786 Minimum cost, 695, 696, 697, 706, 740, 977, 1019 Mobile homes manufactured, 205 Monthly cost, 103, 114 Monthly profit, 87 Monthly sales, 92 Monthly flight cost, 124 National defense budget, 205 National defense outlays, 332 National deficit, 675 Negotiating a price, 606 Number of Kohl’s stores, 901 Office space, 986 Optimal cost, 267, 336, 456, 459 profit, 267, 336, 455, 458, 459, 460, 465, 466 revenue, 266, 336, 459, 465 Owning a franchise, 557 Patents issued, 200 Payroll mix-up, 1181 Point of diminishing returns, 675, 677 Point of equilibrium, 422, 425, 440, 462, 466 Price-earning (P/E) ratio, 237 Price of a product, 153 Production, 264, 640, 865, 952, 955, 985 cost, 102 limit, 91 Productivity, 677 of a new employee, 363 Profit, 154, 155, 170, 227, 247, 268, 288, 297, 303, 321, 337, 403, 506, 595, 596, 624, 625, 645, 648, 658, 668, 697, 707, 728, 735, 740, 741, 795, 803, 816, 839, 867, 900, 955, 975, 1019, 1107, 1156 Profit analysis, 656, 658 Projected expenses, 90 Projected profit, 151 Projected revenue, 90, 151 Property tax, 190, 251 Purchasing power of the dollar, 193, 900 Quality control, 9, 606, 921, 1230 Raw materials, 505, 531 Real estate, 1020 Reimbursed expenses, 191 Returning phone calls, 1225 Revenue, 181, 189, 192, 218, 253, 321, 338, 401, 463, 566, 577, 580, 595, 707, 735, 740, 795, 800, 801, 804, 832, 853, 865, 868, 880, 890, 900, 975, 996, 1019, 1098, 1194, 1230 Revenue per share, 153, 192, 300, 438, 577, 613, 685, 795 Salary contract, 557, 621 Sales, 136, 174, 181, 251, 382, 425, 648, 678, 684, 792, 795, 832, 926, 1041, 1050, 1051, 1052, 1116, 1155, 1157, 1230 Avon Products, 759, 868 Bausch & Lomb, 625 of concert tickets, 449, 464 of e-commerce companies, 786 of exercise equipment, 795 of gasoline, 596 Home Depot, 622, 623 of insect control products, 1089 of movie tickets, 425 of petroleum and coal products, 217 PetSmart, 869 of prescription drugs by mail order, 153 Procter & Gamble, 707 Safeway, 1077 Scotts Miracle-Gro, 567, 580 of shoes, 425 sporting goods, 88 Starbucks, 750 Sales analysis, 607 Sales commission, 351 Sales, equity, and earnings per share, Johnson & Johnson, 1018 Sales growth, 677 Sales per share, 113, 206, 302, 340, 392, 439, 581, 613, 707 Sales price and list price, 191 Seasonal sales, 1057, 1069, 1070, 1076, 1077, 1078 Shareholder’s equity, Wal-Mart, 956, 967 Social Security Trust Fund, 854 State income tax, 183 State sales tax, 183, 190 Straight-line depreciation, 186, 190, 191, 251, 255 Sugar production, 125 Supply and demand, 425, 462 Supply function, 825 Surplus, 446, 449, 464, 850, 853, 854, 868, 869, 900 Tax liability, 285 Testing for defective units, 1226 Total cost, 87 Total profit, 1098 Total revenue, 87, 102, 113, 114, 151, 154 Total sales, 112, 147, 205, 1095, 1098 Trade deficit, 593 Transportation cost, 300 U.S currency, 381 Useful life, 1195, 1205, 1206, 1231 Wages, 191, 1206, 1232 Weekly demand, 1190 Worker’s productivity, 395 Years of service for employees, 1176 Interest Rates Annuity, 842, 845, 867 Balance in an account, 25, 28, 39, 65, 67, 252, 372, 378, 390, 402, 754, 756, 1159 Becoming a millionaire, 28 Bond investment, 505 Borrowing money, 124, 436, 481, 529 Cash advance, 124, 152 Cash settlement, 351 Certificate of deposit, 759 Charitable foundation, 921 College tuition fund, 880 Comparing investment returns, 90 Compound interest, 26, 47, 91, 121, 124, 146, 153, 347, 348, 349, 351, 381, 398, 546, 554, 557, 616, 758, 767, 768, 775, 776, 790, 794, 801, 845, 867, 1089, 1104, 1106, 1155, 1157, 1159 Credit card rate, 616 Doubling time, 774, 776, 804 Doubling and tripling an investment, 378 Effective rate of interest, 755, 758, 801 Effective yield, 794 Endowment, 921 Finance, 777 present value, 926 Future value, 758, 880 Inflation rate, 26, 750, 768, 803 Investment, 382, 449, 463, 466, 956, 967 mix, 90, 414 plan, 398 portfolio, 424, 425, 433, 437, 460, 463 Rule of 70, 794 strategy, 986 time, 362, 399 Monthly payments, 61, 953, 956 Present value, 352, 756, 758, 801, 876, 877, 880, 901, 909, 921, 926, 928 of a perpetual annuity, 919 Savings plan, 44, 47 Scholarship fund, 921 Simple interest, 84, 89, 91, 135, 150, 181, 190, 407, 466 Stock mix, 90 Tripling time, 776 Trust fund, 758 Chemistry and Physical Science Acceleration, 629, 649 Acceleration due to gravity, 630 Accuracy of a measurement, 133, 137, 152 Acid mixture, 462 Acid solution, 87 Acidity of rainwater, 1018 Airplane speed, 421, 424 Automobile aerodynamics, 227 Automobile crumple zones, 382 Average velocity, 584 Biomechanics, Froude number, 1018 Boiling temperature of water, 785 Bouncing ball, 1116 Capacitance in series circuits, 92 Carbon dating, 386, 392, 777, 794 Catenary, 763 Charge of an electron, 28 Chemical reaction, 395 Chemistry experiment, 1229 Circuit analysis, 505 Comet orbit, A25, A28 Dating organic material, 746 Diesel mechanics, 247 Earth and its shape, 947, 977 Earthquake magnitude, Richter scale, 389, 395, 401, 786 Electricity, 684 Electron microscopes, 28 Escape velocity, 35, 38 Estimating speed, 38 Estimating the time of death, 395 Falling object, 97, 101, 112, 114, 1098 Eiffel tower, 111 Grand Canyon, 151 instantaneous rate of change, 585 on the moon, 151 the owl and the mouse, 101 Royal Gorge Bridge, 101 Fluid flow, A28 Geology contour map of seismic amplitudes, 956 crystals, 938 Hot air balloon, 112 Hydrogen orbitals, 1232 Ideal Gas Law, 91 Kinetic energy, 91 Lensmaker’s equation, 92 Measurement errors, 734, 736 Metallurgy, 1205 Meteorology amount of rainfall, 1195 annual snowfall in Reno, Nevada, 193 atmospheric pressure, 956 average monthly precipitation for Bismarck, North Dakota, 1070 for Sacramento, California, 1069 for San Francisco, California, 1077 (continued on back endsheets) College Algebra and Calculus An Applied Approach RON LARSON The Pennsylvania State University The Behrend College A N N E V H O D G K I N S Phoenix College with the assistance of D AV I D C FA LV O The Pennsylvania State University The Behrend College Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States College Algebra and Calculus: An Applied Approach Ron Larson and Anne V Hodgkins VP/Editor-in-Chief: Michelle Julet Publisher: Richard Stratton Senior Sponsoring Editor: Cathy Cantin Associate Editor: Jeannine Lawless Editorial Assistant: Amy Haines Associate Media Editor: Lynh Pham © 2010, Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher Senior Content Manager: Maren Kunert Marketing Specialist: Ashley Pickering Marketing Assistant: Angela Kim Marketing Communications Manager: Mary Anne Payumo Associate Content Project Manager, Editorial Production: Jill Clark For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Art and Design Manager: Jill Haber Senior Manufacturing Buyer: Diane Gibbons Library of Congress Control Number: 2008929478 Senior Rights Acquisition Account Manager: Katie Huha ISBN-13: 978-0-547-16705-3 Text Designer: Jean Hammond ISBN-10: 0-547-16705-9 Art Editor: Larson Texts, Inc Senior Photo Editor: Jennifer Meyer Dare Illustrator: Larson Texts, Inc Cover Designer: Sarah Bishins Cover Image: © Vlad Turchenko, istockphoto Brooks/Cole 10 Davis Drive Belmont, CA 94002 USA Compositor: Larson Texts, Inc Cengage learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locate your local office at: international.cengage.com/region Cengage learning products are represented in Canada by Nelson Education, Ltd For your course and learning solutions, visit www.cengage.com Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Printed in Canada 12 11 10 09 08 Contents iii Contents A Word from the Authors (Preface) Textbook Features x viii Fundamental Concepts of Algebra 0.1 Real Numbers: Order and Absolute Value 0.2 The Basic Rules of Algebra 10 0.3 Integer Exponents 20 0.4 Radicals and Rational Exponents 29 Mid-Chapter Quiz 39 0.5 Polynomials and Special Products 40 0.6 Factoring 48 0.7 Fractional Expressions 55 Chapter Summary and Study Strategies 62 Review Exercises 64 Chapter Test 67 Equations and Inequalities 1.1 Linear Equations 69 1.2 Mathematical Modeling 79 1.3 Quadratic Equations 93 1.4 The Quadratic Formula 104 Mid-Chapter Quiz 114 1.5 Other Types of Equations 115 1.6 Linear Inequalities 126 1.7 Other Types of Inequalities 138 Chapter Summary and Study Strategies Review Exercises 150 Chapter Test 154 Cumulative Test: Chapters 0–1 155 2 68 148 Functions and Graphs 2.1 Graphs of Equations 157 2.2 Lines in the Plane 171 2.3 Linear Modeling and Direct Variation 182 2.4 Functions 194 Mid-Chapter Quiz 207 2.5 Graphs of Functions 208 2.6 Transformations of Functions 219 2.7 The Algebra of Functions 228 2.8 Inverse Functions 238 Chapter Summary and Study Strategies 248 Review Exercises 250 Chapter Test 255 156 iv Contents Polynomial and Rational Functions 256 3.1 Quadratic Functions and Models 257 3.2 Polynomial Functions of Higher Degree 269 3.3 Polynomial Division 279 3.4 Real Zeros of Polynomial Functions 289 Mid-Chapter Quiz 303 3.5 Complex Numbers 304 3.6 The Fundamental Theorem of Algebra 314 3.7 Rational Functions 322 Chapter Summary and Study Strategies 334 Review Exercises 336 Chapter Test 340 Exponential and Logarithmic Functions 4.1 Exponential Functions 342 4.2 Logarithmic Functions 354 4.3 Properties of Logarithms 364 Mid-Chapter Quiz 372 4.4 Solving Exponential and Logarithmic Equations 4.5 Exponential and Logarithmic Models 383 Chapter Summary and Study Strategies 396 Review Exercises 398 Chapter Test 402 Cumulative Test: Chapters 2– 403 Systems of Equations and Inequalities 5.1 Solving Systems Using Substitution 405 5.2 Solving Systems Using Elimination 415 5.3 Linear Systems in Three or More Variables Mid-Chapter Quiz 440 5.4 Systems of Inequalities 441 5.5 Linear Programming 451 Chapter Summary and Study Strategies 461 Review Exercises 462 Chapter Test 466 373 404 427 Matrices and Determinants 6.1 Matrices and Linear Systems 468 6.2 Operations with Matrices 482 6.3 The Inverse of a Square Matrix 497 Mid-Chapter Quiz 507 6.4 The Determinant of a Square Matrix 508 6.5 Applications of Matrices and Determinants Chapter Summary and Study Strategies 527 Review Exercises 529 Chapter Test 533 341 467 518 Contents Limits and Derivatives 7.1 Limits 535 7.2 Continuity 547 7.3 The Derivative and the Slope of a Graph 7.4 Some Rules for Differentiation 569 Mid-Chapter Quiz 581 7.5 Rates of Change: Velocity and Marginals 7.6 The Product and Quotient Rules 597 7.7 The Chain Rule 608 Chapter Summary and Study Strategies 619 Review Exercises 621 Chapter Test 625 v 534 558 582 Applications of the Derivative 626 8.1 Higher-Order Derivatives 627 8.2 Implicit Differentiation 634 8.3 Related Rates 641 Mid-Chapter Quiz 649 8.4 Increasing and Decreasing Functions 650 8.5 Extrema and the First-Derivative Test 659 8.6 Concavity and the Second-Derivative Test 669 Chapter Summary and Study Strategies 681 Review Exercises 683 Chapter Test 687 Further Applications of the Derivative 688 9.1 Optimization Problems 689 9.2 Business and Economics Applications 698 9.3 Asymptotes 708 Mid-Chapter Quiz 719 9.4 Curve Sketching: A Summary 720 9.5 Differentials and Marginal Analysis 729 Chapter Summary and Study Strategies 739 Review Exercises 740 Chapter Test 743 10 Exponential and Logarithmic Functions 10.1 Exponential Functions 745 10.2 Natural Exponential Functions 751 10.3 Derivatives of Exponential Functions 760 Mid-Chapter Quiz 768 10.4 Logarithmic Functions 769 10.5 Derivatives of Logarithmic Functions 778 10.6 Exponential Growth and Decay 787 Chapter Summary and Study Strategies 798 Review Exercises 800 Chapter Test 804 744 vi Contents 11 Integration and Its Applications 805 11.1 11.2 Antiderivatives and Indefinite Integrals 806 Integration by Substitution and The General Power Rule 817 11.3 Exponential and Logarithmic Integrals 826 Mid-Chapter Quiz 833 11.4 Area and the Fundamental Theorem of Calculus 834 11.5 The Area of a Region Bounded by Two Graphs 846 11.6 The Definite Integral as the Limit of a Sum 855 Chapter Summary and Study Strategies 863 Review Exercises 865 Chapter Test 869 12 Techniques of Integration 870 12.1 Integration by Parts and Present Value 871 12.2 Partial Fractions and Logistic Growth 881 12.3 Integration Tables 891 Mid-Chapter Quiz 901 12.4 Numerical Integration 902 12.5 Improper Integrals 911 Chapter Summary and Study Strategies 924 Review Exercises 926 Chapter Test 929 13 Functions of Several Variables 13.1 The Three-Dimensional Coordinate System 931 13.2 Surfaces in Space 939 13.3 Functions of Several Variables 948 13.4 Partial Derivatives 957 13.5 Extrema of Functions of Two Variables 968 Mid-Chapter Quiz 977 13.6 Lagrange Multipliers 978 13.7 Least Squares Regression Analysis 987 13.8 Double Integrals and Area in the Plane 997 13.9 Applications of Double Integrals 1005 Chapter Summary and Study Strategies 1015 Review Exercises 1017 Chapter Test 1021 14 Trigonometric Functions (online)* 14.1 Radian Measure of Angles 14.2 The Trigonometric Functions 14.3 Graphs of Trigonometric Functions Mid-Chapter Quiz 14.4 Derivatives of Trigonometric Functions 14.5 Integrals of Trigonometric Functions Chapter Summary and Study Strategies Review Exercises Chapter Test 930 A146 Index Discrete probability, 1184 Discrete random variable, 1183 expected value of, 1185 mean of, 1185 standard deviation of, 1186 variance of, 1186 Discrete variable, 587 Discriminant, 105 Distance between a point and a plane, 946 between two numbers, traveled, formula for, 85 Distance Formula, 158 in space, 933 Distinguishable permutations, 1165 Distribution frequency, 1183 probability, 1184 Distributive Property, 12 for complex numbers, 306 for matrices, 485, 489 Divergence of an improper integral, 912, 915 of an infinite geometric series, 1113, 1123 of an infinite series, 1110 nth-Term Test for, 1112, 1123 of a p-series, test for, 1119, 1123 Ratio Test, 1121, 1123 of a sequence, 1108 Divides evenly, 280 Dividing fractions, 14 Dividing out technique for evaluating a limit, 539 Division, 11 Algorithm, 280 long, of polynomials, 279 Remainder Theorem, 283 synthetic, 282, 284 Divisors, 15 Domain of an expression, 55 feasible, 689 of a function, 194, 201, 948 implied, 198, 201 of a rational function, 322 Double angle formulas, 1032 Double inequality, 5, 130 Double integral, 998 finding area with, 999 finding volume with, 1005 Double solution, 94 Double subscript, 468 Doyle Log Rule, 624 E e, natural base, 346, 751 e, limit definition of, 751 Ebbinghaus model, 767 Effective rate, 754 Elastic demand, 702 Elementary functions, power series for, 1132 Elementary row operations, 469 Elimination Gaussian, 428 with back-substitution, 474 Gauss-Jordan, 475 method of, 415, 417 Ellipsoid, 943 Elliptic cone, 942 Elliptic paraboloid, 942 Encoding messages, 521 Endpoint, continuity at, 550 Endpoints of an interval, 126 Entry of a matrix, 468 Equal matrices, 482 Equality of complex numbers, 304 hidden, 79 properties of, 16 Equation(s), 16, 69 absolute value, 119 algebraic, 79 checking a solution, 71 circle, standard form, 164, 165 conditional, 69 differential, 811 equivalent, 70 logistic, 885 general form, circle, 165 graph of, 160 identity, 69 of a line general form, 176 horizontal, 176 intercept form, 180 point-slope form, 173, 176 slope-intercept form, 175, 176 summary of, 176 two-point form, 174, 520 vertical, 176 linear, 70, 679 of a plane in space, general, 939 polynomial, second degree, 93 position, 97 primary, 689, 690 quadratic, 93, 679 quadratic type, 116 recognition, 164 secondary, 690 solution(s) of, 69, 160 solving, 69 absolute value, 119 exponential, 373, 773, 796 linear, 71, 679 logarithmic, 373, 376, 773, 797 quadratic, 93, 95, 104, 679 radical, 117, 679 review, 679, 737 trigonometric, 1037, 1071 of a sphere, standard, 934 system of, 405 true, 69 Equilibrium, point of, 422, 446 Equimarginal Rule, 985 Equivalent equations, 70 expressions, 55 fractions, 14 inequalities, 128 systems of equations, 416, 428 Error percentage, 734 propagation, 734 relative, 734 in Simpson’s Rule, 906 in the Trapezoidal Rule, 906 Errors, sum of squared, 987, 988 Evaluating an algebraic expression, 11 Evaluating a limit direct substitution, 537 dividing out technique, 539 of a polynomial function, 538 Replacement Theorem, 539 of a trigonometric function, 1045 Even function, 213, 841 integration of, 841 Event(s), 1171 certain, 1172 complement of, 1178 impossible, 1172 independent, 1176 mutually exclusive, 1175 probability of, 1172 Existence of a limit, 541 Existence theorem, 314 Expanding a binomial, 1221 by cofactors, 511 a logarithmic expression, 366, 772 Expected value, 1185, 1197 of a continuous random variable, 1197 Index of a discrete random variable, 1185 Experiment, 1171 Explicit form of a function, 634 Exponent(s), 20 properties of, 21, 33, 745 rational, 32, 33 Exponential decay model, 383, 787, 789 equation, 373, 773, 796 form, 20, 769 function, 342, 344, 745, 748 growth model, 383, 752, 787, 789 model, least squares regression, 791 notation, 20 probability density function, 1195, 1202 Exponential growth and decay, law of, 787 Exponential Rule for integration (General), 826 for integration (Simple), 826 Exponentiating, 376 Exponents and logarithms inverse properties of, 373, 771 One-to-One Properties, 373 Expression(s) algebraic, 10 domain of, 55 equivalent, 55 fractional, 56 logarithmic, 772 radical, simplest form of, 31 rational, 56 rewriting with sigma notation, 1152 simplifying, 617 factorial expressions, 1151 “unsimplifying,” 861 Extended Principle of Mathematical Induction, 1209 Extracting square roots, 95 Extraneous solution, 73, 117, 679 Extrapolation, linear, 174 Extrema absolute, 664 on a closed interval, finding, 665 relative, 659 First-Derivative Test for, 660 First-Partials Test for, 969 function of two variables, 968, 971 Second-Derivative Test for, 674 Second-Partials Test for, 971 of trigonometric functions, 1056 Extreme Value Theorem, 664 Extremum, relative, 659 F f of x, 196 Factor(s), 15 of a polynomial, 273, 318 Factor Theorem, 283 Factorial, 1082 expressions, simplifying, 1151 Factoring, 48 difference of two cubes, 49 difference of two squares, 49 by grouping, 52 perfect square trinomial, 49 solving a quadratic equation by, 93 special polynomial forms, 49 sum of two cubes, 49 Falling object, position equation for, 97, 109 Family of functions, 220, 806 Feasible domain of a function, 689 Feasible solutions, 451 Finding antiderivatives, 808 area with a double integral, 999 extrema on a closed interval, guidelines, 665 a formula for the nth term of a sequence, 1212 inverse functions, 241 an inverse matrix, 499 test intervals for a polynomial, 138 volume with a double integral, 1005 volume of a solid, guidelines, 1008 zeros of a polynomial, 289 Finite sequence, 1080 series, 1084 First derivative, 627 First-Derivative Test for relative extrema, 660 First differences, 1214 First partial derivatives, 957, 958 First-Partials Test for relative extrema, 969 FOIL Method, 42 Forming equivalent equations, 70 Formula(s), 85 alternative, for variance, 1199 change-of-base, 364, 782 common, for area, perimeter, and volume, 85 for compound interest, 348, 753 Distance, 158 in space, 933 for distance traveled, 85 A147 double angle, 1032 half angle, 1032 Midpoint, 159 in space, 933 miscellaneous common, 85 Pythagorean Theorem, 98 Quadratic, 104 recursion, 1092 reduction, 897 simple interest, 85 temperature, 85 trigonometric reduction formulas, 1032 Formulas and terms, business, summary of, 704 Fractal geometry, 309 Fraction(s), adding, 14 complex, 59 denominator, 12 dividing, 14 equivalent, 14 least common denominator, 15 multiplying, 14 numerator, 12 partial, 881 properties of, 14 rules of signs, 14 subtracting, 14 Fractional expression, 56 Frequency, 1183 Frequency distribution, 1183 Function(s), 194, 201 absolute value, graph of, 214 acceleration, 629 algebraic, 342 approximating zeros using Newton’s Method, 1143, 1144 average cost, 699 average value, 840, 1010 Cobb-Douglas production, 640, 952 common graphs of, 214 composition of, 230 constant, 210, 214, 257, 650, 726 continuity of, 548 continuous, 269, 547 cosecant, 1031 cosine, 1031 cotangent, 1031 critical number of, 652 cubic, 726 cubing, graph of, 214 decreasing, 210, 650 defined, 201 demand, 589 A148 Index dependent variable, 195, 201 derivative of, 563 difference of, 228 domain of, 194, 198, 201 elementary, power series for, 1132 even, 213, 841 explicit form of, 634 exponential, 342, 745 exponential with base a, derivative of, 783 exponential probability density, 1195, 1202 family of, 220, 806 feasible domain of, 689 graph of, 208 greatest integer, 212, 551 guidelines for analyzing the graph of, 720 identity, graph of, 214 implicit form of, 634 implied domain, 198, 201 increasing, 210, 650 independent variable, 195, 201 inverse, 238, 239 limit of, 537 linear, 257, 726 logarithmic, 354, 769 logarithmic to the base a, derivative of, 783 logistic growth, 752, 885 modeling demand, 590 name of, 201 natural exponential, 346, 751 natural logarithmic, 358, 769 normal probability density, 765, 917, 1202 notation, 196 objective, 451 odd, 213, 841 piecewise-defined, 197 polynomial, 257 population density, 1009 position, 586, 629 power series for elementary functions, 1132 probability density, 898, 1188 exponential, 1195, 1202 normal, 765, 917, 1202 standard normal, 1202 uniform, 1201 product of, 228 quadratic, 257, 726 quotient of, 228 range of, 194, 201, 208 rational, 322, 325 relative maximum of, 210, 211, 659 relative minimum of, 210, 211, 659 revenue, 589 secant, 1031 sine, 1031 square root, graph of, 214 squaring, graph of, 214 standard normal probability density, 1202 step, 212, 551 sum of, 228 tangent, 1031 terminology, summary of, 201 test for even and odd, 213 test for increasing and decreasing, 650, 652 of three variables, 948, 962 transcendental, 342 trigonometric, 1031 of two variables, 948 unbounded, 543 undefined, 201 uniform probability density, 1201 value at x, 196, 201 velocity, 586, 629 Vertical Line Test for, 209 zero of, 208, 273 zeros, approximating using Newton’s Method, 1143, 1144 Fundamental Counting Principle, 1162 Fundamental Theorem of Algebra, 314 Fundamental Theorem of Arithmetic, 15 Fundamental Theorem of Calculus, 835, 836 G Gaussian elimination, 428 with back-substitution, 474 Gaussian model, 383, 387 Gauss-Jordan elimination, 475 General equation of a plane in space, 939 General Exponential Rule, for integration, 826 General form of the equation of a circle, 165 of a line, 176 General Logarithmic Rule, for integration, 828 General Power Rule for differentiation, 610 for integration, 817 General solution of a differential equation, 811 Geometric sequence, 1099 common ratio of, 1099 finite, sum of, 1102 nth term of, 1100 Geometric series, 1103 convergence of, 1113, 1123 divergence of, 1113, 1123 sum of, 1103 Geometry, solid analytic, 931 Graph(s) of absolute value function, 214 area of a region between two, 846 of constant function, 214 of cubing function, 214 of an equation, 160 of an exponential function, 343, 747 of a function, 208 guidelines for analyzing, 720 of a function of two variables, 949 horizontal shift of, 219 of identity function, 214 of an inequality, 126 in two variables, 441 of a logarithmic function, 356 of the natural logarithmic function, 769 nonrigid transformation of, 223 of a rational function, 325 reflection of, 221 rigid transformation of, 223 slope of, 559, 560, 582 of square root function, 214 of squaring function, 214 stacked bar, 235, 236 summary of simple polynomial graphs, 726 tangent line to, 558 of trigonometric functions, 1043 turning points of, 273 vertical shift of, 219 vertical shrink of, 223 vertical stretch of, 223 Graphical interpretation of partial derivatives, 959 of solutions of systems of linear equations, 419 Graphing, point-plotting method, 160 Gravity, acceleration due to, 630 Greater than, or equal to, Greatest integer function, 212, 551 Guidelines for analyzing the graph of a function, 720 for applying concavity test, 670 for applying increasing/decreasing test, 652 Index for finding extrema on a closed interval, 665 for finding the volume of a solid, 1008 for graphing rational functions, 325 for integration by parts, 871 for integration by substitution, 821 for modeling exponential growth and decay, 789 for solving optimization problems, 690 for solving a related-rate problem, 643 for using the Fundamental Theorem of Calculus, 836 for using the Midpoint Rule, 856 H Half angle formulas, 1032 Half-life, 349, 788 Hardy-Weinberg Law, 976 Harmonic series, 1118 Hidden equality, 79 product, 84 Higher-order derivative, 627, 628 Higher-order partial derivatives, 963 Horizontal asymptote, 323, 324, 712, 713 Horizontal line, 176 Horizontal Line Test, 243 Horizontal shift, 219 Hyperbola, 323, 637 Hyperbolic paraboloid, 942 Hyperboloid of one sheet, 943 of two sheets, 943 I Identities, trigonometric, 1032 Identity, 69 function, graph of, 214 matrix, 489 Imaginary axis, 309 Imaginary number, 304 pure, 304 Imaginary unit i, 304 Implicit differentiation, 634, 636 Implicit form of a function, 634 Implied domain, 198, 201 Impossible event, 1172 Improper integrals, 911 convergence of, 912, 915 divergence of, 912, 915 infinite discontinuity, 911 infinite integrand, 915 infinite limit of integration, 912 Improper rational expression, 280 Inclusive or, 14 Inconsistent system, 419 Increasing function, 210, 650 Indefinite integral, 807 Independent events, 1176 probability of, 1177 Independent system, 419 Independent variable, 195, 201 Index of a radical, 29 of summation, 1084 Induction, mathematical, 1207 Inelastic demand, 702 Inequalities absolute value, solving, 131 double, 5, 130 equivalent, 128 graph of, 126 linear, 129 in two variables, 441 properties of, 128 satisfying, 126 solution set of, 126 solutions of, 126 solving, 126 symbols, in two variables, 442 Infinite discontinuity, 911 integrand, 915 limit, 708 limit of integration, 912 sequence, 1080 wedge, 445 Infinite series, 1084, 1110 convergence of, 1110 divergence of, 1110 geometric, 1103, 1113, 1123 harmonic, 1118 nth Term Test for divergence, 1112, 1123 power, 1126, 1127 binomial, 1132 for elementary functions, 1132 Maclaurin series, 1129 Taylor series, 1129 properties of, 1111 p-series, 1118, 1119, 1123 Ratio Test, 1121, 1123 sum of, 1110 summary of tests of, 1123 A149 Infinity limit at, 712 negative, 127 positive, 127 Inflection, point of, 672 Initial condition, 811 Initial ray, 1023 Initial value, 787 Instantaneous rate of change, 585 and velocity, 585 Integer(s), negative, positive, Integral(s) approximating definite, Midpoint Rule, 855 Simpson’s Rule, 904 Trapezoidal Rule, 902 using a power series, 1140 definite, 834, 836 double, 998 of even functions, 841 of exponential functions, 826 improper, 911, 912, 915 indefinite, 807 of logarithmic functions, 828 notation of antiderivatives, 807 of odd functions, 841 partial, with respect to x, 997 table of, 892 of trigonometric functions, 1062, 1066 Integral sign, 807 Integrand, 807 infinite, 915 Integration, 807 basic rules, 808 by change of variables, 821 constant of, 807 Constant Multiple Rule, 808 Constant Rule, 808 Difference Rule, 808 of even functions, 841 of exponential functions, 826 General Exponential Rule, 826 General Logarithmic Rule, 828 General Power Rule, 817 infinite limit of, 912 of logarithmic functions, 828 lower limit of, 834 numerical Simpson’s Rule, 904 Trapezoidal Rule, 902 of odd functions, 841 partial, with respect to x, 997 by partial fractions, 881 A150 Index by parts, 871, 875 reduction formulas, 897 Simple Exponential Rule, 826 Simple Logarithmic Rule, 828 Simple Power Rule, 808 by substitution, 821 Sum Rule, 808 by tables, 891 techniques, and algebra, 922 of trigonometric functions, 1062, 1066 upper limit of, 834 Intercept x-intercept, 162 y-intercept, 162 Intercept form of the equation of a line, 180 Interest compound, 347, 348, 753 continuously compounded, 347, 348 simple, 85 Intermediate Value Theorem, 292 Interpolation, linear, 174 Intersection of A and B, 1175 Intersection, point of, 409 using Newton’s Method to approximate, 1147 Interval bounded, 126 closed, 126 endpoints of, 126 open, 126 unbounded, 127 Inverse additive, 12 multiplicative, 12 of a square matrix, 497, 499 Inverse function, 238, 239, 241 Horizontal Line Test for, 243 Inverse Property of exponential equations, 373, 771 of logarithmic equations, 373, 771 Invertible matrix, 498 Irrational, Irreducible over the integers, 48 over the rationals, 318 over the reals, 318 Iteration, 1144 L Lagrange multipliers, 978 with one constraint, 978 with two constraints, 983 Law of exponential growth and decay, 787 Law of Trichotomy, Leading coefficient of a polynomial, 40 Leading Coefficient Test, 271 Leading 1, 472 Least common denominator, 15 Least-Cost Rule, 985 Least squares regression exponential, 791 line, 990 quadratic, 992 Left-handed orientation, three-dimensional coordinate system, 931 Less than, or equal to, Level curve, 950 Like radicals, 34 Like terms of a polynomial, 41 Limit direct substitution, 537 dividing out technique, 539 existence of, 541 of a function, 537 infinite, 708 at infinity, 712 of integration, 834 infinite, 912 from the left, 541 one-sided, 541 operations with, 538 of a polynomial function, 538 properties of, 537 Replacement Theorem, 539 from the right, 541 of a sequence, 1108 of trigonometric functions, 1045 Limit definition of e, 751 Limited total demand, 982 Line(s) equation of general form, 176 intercept form, 180 point-slope form, 173, 176 slope-intercept form, 175, 176 summary of, 176 two-point form, 174, 520 horizontal, 176 least squares regression, 990 parallel, 177 perpendicular, 177, 178 secant, 560 slope of, 171, 173 tangent, 558 vertical, 176 Linear equation, 70 solving, 71, 679 Linear extrapolation, 174 Linear Factorization Theorem, 314 Linear function, 257, 726 Linear inequality, 129 in two variables, 442 system of, 443 Linear interpolation, 174 Linear programming, 451 Linear programming problem optimal solution of, 451 solving, 453 Linear regression, 182, 187 Logarithm(s) to the base a, 782 common, 769, 782 properties of, 355, 365, 771 Logarithmic equation Inverse Property, 373 One-to-One Property, 373 solving, 373, 376, 773, 797 Logarithmic and exponential form, 769 Logarithmic expression condensing, 366, 772 expanding, 366, 772 Logarithmic function with base a, 354 derivative of, 783 change-of-base formula, 364 characteristics of, 357 common, 355 integral of, 828 natural, 358, 769 properties of, 357, 769 Logarithmic model, 383, 389 Logarithmic Rule for integration (General), 828 for integration (Simple), 828 Logarithms and exponents, inverse properties of, 771 Logistic curve, 388, 885 differential equation, 885 growth model, 383, 388, 752, 885 Long division of polynomials, 279 Lorenz curve, 854 Lower limit of integration, 834 of summation, 1084 Lower triangular matrix, 514 M Maclaurin series, 1129 Main diagonal entries, 468 Index Mandelbrot Set, 309 Map, contour, 950 Marginal analysis, 731, 839 cost, 587 profit, 587 revenue, 587 Marginal productivity of money, 981 Marginal propensity to consume, 823 Marginals, 587 Mathematical induction, 1207 Mathematical model, 79, 182 measuring the accuracy of, 987 Mathematical modeling, 79 Matrix (matrices), 468 addition, 483, 485 additive identity, 486 adjoining, 499 augmented, 469 coefficient, 469 column, 468 column of, 468 determinant of, 501, 508, 511 diagonal, 514 Distributive Property, 485, 489 elementary row operations, 469 entry of, 468 main diagonal, 468 equal, 482 finding an inverse, 499 identity, 489 invertible, 498 multiplication, 487, 489 nonsingular, 498 order of, 468 product of two, 487 row, 468 coded and uncoded, 521 row-echelon form, 472 reduced, 472 row-equivalent, 469 row of, 468 scalar, 483 scalar multiple, 483 scalar multiplication, 483, 485 singular, 498 square, 468 cofactors of, 510 determinant of, 501, 508, 511 inverse of, 497 minors of, 510 stochastic, 496 sum of, 483 triangular, 514 lower and upper, 514 zero, 486 Maxima, relative, 659 Maximum absolute, 664 relative, 210, 211, 659 function of two variables, 968, 971 Mean of a continuous random variable, 1197 of a discrete random variable, 1185 of a probability distribution, 765 Measure of central tendency, 1185, 1200 Measuring the accuracy of a mathematical model, 987 Median, of a continuous random variable, 1200 Method of elimination, 415, 417 Method of Lagrange multipliers, 978 Method of substitution, 405 Midpoint Formula, 159 in space, 933 Midpoint Rule for approximating a definite integral, 855, 856 Minima, relative, 659 Minimum absolute, 664 relative, 210, 211, 659 function of two variables, 968, 971 Minors of a square matrix, 510 Miscellaneous common formulas, 85 Mixed partial derivative, 963 Mixture problem, 84 Model Ebbinghaus, 767 exponential decay, 383, 787, 789 exponential growth, 383, 752, 787, 789 Gaussian, 383, 387 least squares regression exponential, 791 logarithmic, 383, 389 logistic growth, 383, 388, 752, 885 mathematical, 79, 182 verbal, 79 Modeling a demand function, 590 exponential growth and decay, 789 Money, marginal productivity of, 981 Monomial, 40 Multiplication, 11 by a constant in an inequality, 128 matrix, 487 scalar, 483 Multiplicative Identity Property, 12 Multiplicative Inverse Property, 12 Multiplicity, 274 Multiplying fractions, 14 A151 Mutually exclusive events, 1175 N n factorial, 1082 Name of a function, 201 Natural base, 346 Natural exponential function, 346, 751 derivative of, 760 Natural logarithmic function, 358, 769 base of, 769 derivative of, 778 properties of, 358, 365 Natural number, Negation, properties of, 13 Negative infinity, 127 integers, number, Newton’s Method, 1143, 1144, 1146 Nominal rate, 754 Nonnegative real numbers, Nonremovable discontinuity, 549 Nonrigid transformation of a graph, 223 Nonsingular matrix, 498 Nonsquare system, 432 Normal probability density function, 765, 917, 1202 standard normal, 1202 Normally distributed population, 387 Not equal to, Notation exponential, 20 for first partial derivatives, 958 function, 196 for higher-order derivatives, 627 integral, of antiderivative, 807 scientific, 23 sigma, 1084 summation, 1084 nth partial sum, 1084 of an arithmetic sequence, 1094 nth remainder, 1139 nth root of a number, 29 principal, 29 nth term of an arithmetic sequence, 1091 of a geometric sequence, 1100 nth-Term Test for divergence of an infinite series, 1112, 1123 Number(s) of combinations of n elements taken r at a time, 1166 complex, 304 composite, 15 A152 Index critical, 652 imaginary, 304 pure, 304 irrational, natural, negative, nth root of, 29 of permutations of n elements, 1163 taken r at a time, 1164 positive, prime, 15 principal nth root of, 29 rational, real, nonnegative, of solutions of a linear system, 430 Numerator, 12 Numerical integration Simpson’s Rule, 904 Trapezoidal Rule, 902 O Objective function, 451 Oblique asymptote, 327 Obtuse angle, 1023 Occurrences of relative extrema, 659 Octants, 931 Odd function, 213, 841 integration of, 841 One sided limit, 541 One-to-One Property of exponential equations, 373 of logarithmic equations, 373 Open interval, 126 continuous on, 547 Open region, 969 Operations with limits, 538 Operations that produce equivalent systems, 428 Optimal solution of a linear programming problem, 451 Optimization, 451 Optimization problems business and economics, 698 constrained, 978 Lagrange multipliers, 978 primary equation, 689 secondary equation, 690 solving, 689, 690 Order of a matrix, 468 Order on the real number line, Ordered pair, 157 Ordered triple, 427, 931 Orientation for a three-dimensional coordinate system, 931 Origin real number line, rectangular coordinate system, 157 Origin symmetry, 163 Outcomes, 1171 P Parabola, 257 axis of, 258 axis of symmetry, 258 vertex of, 258 Paraboloid elliptic, 942 hyperbolic, 942 Parallel lines, 177 Partial derivative, 957 first, 957, 958 function of three variables, 962 function of two variables, 957 graphical interpretation of, 959 higher-order, 963 mixed, 963 Partial differentiation, 957 Partial fractions, 881 Partial integration with respect to x, 997 Partial sums, sequence of, 1110 Particular solution of a differential equation, 811 Parts, integration by, 871, 875 Pascal’s Triangle, 1220 Percentage error, 734 Perfect cubes, 30 square trinomial, factoring, 49 squares, 30 Perimeter, common formulas for, 85 Period, 1042 Permutation(s), 1163 distinguishable, 1165 of n elements, 1163 taken r at a time, 1164 Perpendicular lines, 178 Perpetual annuity, 918, 919 Perpetuity, 918, 919 Phase shift, 1050 Piecewise-defined function, 197 Plane parallel to coordinate axes, 940 parallel to coordinate planes, 940 xy-plane, 931 xz-plane, 931 yz-plane, 931 Plane in space, general equation of, 939 Point(s) continuity of a function at, 547 critical, 969 of diminishing returns, 675 of equilibrium, 422, 446 of inflection, 672 of intersection, 409 saddle, 969, 971 Point-plotting method of graphing, 160 Point-slope form of the equation of a line, 173, 176 Polynomial(s), 40 addition of, 41 complex zeros, 317 constant term, 40 degree of, 40, 41 division long, 279 synthetic, 282 equation second-degree, 93 solution of, 273 factor(s) of, 273, 318 Factor Theorem, 283 finding test intervals for, 138 function, 257 graphs, summary of simple, 726 inequality, 138 Intermediate Value Theorem, 292 irreducible over the integers, 48 leading coefficient of, 40 like terms of, 41 prime, 48 product of, 42 Rational Zero Test, 289 special products of, 43 standard form of, 40 subtraction of, 41 Taylor, 1136 term, 40 in x, 40 x-intercept of the graph of, 273 zero polynomial, 41 zeros of, 138 Population density function, 1009 Position equation, 97, 109, 586, 629 Positive infinity, 127 integers, number, Power, 20 Power Rule differential form of, 733 for differentiation (General), 610 for differentiation (Simple), 570 Index for integration (General), 817 for integration (Simple), 808 Power series, 1126 approximating a definite integral using, 1140 binomial, 1132 centered at c, 1126 convergence of, 1127 for elementary functions, 1132 Maclaurin series, 1129 radius of convergence of, 1127 Taylor series, 1229 Powers of integers, sums of, 1211 Present value, 755, 876 of a perpetual annuity, 919 of a perpetuity, 919 Price elasticity of demand, 702 Primary equation, 689, 690 Prime factorization, 15 number, 15 polynomial, 48 Principal nth root of a number, 29 Principal square root of a negative number, 308 Principle of Mathematical Induction, 1208 Extended, 1209 Probability, 1171 of a complement, 1178 discrete, 1184 of an event, 1172 of independent events, 1177 of mutually exclusive events, 1175 of the union of two events, 1175 Probability density function, 898, 1188 exponential, 1195, 1202 normal, 765, 917, 1202 standard normal, 1202 uniform, 1201 Probability distribution, 1184 Problem-solving strategies, 739 Producer surplus, 446, 850 Product of polynomials, 42 of two functions, 228 of two matrices, 487 Product Rule differential form of, 733 for differentiation, 597 Productivity of money, marginal, 981 Profit marginal, 587 total, 587 Propensity to consume, marginal, 823 Proper rational expression, 280 Properties of absolute value, of algebra, 12 of complex numbers, 306 of definite integrals, 836 of Equality, 16 Reflexive, 16 Symmetric, 16 Transitive, 16 of exponents, 21, 33, 745 of fractions, 14 of inequalities, 128 of infinite series, 1111 inverse, 373 of logarithms and exponents, 373, 771 of limits, 537 of logarithms, 355, 365, 769, 771 of matrix addition, 485 of matrix multiplication, 489 of natural logarithms, 358, 365 of negation, 13 One-to-One, of logarithms and exponents, 373 of probability of an event, 1172 of radicals, 30 of scalar multiplication, 485 of sums, 1085 of zero, 14 Zero-Factor, 14, 93 Property of points of inflection, 672 Proportion, 83 Proportionality, constant of, 183, 787 p-series, 1118 approximating the sum of, 1120 test for convergence of, 1119, 1123 test for divergence of, 1119, 1123 Pure imaginary number, 304 Pursuit curve, 777 Pythagorean identities, 1032 Pythagorean Theorem, 98, 1027 Q Quadrants, 157 Quadratic, least squares regression, 992 Quadratic equation, 93 double solution, 94 repeated solution, 94 solutions of, 105 solving, 679 by extracting square roots, 95 by factoring, 93 using Quadratic Formula, 104 A153 Quadratic Formula, 104 discriminant, 105 Quadratic function, 257, 726 standard form of, 260 Quadratic type, 116 Quadric surface, 941 Quotient Rule differential form of, 733 for differentiation, 600 Quotient of two functions, 228 R Radian measure of angles, 1025 Radians to degrees, converting, 1025 Radical(s) conjugate, 32 equation, solving, 117, 679 index of, 29 like, 34 properties of, 30 simplest form, 31 symbol, 29 Radicand, 29 Radioactive decay, 788 Radius of a circle, 165 Radius of convergence of a power series, 1127 Random variable, 1183 continuous, 1188 discrete, 1183 Range of a function, 194, 201, 208 of two variables, 948 Rate, 171 constant, 644 effective, 754 nominal, 754 related, 641 stated, 754 variable, 644 Rate of change, 171, 182, 185, 582, 585 average, 582 instantaneous, 585 and velocity, 585 Ratio, 83, 171 Ratio Test for an infinite series, 1121, 1123 Rational exponent, 32, 33 expression, 56 improper, 280 proper, 280 function, 322 inequality, critical numbers of, 142 A154 Index number, Rational Zero Test, 289 Rationalizing the denominator, 31, 32 Ray initial, 1023 terminal, 1023 Real axis, 309 Real number(s), nonnegative, Real number line, bounded intervals on, 126 coordinate, order on, origin of, unbounded intervals on, 127 Real zeros of polynomial functions, 273 Reciprocal, 12 Rectangle area of, 85 perimeter of, 85 Rectangular coordinate system, 157 origin of, 157 quadrants, 157 x-axis, 157 y-axis, 157 Rectangular solid, volume of, 85 Recursion formula, 1092 Red herring, 92 Reduced row-echelon form, 472 Reduction formulas integral, 897 trigonometric, 1032 Reference angle, 1034 Reflection, 221 in the x-axis, 221 in the y-axis, 221 Reflexive Property of Equality, 16 Region average value of a function over, 1010 closed, 969 open, 969 solid, volume of, 1005 Region bounded by two graphs, area of, 846 Regression exponential, least squares, 791 line, least squares, 990 quadratic, least squares, 992 Related-rate problem, guidelines for solving, 643 Related rates, 641 Related variables, 641 Relative error, 734 Relative extrema, 659 First-Derivative Test for, 660 First-Partials Test for, 969 function of two variables, 968, 971 occurrences of, 659 Second-Derivative Test for, 674 Second-Partials Test for, 971 of trigonometric functions, 1056 Relative extremum, 659 Relative maxima, 659 Relative maximum, 210, 211, 659 function of two variables, 968, 971 Relative minima, 659 Relative minimum, 210, 211, 659 function of two variables, 968, 971 Remainder, nth, 1139 Remainder Theorem, 283 Removable discontinuity, 549 Repeated solution, 94 Repeated zero, 274 Repeating decimal, Replacement Theorem, 539 Revenue marginal, 587 total, 587 Revenue function, 589 Review of solving equations, 679, 737 Rewriting expressions with sigma notation, 1152 Right angle, 1023 Right-handed orientation, three-dimensional coordinate system, 931 Right triangle, solving a, 1036 Right triangle definition of the trigonometric functions, 1031 Rigid transformation of a graph, 223 Root cube, 29 nth, 29 principal, 29 square, 29 principal, of a negative number, 308 Rounded decimal approximation, Rounding decimals, 17 Row-echelon form, 472 reduced, 472 of a system of linear equations, 427 Row-equivalent matrices, 469 Row matrix, 468 coded, 521 uncoded, 521 Row of a matrix, 468 Row operations, 428 Rules of signs for fractions, 14 S Saddle point, 969, 971 Sample space, 1171 Satisfying an inequality, 126 Scalar, 483 Identity Property, 485 multiple, 483 multiplication, 483, 485 Scatter plot, 187 Scientific notation, 23 Secant function, 1031 Secant line, 560 Second-degree polynomial equation in x, 93 Second derivative, 627 Second-Derivative Test, 674 Second differences, 1214 Second-Partials Test for relative extrema, 971 Secondary equation, 690 Sequence, 1080 arithmetic, 1090, 1091 bounded, 309 convergence of, 1108 divergence of, 1108 finite, 1080 geometric, 1099, 1100 infinite, 1080 limit of, 1108 terms of, 1080 unbounded, 309 Sequence of partial sums, 1110 Series binomial, 1132 finite, 1084 geometric, 1103, 1113, 1123 harmonic, 1118 infinite, 1084, 1110 power, 1126 binomial, 1132 for elementary functions, 1132 Maclaurin series, 1129 Taylor series, 1129 p-series, 1118 sum of, 1110 Set, of real numbers, Shift horizontal, 219 vertical, 219 Sigma notation, 1084 rewriting expressions with, 1152 Sigmoidal curve, 388 Sign, integral, 807 Index Similar triangles, 1027 Simple Exponential Rule, for integration, 826 Simple interest formula, 25, 85 Simple Logarithmic Rule, for integration, 828 Simple Power Rule for differentiation, 570 for integration, 808 Simplest form of a radical, 31 Simplifying algebraic expressions, 617 derivatives, 603, 612 factorial expressions, 1151 Simpson’s Rule, 904 error in, 906 Sine function, 1031 Singular matrix, 498 Slant asymptote, 327 Slope of a graph, 559, 560, 582 and the limit process, 560 in x-direction, 959 in y-direction, 959 Slope-intercept form of the equation of a line, 175, 176 Slope of a line, 171, 173 Solid analytic geometry, 931 Solid region, volume of, 1005, 1008 Solution(s) checking, 71 of a differential equation, 811 double, 94 of an equation, 69, 160 extraneous, 73, 117, 679 feasible, 451 of an inequality, 126, 441 of a polynomial equation, 273 of a quadratic equation, 105 repeated, 94 set of an inequality, 126 of a system of equations, 405 of a system of linear inequalities, 443 Solving an absolute value equation, 119 an absolute value inequality, 131 an equation, 69, 679, 737 an equation with fractions, 118 an equation of quadratic type, 116 an equation with radicals, 117, 679 an equation with rational exponents, 117 an exponential equation, 373, 773, 796 an inequality, 126 a linear equation, 71, 679 a linear programming problem, 453 a logarithmic equation, 373, 376, 773, 797 optimization problems, 689 a quadratic equation, 679 by extracting square roots, 95 by factoring, 93 using the Quadratic Formula, 104 a related-rate problem, 643 a right triangle, 1036 a system of equations, 405, 1013 by Gaussian elimination, 428 with back-substitution, 474 by method of elimination, 415, 417 by method of substitution, 405 trigonometric equations, 1037, 1071 word problems, strategy, 86 Special products of polynomials, 43 cube of a binomial, 43 square of a binomial, 43 sum and difference of two terms, 43 Speed, 586 Sphere, 934 standard equation of, 934 volume of, 85 Square(s) area of, 85 of a binomial, 43 completing the, 104 factoring the difference of two, 49 perfect, 30 perimeter of, 85 Square matrix, 468 cofactors of, 510 determinant of, 501, 508, 511 inverse of, 497 minors of, 510 Square root, 29 extracting, 95 function, graph of, 214 principal, of a negative number, 308 Square system, 432 Squared errors, sum of, 987, 988 Squaring function, graph of, 214 Stacked bar graph, 235, 236 Standard deviation of a continuous random variable, 1198 of a discrete random variable, 1186 of a probability distribution, 765 Standard equation of a sphere, 934 Standard form of a complex number, 304 of the equation of a circle, 164, 165 of a polynomial, 40 A155 of a quadratic function, 260 Standard normal probability density function, 1202 Standard position of an angle, 1023 Stated rate, 754 Step function, 212, 551 Stochastic matrix, 496 Straight angle, 1023 Strategies, problem-solving, 739 Strategies for solving exponential and logarithmic equations, 373 Strategy for solving word problems, 86 Subset, Substitute products, 961 Substitution, integration by, 821 Substitution, method of, 405 Substitution Principle, 11 Subtracting fractions, 14 Subtraction, 11 of complex numbers, 305 of polynomials, 41 Sum(s) of a finite arithmetic sequence, 1093 of a finite geometric sequence, 1102 of a geometric series, 1103 of matrices, 483 nth partial, 1084, 1094 of powers of integers, 1211 properties of, 1085 of a p-series, approximating, 1120 sequence of partial, 1110 of a series, 1110 of two angles, 1032 of two cubes, factoring, 49 of two functions, 228 Sum and difference of two terms, 43 Sum Rule differential form of, 733 for differentiation, 575 for integration, 808 Sum of the squared errors, 987, 988 Summary of business terms and formulas, 704 of common uses of integration by parts, 875 of compound interest formulas, 753 of curve-sketching techniques, 720 of differentiation rules, 614 of equations of lines, 176 of function terminology, 201 of rules about triangles, 1027 of simple polynomial graphs, 726 of tests of series, 1123 A156 Index Summation index of, 1084 lower limit of, 1084 notation, 1084 upper limit of, 1084 Surface quadric, 941 in space, 935 trace of, 936 Surplus, consumer and producer, 446, 850 Symmetric Property of Equality, 16 Symmetry, 163 axis of, 258 tests for, 164 with respect to origin, 163 with respect to x-axis, 163 with respect to y-axis, 163 Synthetic division, 282 uses of the remainder in, 284 System of equations, 405 equivalent, 416, 428 point of intersection, 409 solution of, 405 solving, 405, 1013 Gaussian elimination with back-substitution, 474 by method of elimination, 415, 417 by method of substitution, 405 with a unique solution, 502 System of linear equations consistent system, 419 dependent system, 419 graphical interpretation of solutions, 419 inconsistent system, 419 independent system, 419 nonsquare, 432 number of solutions of, 430 row-echelon form, 427 row operations, 428 solving, Gaussian elimination, 428 square, 432 System of linear inequalities, 443 solution of, 443 T Table of integrals, 892 Tables, integration by, 891 Tangent function, 1031 Tangent line, 558 approximation, 729 Taylor polynomial, 1136 series, 1129 Taylor’s Theorem, 1129 with Remainder, 1139 Temperature formula, 85 Term(s) of an algebraic expression, 10 constant, 10 of a sequence, 1080 sum and difference of two, 43 variable, 10 Terminal ray, 1023 Terminating decimal, Terms and formulas, business, summary of, 704 Test(s) for collinear points, 519 for concavity, 669, 670 for convergence and divergence of a p-series, 1119, 1123 for even and odd functions, 213 First-Derivative Test, 660 First-Partials Test, 969 Horizontal Line Test, 243 for increasing and decreasing functions, 650, 652 Leading Coefficient Test, 271 nth-Term Test for divergence of an infinite series, 1112, 1123 Ratio Test for an infinite series, 1121, 1123 Rational Zero Test, 289 Second-Derivative Test, 674 Second-Partials Test, 971 of series, summary of, 1123 for symmetry, 164 Vertical Line Test, 209 Test intervals of a polynomial inequality, 138 Theorem Binomial, 1218, 1228 Extreme Value, 664 Factor, 283 Fundamental, of Algebra, 314 Fundamental, of Arithmetic, 15 Fundamental, of Calculus, 835, 836 Intermediate Value, 292 Linear Factorization, 314 Pythagorean, 98, 1027 Remainder, 283 Replacement, 539 Taylor’s Theorem, 1129 with Remainder, 1139 Theta, ␪, 1023 Third derivative, 627 Three-dimensional coordinate system, 931 Three variables, function of, 948, 962 partial derivatives of, 962 Total cost, 587 demand, limited, 982 profit, 587 revenue, 587 Trace of a surface, 936 Tractrix, 777 Transcendental function, 342 Transformations of graphs horizontal shift, 219 nonrigid, 223 reflection, 221 rigid, 223 vertical shift, 219 vertical shrink, 223 vertical stretch, 223 Transitive Property of Equality, 16 Transitive Property of Inequality, 128 Translating key words and phrases, 80 Trapezoidal Rule, 860, 902 error in, 906 Triangle(s), 1027 area of, 85, 518 perimeter of, 85 similar, 1027 solving a right triangle, 1036 summary of rules about, 1027 Triangular matrix, 514 lower, 514 upper, 514 Trigonometric equations, solving, 1037, 1071 Trigonometric functions cosecant, 1031 cosine, 1031 cotangent, 1031 definitions of, 1031 derivatives of, 1053 graphs of, 1043 integrals of, 1062, 1066 limits of, 1045 relative extrema of, 1056 secant, 1031 sine, 1031 tangent, 1031 Trigonometric identities, 1032 Trigonometric reduction formulas, 1032 Trigonometric values of common angles, 1033 Trinomial, 40 perfect square, factoring, 49 Index True equation, 69 Truncating a decimal, 551 Turning points of a graph, 273 Two-point form of the equation of a line, 174, 520 Two variables, function of, 948 domain, 948 graph of, 949 partial derivatives of, 957 range, 948 relative extrema, 968, 971 relative maximum, 968, 971 relative minimum, 968, 971 U Unbounded behavior, 543 function, 543 intervals on the real number line, 127 region, 454 sequence, 309 Uncoded row matrices, 521 Undefined function, 201 Uniform probability density function, 1201 Union of two events, probability of, 1175 Unit elasticity, 702 Units of measure, 620 “Unsimplifying” an algebraic expression, 861 Upper limit of integration, 834 of summation, 1084 Upper triangular matrix, 514 Uses of the remainder in synthetic division, 284 random, 1188 dependent, 195, 201 discrete, 587 discrete random, 1183 independent, 195, 201 random, 1183 terms, 10 Variable rate, 644 Variables, change of, integration by, 821 Variables, related, 641 Variance of a continuous random variable, 1198, 1199 of a discrete random variable, 1186 Variation constant of, 183 direct, 182, 183 Velocity average, 584 function, 586, 629 and instantaneous rate of change, 585 Verbal model, 79 Vertex of an angle, 1023 of a parabola, 258 Vertical asymptote, 323, 324, 708, 709 Vertical line, 176 Vertical Line Test, 209 Vertical shift, 219 Vertical shrink, 223 Vertical stretch, 223 Volume common formulas for, 85 finding with a double integral, 1005, 1008 of a solid region, 1005 V Value of f at x, 196, 201 Variable(s), 10 continuous, 587 W Word problems, strategy for solving, 86 A157 X x, change in, 560 x, differential of, 729 x-axis, 157 reflection in, 221 symmetry, 163 x-coordinate, 157 x-direction, slope in, 959 x-intercept, 162 xy-plane, 931 xz-plane, 931 Y y, change in, 560 y, differential of, 729 y-axis, 157 reflection in, 221 symmetry, 163 y-coordinate, 157 y-direction, slope in, 959 y-intercept, 162 yz-plane, 931 Z z-axis, 931 Zero(s), of a function, 208, 273 approximating, 292, 293, 1143, 1144 multiplicity of, 274 of a polynomial, 138 properties of, 14 of a rational expression, 142 repeated, 274 Zero-Factor Property, 14, 93 Zero matrix, 486 Zero polynomial, 41 Zoom-and-trace technique, 293 (continued from front endsheets) average monthly temperature in Duluth, Minnesota, 559 average temperature, 1067 contour map of average precipitation for Iowa, 1017 hours of daylight in New Orleans, Louisiana, 1061 isotherms, 977 mean monthly temperature and precipitation for Honolulu, Hawaii, 1061 monthly normal high and low temperatures for Erie, Pennsylvania, 1051 monthly normal temperature for New York City, 685 for Pittsburgh, Pennsylvania, 728 monthly rainfall, 1232 normal average daily temperature, 1060 record January temperatures for Flagstaff, Arizona, for McGrath, Alaska, weather report, 1196 Mixture, 91, 151, 1168 acid, 424, 437 fuel, 424 Molecular velocity, 658 Oxidation-reduction reactions, 1169 Path of an object, 153, 199, 205 Period of a pendulum, 38 Peripheral vision, 1036 pH levels, 389, 395 Position function, 812 Pressure on a scuba diver, 181 Projectile motion, 633, 683 Radio waves, 90 Radioactive carbon isotopes, rate of change, 783 Radioactive decay, 349, 352, 392, 400, 402, 749, 788, 793, 803, 804 Resistors, 147 Solar energy, 301 Sound intensity, 368, 370, 371, 395, 785 Speed of a baseball, 206 Speed of light, 24 Speed of revolution, 1030 Surveying, 909 Temperature, 103, 181 of an apple pie, 741 of the core of the sun, 28 of food placed in a freezer, 624 of food placed in a refrigerator, 606 Temperature change, 1058 Thawing a package of steaks, 395, 401 Throwing an object, 109, 111, 112, 252 Tides, 1061 Velocity of a bicyclist, 623 of a diver, 586, 683 of a falling object, 594, 623 of a racecar, 594 Velocity and acceleration, 631, 633, 683, 868 Vertical motion, 816, 865 Wave properties, 1051 Wind chill, 38, 594 Wind resistance, 101 Work, 362 Consumer American Express credit cards, 277 Annual salary, 79, 181 Average price of a movie ticket, 67, 247 of prescription drugs, 440 Cellular phone charges, 622 Charitable contributions, 264, 275 Choice of two camping outfitters, 414 Choice of two jobs, 414 College costs, 102 Comparative shopping, 132, 135 Computer systems, 1168, 1229 Consumer awareness, 237 Consumer credit, 78 Consumer Price Index, 189 Consumption of bottled water, 651 of energy, 1069 of Italian cheeses, 651 of milk, 947, 967 of petroleum, 851 of pineapples, 854 Cost of college, 28 of dental care, 301 of fuel, 596 of overnight delivery, 218, 253, 542, 557 of photocopies, 621 of higher education, 147, 268 to stay in college dormitory, 154 Coupons used in a grocery store, 1206 Discount, 87, 91 Discount rate, 89, 150 Energy imports, 481 Expenditures for health services and supplies, 993 for health care 193, 333 Fuel mileage, 759, 1206 Home mortgage, 786, 802 debt, 845 monthly payment, 363 Home prices, 65, 66, 275 Hourly wages, 802, 991 Job offer, 853, 1097, 1156 List price, 89, 150 Long distance phone plans, 411, 491, 496 Lumber use, 910 Magazine subscribers, 910 Magazine subscription, 929 Marginal propensity to consume, 823, 825 Marginal utility, 967 Markup, 91 Median sales prices of homes, 750 New vehicle sales, 89 Newspaper circulation, 686 Original price, 80 Percent of a raise, 81 Percent of a salary, 81 Pet spending, 19 Prescription drug expenditures, 113 Price of brand name drugs, 137 of gasoline, 704, 867 of generic drugs, 137 of ground beef, 607 of a telephone call, 212 of tomatoes, 704 Prices of homes in the South, 633 Property value, 750, 800 Queuing model, 955 Reduced rates, 120 Repaying a loan, 191 Retail values of motor homes, 633 Sailboats purchased, 438 Salary, 88, 1107, 1117 and bonus, 254 increase, 80, 135, 150 and savings account, 206 Sales commission, 191 Sales tax and selling price, 206 Saving money, 191 Sharing the cost, 124, 152 Sound recordings purchased, 439 Sound system, 1233 U.S Postal Service first class mail rates, 557 Utilized citrus fruit production, 683 Vacation packages, 494 Weekly paycheck, 87 Weekly salary, 90 Wholesale price, 89 U.S Demographics Age at first marriage, 353 Air travel, 218 Average heights, 382 Average salary for school nurses, 832 Cable TV subscribers, 267 Cars per household, 1231 Cellular telephone subscribers, 66, 622, 624, 991 Child support collections, 506 College enrollment, 181 Comparing populations, 414, 462 Computer science field of study, 531 Doctorates in science, 336 Early childhood development, 103 Education ACT scores, 928, 1206 GMAT scores, 1202 SAT and ACT participants, 414 SAT scores, 387, 928 Employment, 767 amusement park workers, 1060 construction workers, 1050, 1060, 1069 dentist office employees, 187 health services industry employees, 193 Federal School Breakfast Program, 372 Female labor force, 236 Grade level salaries for federal employees, 218 High school dropouts, 686 Hospital employment, 353 Hourly earnings, employees at outpatient care centers, 75 Hours of TV usage, 685 Houses for sale by region, 1181 Income median, 995 personal, 1194 Income distribution, 854 Life expectancy, 124, 125 Lorenz curve, 854 Married couples, rate of increase, 816 Media usage, 89 Median age, 910 Medical degrees, number of, 658 Medicare enrollees, 440 Men’s heights, 392, 917, 1232 Miles traveled by vehicles, 169 Minimum wage, 78 New homes, 125 Nonfarm employees, 1224 Non-wage earners, 189 Numbers of children in families, 1231 Oil domestic demand, 137, 333, 394 imported, 137, 150 strategic reserve, 218 Per capita gross domestic product, 155 income, 112 land area, 329 Personal income, 78 Political makeup of the U.S Senate, 232 Population of the District of Columbia, 687 immigrant, 278 of Las Vegas, Nevada, 759 median age of U.S., 363 of Orlando, Florida, 186 of people age 18 and over, 301 of people 65 years old and over, 801 projection for children under five, 255 projection for people 85 and older, 393 of Reno, Nevada, 193 of the United States, 47, 65, 103, 394, 668, 795, 1086, 1177 Population density, 1009, 1012 contour map of New York, 1018 Population growth, 803, 804 Horry County, South Carolina, 816 Houston, Texas, 776 Orlando, Florida, 776 United States, 750, 890 Prescriptions filled, 353, 425 Public college enrollment, 136 Ratio of males to females, 1089 School enrollment, 794 Social Security benefits, 728 Visitors to a national park, 567, 594 Women in the work force, 1020 Women’s heights, 392, 921 Geometry Arc length, 910, 1030 Area, 87, 91, 137, 201, 254, 523, 533, 647, 695, 696, 697, 735, 736, 742 of the first floor of a clinic, 288 of a forest region, 525 optimal, 266 of a parking lot, 109 of a pasture, 695 of a room, 288 of a sector of a circle, 91 sprinkler system, 1030 windshield wiper, 1030 of a shaded region, 47, 1107 of a tract of land, 525 Area and circumference of a circle, 207 Average elevation, 1020 Changing area, 642 Changing volume, 644 Depth of an underwater cable, 151 of a whale, 102 of a whale shark, 102 Diagonals of a polygon, 1170 Diameter of the sun, 65 Dimensions of a billboard, 101, 151 of a box, 299, 300 of a building, 101 of a corral, 111, 300 of a cube, 37, 39 of a cylindrical container, 199 of a lot, 101 of a picture frame, 89 of a room, 82, 89, 96, 150 of a square base, 111, 114 of a square classroom, 37 of a storage bin, 300 of a terrarium, 300 of a volleyball court, 150 English and metric systems, 65, 184, 190, 251 Ferris wheel London Eye, 170 Star of Nanchang, 170 Floor plan, 47 Height, 1075 of a balloon, 204 of a baseball, 302 of a broadcasting tower, 1041 of a building, 90, 1036 of a can, 86 of the Empire State Building, 1041 of a flare, 153 of a mountain, 1041 of a mountain climber, 185 of a parachutist, 190 of Petronas Tower, 83 of a pipe, 86 of a projectile, 146, 153 of a streetlight, 1029 of a tree, 83, 90, 1036, 1076 Increasing radius, 687 Lateral surface area of a cylinder, 92 Length, 1041 of a block of ice, 86 of a digital camera tripod leg, 1078 of a field, 146, 153 of a guy wire, 1030, 1075 of a room, 54, 146, 153 of the sides of a triangle, 102 of a tank, 91 Maximum area, 695, 696, 697, 719 Maximum height, 262, 267 Maximum volume, 689, 695, 697, 740, 973 Maximum width, 136 Micron, 27 Minimum area, 693, 697, 719 Minimum length, 696, 740 Minimum perimeter, 695 Minimum surface area, 696, 697, 743 Nail length, 370 Perimeter of a rectangle, 87, 91 Ratio of volume to surface area, weather balloon, 22 Ripples in a pond, 206, 237 Sailboat stays, 125 Square pattern, 1107 Surface area, 92, 647, 648, 686 of a golf green, 860 of an oil spill, 868 of a pond, 860 Thickness of a soap bubble, 27 Volume, 647, 648, 735, 736, 976, 985 of a box, 45, 47, 111, 152, 204, 252, 278, 696 of a rectangular prism, 91 of a rectangular solid, 86 of a right circular cylinder, 91 of a soft drink container, 696 and surface area of a sphere, 22, 742 of two spherical balloons, 86 Water level, 684 Width of a deck, 101 of a human hair, 28 of a path, 101 of a river, 1041 Time and Distance Braking distance, 1217 Catch-up time, 90 Cutting across the lawn, 98 Distance, 82, 150, 695, 1030, 1041, 1076 from a dock, 112 of a hit baseball, 268, 336 across a lake, 1052 to a star, 90 between sun and planets, 367 traveled, 9, 87, 190 Flying distance, 102, 112 Light year, 27 Minimum distance, 692, 697, 1150 Minimum time, 697, 1150 New York City Marathon, 91 Stopping distance, 235, 439, 633 Time study, 137 Travel time, 87, 90, 150 Miscellaneous Air traffic control, 648 Aircraft boarding, 1229 Airline routes, 496 Architecture, 938 Athletics baseball, 648 bike race, 1169 freestyle swimming, 333 running, 567, 1225 speed skating, 333 weightlifting, 136 white-water rafting, 622 Average grade on a calculus final, 1186 Baking as a leisure activity, 466 Baseball salaries, 136 Boating, 648 Brick pattern, 1097 Candles, 437 Catalog number, 1162 Cell sites (for cellular telephones), 66, 767 Choice of newscasts, 462 Choosing officers, 1169 Classic cars, 426 Combination lock, 1167, 1169 Community service, 125 Computer filename extension, 1162 Computers and Internet users, 996 Concert seating arrangement, 1169 Cost of seizing an illegal drug, 332, 648, 718 Counting card hands, 1167 Course grade, 89 Course schedule, 1168 Cryptography, 521, 522, 523, 525, 526, 532 Digital cinema screens, 352 Exam scores, 1205 Exercise program, 132 Extended application, 47, 113, 206, 302, 353, 439, 496, 633, 707, 795, 854, 900, 996, 1061, 1224 Fatal crashes, 181 Fitness, 150 Flower arrangements, 1167 Forming a committee, 1170 Game show, 1170, 1180, 1181, 1229, 1233 Games of chance, 1195 Hair products, 437 Humidity control, 137 Jury selection, 1170 Land area of crops, 303 Law enforcement, 1170 License plate numbers, 1168 License renewal, 1205 Lottery, 1169, 1174, 1230 Lunch drinks, 1171 Maximum product, 740 Minimum sum, 740 Movie sequels, 88 Music, tuning a piano, 1050 Notes on a musical scale, 38 Olympic diver, 101 Password, 1196, 1225 Phishing, 678 PIN numbers, 1167 Pizza toppings, 1170, 1233 Play auditions, 1170 Poker hand, 1170, 1181 Political fundraiser, 580 Population of a city, 207, 391, 392, 400, 402 growth, 352, 362, 803, 804 of Japan, 192, 595 of North America, 170 of a town, 398 of the world, 147, 384, 995 Preparing for a test, 1180, 1226 Prize money at the Indianapolis 500, 188 Probability, 909, 1171 alumni association, 1180 average time between incoming calls, 759 baseball player getting a hit, 1181, 1182 birthday problem, 1178 blogging, 1182 cash scholarship, 1181 college bound, 1180, 1229 drawing a card, 1172, 1175, 1179, 1180, 1229 drawing marbles, 1179, 1180 iron in ore samples, 900 letter mix-up, 1181 oil and gas deposits, 927 random number generator, 1177, 1179, 1180 science news, 1182 scientific discoveries, 1182 Random bar code, 1230 Red herring, 92 Research and development, 593, 1117 Research project, 19, 237, 313, 371, 439, 526, 607, 678, 707, 777, 786, 854, 890, 967, 1061, 1170 SAT scores, 767 Seating, 1156 Seating capacity, 111, 1094, 1097 Size inflation, food in restaurants, 88 Snow removal, 399 Social security numbers, 1167 Super Bowl ad cost and revenue, 393 Taste testing, 1179 Telephone numbers, 1162, 1229 Test scores, 206, 401 Toboggan ride, 1168 Tossing coins, 1171, 1172, 1179, 1181, 1183, 1184, 1185, 1192, 1195, 1229, 1233 dice, 1173, 1179, 1183, 1184, 1185, 1230, 1233 Transportation, 1205 True-false exam, 1168, 1192 Video game, 191 Voting preference, 496 Waiting time, 1195, 1205, 1231 Weight loss program, 135 Winning an election, 1180 Work rate, 125 World Internet users, 88, 816 and computers, 996 ... precipitation for Bismarck, North Dakota, 1070 for Sacramento, California, 1069 for San Francisco, California, 1077 (continued on back endsheets) College Algebra and Calculus An Applied Approach RON LARSON. .. Calculus: An Applied Approach, Eighth Edition Applied Calculus for the Life and Social Sciences College Algebra and Calculus: An Applied Approach Many students take college algebra as a prerequisite... is called the denominator The basic rules of algebra, listed below, are true for variables and algebraic expressions as well as for real numbers Basic Rules of Algebra Let a, b, and c be real