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www.EngineeringBooksPDF.com INDEX OF APPLICATIONS Titles or page numbers in italics indicate applications of greater generality or significance, most including source citations that allow those interested to pursue these topics in more detail Athletics Altitude and Olympic games, 274 Athletic field design, 222 Cardiovascular zone, 50 Disappearance of the 400 baseball hitter, 543 Fastest baseball pitch, 175 Fluid absorption, 422 How fast old men slow down?, 305 Juggling, 49 Muscle contraction, 50 Olympic medals, 507, 520 Pole vaulting improvement, 297 Pythagorean baseball standings, 507, 520 World record 100-meter run, 305 World record mile run, 3, 17 Biomedical Sciences AIDS, 152 Allometry, 31, 32, 488 Aortic volume, 366 Aspirin dose-response, 193 Bacteria, 192, 223, 250, 274, 378, 472 Blood flow, 123, 164, 176, 520 and Reynolds number, 306 Blood vessel volume, 571 Body surface area, 505 Body temperature, 138, 337, 409 Cardiac output, 570 Cell growth, 49, 348, 470 Chernobyl radioactive contamination, 274 Cholesterol reduction, 402 Contagion, 232 Coughing, 223 Drug absorption, 366, 445, 486 Drug concentration, 231, 306, 321 Drug dosage, 273, 288, 290, 304, 322, 422, 531 Drug dose-response curve, 207, 208 Drug sensitivity, 163, 164 Efficiency of animal motion, 223, 254 Epidemics, 123, 340, 347, 366, 482, 486, 493 Fever, 151 Fever thermometers, 492, 493 Fick’s law, 473 Future life expectancy, 20 Gene frequency, 426, 432 Glucose levels, 471, 487 Gompertz growth curve, 291, 306, 445, 488 Half-life of a drug, 291 Heart function, 473 Heart medication, 193 Heart rate, 32 Height of a child, 365 Heterozygosity, 291 Hill’s equation, 250 Leukemic cell growth, 70 Life expectancy, 19, 20 Life expectancy and education, 125 Longevity and exercise, 221 Lung cancer and asbestos, 124 Medication ingestion, 256 Mosquitoes, 273 Murrell’s rest allowance, 141 Muscle contraction, 250 Nutrition, 587 Oxygen consumption, 507 Penicillin dosage, 283 Poiseuille’s law and blood flow, 251, 367 Pollen count, 220 Population and individual birthrate, 488 Reed-Frost epidemic model, 274 Ricker recruitment, 291, 306 Smoking and longevity, 543 Tumor growth, 250 Weight of a teenager, 402, 406 Environmental Sciences Air pollution, 582 Air temperature and altitude, 74 Animal size, 73 Beverton-Holt recruitment curve, 21, 140 Biodiversity, 33 Carbon dioxide pollution, 74 Carbon monoxide pollution, 164 Consumption of natural resources, 343, 348, 349, 365, 405, 406, 491 Cost of cleaner water, 129 Deer population, 486 Flexfast Rubber Company, 471 Global temperatures, 151, 337 Greenhouse gases and global warming, 164, 406 Harvest yield, 226, 230 Light penetrating seawater, 273 Maximizing farm revenue, 255 Maximum sustainable yield, 238, 239, 240, 256 Nuclear waste, 290 Oil slick growth, 157 Photovoltaics, 70 Pollution, 221, 337, 377, 398, 402, 422 Pollution and absenteeism, 544 Predicting animal population, 481 Radioactive medical tracers, 289 Radioactive waste, 490 Rain forest depletion, 289 Sea level, 151 Sulfur oxide pollution, 247 Tag and recapture estimates, 506 Water quality, 123, 138, 492 Water reservoir average depth, 399 Water usage, 60 Wind energy, 50 Wind power, 221 World solar cell production, 304 Management Science, Business, and Economics 3D movies, 73, 123 Advertising, 75, 108, 123, 274, 288, 322, 493, 586 Advertising effectiveness, 290 Copyright 2011 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com Aging markets, 586 Anheiser-Busch bonds, 290 Apple average net income, 378 Apple net income, 337 Apple stock price, 318 Asset appreciation, 272 AT&T stock price, 349 AudioTime, 122 Automobile sales, 318, 319 Average sales, 402 Balance of trade, 379, 407 Bank failures, 305 Biotechnology index, 19 Boeing Corporation, 27 Book sales, 491 Break-even point, 42, 49, 50, 74 Broadband subscribers, 33 Cable TV revenue, 75 Capital value of an asset, 367, 444 Car loan rates, 139 Car phone sales, 486 Car rentals, 74 CD sales, 138, 139 Cézanne painting appreciation, 273 Cigarette price and demand, 323 Cigarettes sales, 19 City bus revenues, 319 Cobb-Douglas production function, 498, 505, 506, 514, 520, 552, 558–560, 586, 587 Comparing interest rates, 273 Competition and collusion, 528–530, 532 Competitive commodities, 521 Complementary commodities, 521 Compound interest, 176, 377 Compound interest growth times, 291 Computer expenditures, 493 Computer sales, 17 Consumer credit, 139 Consumer electronics index, 50, 109 Consumer expenditure, 298, 305, 323 Consumer price index, 122, 543 Consumers’ surplus, 382, 408 Continuous annuity, 471 Copier repair, 220 Cost, 332, 336, 358, 365, 395, 402, 405, 406, 409, 421, 433, 491 Cost function, 38, 48, 497, 506 Cost of labor contract, 380 Cumulative profit, 380 Demand equation, 244, 250 Depreciation, 321 Digital alarm clocks, 138 Digital camera sales, 486 Diminishing returns, 200, 208, 506 Disposable income, 51 Does money buy happiness?, 19 DSG International bonds, 290 E-commerce, 70 Elasticity of demand, 313, 323, 470 Elasticity of supply, 320 Energy usage, 17 Estimating additional profit, 564 EZCie LED flashlight, 116 Flash memory, 138 GDP relative growth rate, 323 Gini index, 408 Google revenue, 73 Gross domestic product, 309, 333 Gross world product, 456 HDTV sales, 28 Higher education expenses, 75 Hybrid cars, 70 Income tax, 69 Indifference curve, 506 Insurance reserves, 69 Interest compounded continuously, 94 Investment growth, 455 Isocosts and isoquants, 18, 32, 69, 506, 559, 560 Learning curve in airplane production, 27, 32, 174 Least cost rule, 560 Liquor and beer: elasticity and taxation, 319 Liquor sales, 318 Long-run average cost, 193 Lot size, 239, 240, 255 Lottery tickets, 33 Macintosh computers, 45, 102 Marginal average cost, 131, 138, 175 Marginal average profit, 138, 175 Marginal average revenue, 138 Marginal cost, 116, 122, 163 Marginal productivity, 560, 586 of capital, 514 of labor, 514 Marginal profit, 176, 519 Marginal rate of substitution, 250, 560 Marginal utility, 123, 124 Marketing to young adults, 122 Maximizing present value, 323 Maximizing production, 552, 558–560, 587 Maximum profit, 42, 49, 50, 74, 214, 221, 225, 230–232, 255, 526, 531, 532, 586, 587 Maximum revenue, 221, 230, 305, 323, 532 MBA salaries, 18 Median weekly earnings, 139 Memory chips, 208 Mineral deposit value, 583 Minimizing inventory costs, 233, 235 Minimizing package materials, 227 Minimum cost, 255 Mobile phones, 33 Money stock measure, 365 Movie prices, 51, 493, 545 Multimedia messaging service, 64 National debt, 151, 318 Net savings, 379 New Jersey cigarette taxes, 319 Newspaper sales, 319 Oil demand, 322 Oil prices, 230, 319 Oil well output, 444 Optical computer mice, 175 Oracle stock price, 318 Organic food, 70 Pareto’s law of income distribution, 367 Pasteurization temperature, 108 Per capita cigarette production, 221 Per capita gross domestic product, 520 Per capita national debt, 139 Per capita personal income, 17 Personal computer sales, 486 Phillips curves, 32, 122 POD (printing on demand), 131 PowerZip, 122 Predicting sales, 534, 542 Present value of a continuous stream of income, 417, 421, 422, 490 Present value of preferred stock, 445 Price and quantity, 224 Copyright 2011 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com Price discrimination, 531, 532, 586 Producers’ surplus, 384 Product recognition, 422, 485 Product reliability, 444 Production possibilities, 558 Production runs, 239, 255 Profit, 152, 197, 199, 246, 250, 256, 379, 515, 570 Pulpwood forest value, 223 Quality control, 274 Research expenditures, 69 Research in Motion average revenue, 378 Research in Motion revenue, 337 Research In Motion stock price, 349 Returns to scale, 506 Revenue, 207, 251, 256, 336, 402, 421 Rule of 6, 31 Rule of 72, 291 Salary, 48 Sales, 138, 175, 207, 250, 251, 305, 322, 347, 365, 366, 377, 445, 472, 520, 587 Sales from celebrity endorsement, 371 Sales growth, 483, 493 Satellite radio, 33, 290 Semiconductor sales, 208 Simple interest, 74 Stock “limiting’’ market value, 486 Straight-line depreciation, 18, 73 Super Bowl ticket costs, 545 Supply, 250, 252 Tax revenue, 229, 231 Timber forest value, 212, 221 Total productivity, 359 Total profit, 406 Total sales, 342, 402, 425, 432, 485, 493 Total savings, 348 U.S oil production, 70 Unemployment rate, 122, 305 Value of a building, 472 Value of an MBA, 520 Wage inflation, 122 Warranties, 445 Wholesale trade output index, 139 Wikipedia articles, 199 Word Search Maker, 174 Work hours, 250 World economies, 273 Zero coupon bond, 273 Personal Finance and Management Annual percentage rate (APR), 269, 272 Art appreciation, 337, 475 Automobile depreciation, 304 Automobile driving costs, 542 College trust fund, 272 Comparing interest rates, 268, 321 Compound interest, 163, 263, 304, 321, 407 Continuous compounding, 267 Cost of maintaining a home, 348 Depreciating a car, 264, 288 Earnings and calculus, 275, 304 Federal income tax, 58 Home appreciation, 485 Honus Wagner baseball card, 273 Income tax, 69 Investment growth times, 281, 282, 288, 290, 322 Loan sharks, 272 Picasso painting appreciation, 288 Present value, 264, 268, 272 Price-earnings ratio, 505 Rate of return, 274 Real estate, 407 Solar water heater savings, 349, 405 Stamp appreciation, 485 Stock price, 407 Stock yield, 505 Toyota Corolla depreciation, 273 Value of an investment, 348 Wealth accumulation, 467, 471, 492 Zero coupon bond, 272 Social and Behavioral Sciences Absenteeism, 532 Age at first marriage, 18 Campaign expenses, 231 Cigarette tax revenue, 255 Cost of congressional victory, 545 Crime, 543 Dating older women, 289 Diffusion of information, 286, 288, 305, 322, 323, 477 Divorces, 348 Early human ancestors, 289 Ebbinghaus model of memory, 304 Education and income, 290 Election costs, 274 Employment seekers, 433 Equal pay for equal work, 19 Forgetting, 274, 288 Fund raising, 422 Gender pay gap, 495 Gini index for wealth, 388 Gini index of income distribution, 387–389 Health club attendance, 50 “Iceman’’, 290 Immigration, 51, 108 IQ, 452, 455 Learning, 108, 117, 123, 164, 192, 285, 288, 323, 366, 406, 478, 486, 493 Longevity, 50 Lorenz curve, 389 Marriages, 366 Mazes, 444 Population relative rate of change, 323 Practice and rest, 531 Practice time, 377 Prison terms, 444 Procrastination, 521 Repetitive tasks, 366, 402, 406 Response rate, 433 Smoking and income, 19 Spread of rumors, 482, 486, 493 Status, income, and education, 163, 207, 520 Stevens’ Law of Psychophysics, 179 Stimulus and response, 207 Traffic accidents, 251 Violent crime, 587 Voting, 486 Welfare, 251 World energy output, 288 World population, 69, 147, 273 Topics of General Interest Accidents and driving speed, 125 Aging world population, 545 Airplane flight path, 192, 208 Approximation of , 456 Area between curves, 366, 402, 422, 444 Copyright 2011 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com Automobile age, 491 Automobile fatalities, 487 Average population, 402, 588 Average temperature, 377, 578, 582 Birthrate in Africa, 379 Boiling point and altitude, 49 Box design, 255, 506 Building design, 558, 559 Bus shelter design, 231 Carbon-14 dating, 259, 284, 289, 290 Cave paintings, 289 Cigarette smoking, 325, 366 College tuition, 124 Consumer fraud, 272 Container design, 557, 559, 587 Cooling coffee, 274, 304 Cost of college education, 545 Dam construction, 366 Dam sediment, 486 Dead Sea Scrolls, 284 Designing a can, 549 Dinosaurs, 31 Dog years, 69 Driving accidents and age, 220 Drug interception, 193 Drunk driving, 545 Duration of telephone calls, 444 Earthquakes, 32 Elasticity of demand, 319 Electrical consumption, 365 Emergency stopping distance, 570 Estimating error in calculating volume, 565, 567 Eternal recognition, 411 Expanding ripples, 245 Fencing a region, 557 First-class mail, 94 Fossils, 322 Freezing ice, 348 Friendships, 471 Fuel economy, 139, 220 Fuel efficiency, 254 Fund raising, 485 Grades, 17 Graphics design, 379, 407 Gravity model for telephone calls, 506 Gutter design, 222 Hailstones, 250 Happiness and temperature, 164 Highway safety, 520 Ice cream cone price increases, 365 Impact time of a projectile, 49 Impact velocity, 49, 151 Internet host computers, 422 Largest enclosed area, 216, 222, 230, 254, 547 Largest postal package, 230, 558 Largest product with fixed sum, 222 Learning, 337 Lives saved by seat belts, 380 Manhattan Island purchase, 272 Maximum height of a bullet, 151 Measurement errors, 570 Melting ice, 256 Mercedes-Benz Brabus Rocket speed, 337 Millwright’s water wheel rule, 221 Minimizing cost of materials, 230, 231 Minimum perimeter rectangle, 231 Moment magnitude scale, 32 Moore’s law of computer memory, 322 Most populous countries, 270 Most populous states, 274 Newsletters, 50 Nuclear meltdown, 273 “Nutcracker man’’, 322 Oldest dinosaur, 290 Package design, 217, 222, 223, 254, 255, 558 Page layout, 231 Parking lot design, 222 Permanent endowments, 439, 443, 446, 491 Population, 108, 164, 175, 318, 366, 405, 422, 432, 488, 491 Porsche Cabriolet speed, 336 Potassium-40 dating, 289, 290 Raindrops, 487 Rate of growth of a circle, 174 Rate of growth of a sphere, 174 Refining tower temperature, 207 Relative error in calculations, 570, 588 Relativity, 94 Repetitive tasks, 365 Richter scale, 32 Rocket tracking, 251 Scuba dive duration, 505, 570 Seat belt use, 20 Shroud of Turin, 259, 289 Smoking, 543 Smoking and education, 50, 124 Smoking mortality rates, 536 Snowballs, 250 Soda can design, 255 Speed and skid marks, 33 Speeding, 251 St Louis Gateway Arch, 275 Stopping distance, 49 Superconductivity, 77, 94 Survival rate, 176 Suspension bridge, 456 Telephone calls, 570 Temperature conversion, 18 Thermos bottle temperature, 323 Time of a murder, 471 Time saved by speeding, 132 Total population of a region, 583 Total real estate value, 588 Traffic safety, 123 Tsunamis, 49 Typing speed, 285 U.S population, 304, 369, 377, 407 Unicorns, 254 Velocity, 150–152, 175 Velocity and acceleration, 145 Volume and area of a divided box, 500 Volume of a building, 583 Volume under a tent, 577 Warming beer, 305 Water pressure, 49 Waterfalls, 32, 33 Wheat yield, 543 Wind speed, 72 Windchill index, 152, 499, 506, 520, 570 Window design, 222 Wine appreciation, 231 World oil consumption, 455 World population, 539 World’s largest city: now and later, 322 Wyoming population growth, 288 Young-adult population, 337 YouTube users, 14 Copyright 2011 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com Copyright 2011 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com BRIEF appliedcalculus SIXTH EDITION Geoffrey C Berresford Long Island University Andrew M Rockett Long Island University Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Copyright 2011 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does not materially affect the overall learning experience The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest Copyright 2011 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com Brief Applied Calculus, Sixth Edition Geoffrey C Berresford Andrew M Rockett Publisher: Richard Stratton Senior Development Editor: Jay Campbell Senior Editorial Assistant: Haeree Chang © 2013, 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 Associate Media Editor: Andrew Coppola Marketing Manager: Mandee Eckersley Marketing Coordinator: Michael Ledesma Marketing Communications Manager: Mary Anne Payumo Content Project Manager: Jessica Rasile 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 Director: Linda Helcher Manufacturing Planner: Doug Bertke Rights Acquisition Specialist: Shalice Shah-Caldwell Library of Congress Control Number: 2011939959 ISBN-13: 978-1-133-10392-9 Production Service/Compositor: MPS Limited, a Macmillan Company ISBN-10: 1-133-10392-8 Cover and Text Designer: Jay Purcell Brooks/Cole 20 Channel Center Street Boston, MA 02210 USA Cover Image: ©G C Berresford 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.cengagebrain.com Instructors: Please visit login.cengage.com and log in to access instructor-specific resources Printed in Canada 15 14 13 12 11 Copyright 2011 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com CONTENTS Preface ix A User’s Guide to Features Integrating Excel xx Graphing Calculator Basics xvii xxi FUNCTIONS 1.1 1.2 1.3 1.4 Real Numbers, Inequalities, and Lines Exponents 21 Functions: Linear and Quadratic 34 Functions: Polynomial, Rational, and Exponential Chapter Summary with Hints and Suggestions Review Exercises for Chapter 72 71 DERIVATIVES AND THEIR USES 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Limits and Continuity 78 Rates of Change, Slopes, and Derivatives 95 Some Differentiation Formulas 109 The Product and Quotient Rules 125 Higher-Order Derivatives 141 The Chain Rule and the Generalized Power Rule Nondifferentiable Functions 166 Chapter Summary with Hints and Suggestions Review Exercises for Chapter 173 52 153 171 FURTHER APPLICATIONS OF DERIVATIVES 3.1 3.2 3.3 3.4 3.5 3.6 Graphing Using the First Derivative 180 Graphing Using the First and Second Derivatives Optimization 209 Further Applications of Optimization 224 Optimizing Lot Size and Harvest Size 233 Implicit Differentiation and Related Rates 240 Chapter Summary with Hints and Suggestions Review Exercises for Chapter 253 Cumulative Review for Chapters 1–3 195 252 257 v Copyright 2011 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com ... at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com BRIEF appliedcalculus SIXTH EDITION Geoffrey C Berresford Long Island University Andrew M Rockett Long Island... at any time if subsequent rights restrictions require it www.EngineeringBooksPDF.com Brief Applied Calculus, Sixth Edition Geoffrey C Berresford Andrew M Rockett Publisher: Richard Stratton Senior... sciences, and other fields The seven-chapter Brief Applied Calculus contains more than enough material for a one-semester course, and the eleven-chapter Applied Calculus contains additional chapters
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