Student Solutions Manual
to accompany
Calculus for Business,
Economics, and the
Social and Life Sciences
Tenth Edition, Brief
Laurence D. Hoffman
Smith Barney
Gerald L. Bradley
Claremon McKenna College
Prepared by
Devilyna Nichols
Purdue University
,[toAbeAsuppliedAbyApublisher]
,CONTENTS
ChapterA1 Functions,AGraphs,AandALimits 1
1.1 Functions 1
1.2 TheAGraphAofAaAFunction 6
1.3 LinearAFunctions 14
1.4 FunctionalAModels 19
1.5 Limits 26
1.6 One-SidedALimitsAandAContinuity 30
CheckupAforAChapterA1 33
ReviewAProblems 36
ChapterA2AAA Differentiation:ABasicAConcepts 43
2.1 TheADerivative 43
2.2 TechniquesAofA Differentiation 52
2.3 ProductAandAQuotientARules;AHigher-OrderADerivatives 57
2.4 TheAChainARule 64
2.5 MarginalAAnalysis;AApproximationsAUsingAIncrements 72
2.6 ImplicitADifferentiationAandARelatedARates 75
CheckupAforAChapterA2 82
ReviewAProblems 84
ChapterA3AAA AdditionalAApplicationsAofAtheADerivative 93
3.1 IncreasingAandADecreasingAFunctions;ARelativeAExtrema 93
3.2 ConcavityAandAPointsAofAInflection 103
3.3 CurveASketching 114
3.4 Optimization 124
3.5 AdditionalAAppliedAOptimization 132
CheckupAforAChapterA3 141
ReviewAProblems 148
ChapterA4AAA ExponentialAandALogarithmicAFunctions 159
4.1 ExponentialAFunctions 159
4.2 LogarithmicAFunctions 165
4.3 DifferentiationAofALogarithmicAandAExponentialAFunctions 173
4.4 AdditionalAExponentialAModels 182
CheckupAforAChapterA4 199
ReviewAProblems 205
iii
, iv Contents
ChapterA5AAA Integration 219
5.1 Antidifferentiation;AtheAIndefiniteAIntegral 219
5.2 IntegrationAbyASubstitution 226
5.3 TheADefiniteAIntegralAandAtheAFundamentalATheoremAofACalculus 233
5.4 ApplyingADefiniteAIntegration:AAreaABetweenACurvesAandAAverageAValue 238
5.5 AdditionalAApplicationsAtoABusinessAandAEconomics 245
5.6 AdditionalAApplicationsAtoAtheALifeAandASocialASciences 252
CheckupAforAChapterA5 259
ReviewAProblems 262
ChapterA6AAA AdditionalATopicsAinAIntegration 273
6.1 IntegrationAbyAParts;AIntegralATables 273
6.2 IntroductionAtoADifferentialAEquations 284
6.3 ImproperAIntegrals;AContinuousAProbability 292
6.4 NumericalAIntegration 300
CheckupAforAChapterA6 307
ReviewAProblems 312
ChapterA7AAA CalculusAofASeveralAVariables 325
7.1 FunctionsAofASeveralAVariables 325
7.2 PartialADerivatives 329
7.3 OptimizingAFunctionsAofATwoAVariables 336
7.4 TheAMethodAofALeastASquares 346
7.5 ConstrainedAOptimization:ATheAMethodAofALagrangeAMultipliers 353
7.6 DoubleAIntegrals 362
CheckupAforAChapterA7 371
ReviewAProblems 375
to accompany
Calculus for Business,
Economics, and the
Social and Life Sciences
Tenth Edition, Brief
Laurence D. Hoffman
Smith Barney
Gerald L. Bradley
Claremon McKenna College
Prepared by
Devilyna Nichols
Purdue University
,[toAbeAsuppliedAbyApublisher]
,CONTENTS
ChapterA1 Functions,AGraphs,AandALimits 1
1.1 Functions 1
1.2 TheAGraphAofAaAFunction 6
1.3 LinearAFunctions 14
1.4 FunctionalAModels 19
1.5 Limits 26
1.6 One-SidedALimitsAandAContinuity 30
CheckupAforAChapterA1 33
ReviewAProblems 36
ChapterA2AAA Differentiation:ABasicAConcepts 43
2.1 TheADerivative 43
2.2 TechniquesAofA Differentiation 52
2.3 ProductAandAQuotientARules;AHigher-OrderADerivatives 57
2.4 TheAChainARule 64
2.5 MarginalAAnalysis;AApproximationsAUsingAIncrements 72
2.6 ImplicitADifferentiationAandARelatedARates 75
CheckupAforAChapterA2 82
ReviewAProblems 84
ChapterA3AAA AdditionalAApplicationsAofAtheADerivative 93
3.1 IncreasingAandADecreasingAFunctions;ARelativeAExtrema 93
3.2 ConcavityAandAPointsAofAInflection 103
3.3 CurveASketching 114
3.4 Optimization 124
3.5 AdditionalAAppliedAOptimization 132
CheckupAforAChapterA3 141
ReviewAProblems 148
ChapterA4AAA ExponentialAandALogarithmicAFunctions 159
4.1 ExponentialAFunctions 159
4.2 LogarithmicAFunctions 165
4.3 DifferentiationAofALogarithmicAandAExponentialAFunctions 173
4.4 AdditionalAExponentialAModels 182
CheckupAforAChapterA4 199
ReviewAProblems 205
iii
, iv Contents
ChapterA5AAA Integration 219
5.1 Antidifferentiation;AtheAIndefiniteAIntegral 219
5.2 IntegrationAbyASubstitution 226
5.3 TheADefiniteAIntegralAandAtheAFundamentalATheoremAofACalculus 233
5.4 ApplyingADefiniteAIntegration:AAreaABetweenACurvesAandAAverageAValue 238
5.5 AdditionalAApplicationsAtoABusinessAandAEconomics 245
5.6 AdditionalAApplicationsAtoAtheALifeAandASocialASciences 252
CheckupAforAChapterA5 259
ReviewAProblems 262
ChapterA6AAA AdditionalATopicsAinAIntegration 273
6.1 IntegrationAbyAParts;AIntegralATables 273
6.2 IntroductionAtoADifferentialAEquations 284
6.3 ImproperAIntegrals;AContinuousAProbability 292
6.4 NumericalAIntegration 300
CheckupAforAChapterA6 307
ReviewAProblems 312
ChapterA7AAA CalculusAofASeveralAVariables 325
7.1 FunctionsAofASeveralAVariables 325
7.2 PartialADerivatives 329
7.3 OptimizingAFunctionsAofATwoAVariables 336
7.4 TheAMethodAofALeastASquares 346
7.5 ConstrainedAOptimization:ATheAMethodAofALagrangeAMultipliers 353
7.6 DoubleAIntegrals 362
CheckupAforAChapterA7 371
ReviewAProblems 375
