Student Solutions Manual
z z
to accompany
z
Calculus for Business, Ec
z z z
onomics, and the Social a
z z z z
nd Life Sciences
z z
Tenth Edition, Brief z z
Laurence D. Hoffman z z
SmithzBarney
Gerald L. Bradley z z
ClaremonzMcKennazCollege
PreparedzbyzDevil
ynazNicholszPurd
uezUniversity
,[tozbezsuppliedzbyzpublisher]
,CONTENTS
Chapterz1 Functions,zGraphs,zandzLimits 1
1.1 Functions 1
1.2 ThezGraphzofzazFunction 6
1.3 LinearzFunctions 14
1.4 FunctionalzModels 19
1.5 Limits 26
1.6 One-SidedzLimitszandzContinuity 30
CheckupzforzChapterz1 33
ReviewzProblems 36
Chapterz2zzz Differentiation:zBasiczConcepts 43
2.1 ThezDerivative 43
2.2 Techniqueszofz Differentiation 52
2.3 ProductzandzQuotientzRules;zHigher-OrderzDerivatives 57
2.4 ThezChainzRule 64
2.5 MarginalzAnalysis;zApproximationszUsingzIncrements 72
2.6 ImplicitzDifferentiationzandzRelatedzRates 75
CheckupzforzChapterz2 82
ReviewzProblems 84
Chapterz3zzz AdditionalzApplicationszofzthezDerivative 93
3.1 IncreasingzandzDecreasingzFunctions;zRelativezExtrema 93
3.2 ConcavityzandzPointszofzInflection 103
3.3 CurvezSketching 114
3.4 Optimization 124
3.5 AdditionalzAppliedzOptimization 132
CheckupzforzChapterz3 141
ReviewzProblems 148
Chapterz4zzz ExponentialzandzLogarithmiczFunctions 159
4.1 ExponentialzFunctions 159
4.2 LogarithmiczFunctions 165
4.3 DifferentiationzofzLogarithmiczandzExponentialzFunctions 173
4.4 AdditionalzExponentialzModels 182
CheckupzforzChapterz4 199
ReviewzProblems 205
iii
, iv Contents
Chapterz5zzz Integration 219
5.1 Antidifferentiation;zthezIndefinitezIntegral 219
5.2 IntegrationzbyzSubstitution 226
5.3 ThezDefinitezIntegralzandzthezFundamentalzTheoremzofzCalculus 233
5.4 ApplyingzDefinitezIntegration:zAreazBetweenzCurveszandzAveragezValue 238
5.5 AdditionalzApplicationsztozBusinesszandzEconomics 245
5.6 AdditionalzApplicationsztozthezLifezandzSocialzSciences 252
CheckupzforzChapterz5 259
ReviewzProblems 262
Chapterz6zzz AdditionalzTopicszinzIntegration 273
6.1 IntegrationzbyzParts;zIntegralzTables 273
6.2 IntroductionztozDifferentialzEquations 284
6.3 ImproperzIntegrals;zContinuouszProbability 292
6.4 NumericalzIntegration 300
CheckupzforzChapterz6 307
ReviewzProblems 312
Chapterz7zzz CalculuszofzSeveralzVariables 325
7.1 FunctionszofzSeveralzVariables 325
7.2 PartialzDerivatives 329
7.3 OptimizingzFunctionszofzTwozVariables 336
7.4 ThezMethodzofzLeastzSquares 346
7.5 ConstrainedzOptimization:zThezMethodzofzLagrangezMultipliers 353
7.6 DoublezIntegrals 362
CheckupzforzChapterz7 371
ReviewzProblems 375
z z
to accompany
z
Calculus for Business, Ec
z z z
onomics, and the Social a
z z z z
nd Life Sciences
z z
Tenth Edition, Brief z z
Laurence D. Hoffman z z
SmithzBarney
Gerald L. Bradley z z
ClaremonzMcKennazCollege
PreparedzbyzDevil
ynazNicholszPurd
uezUniversity
,[tozbezsuppliedzbyzpublisher]
,CONTENTS
Chapterz1 Functions,zGraphs,zandzLimits 1
1.1 Functions 1
1.2 ThezGraphzofzazFunction 6
1.3 LinearzFunctions 14
1.4 FunctionalzModels 19
1.5 Limits 26
1.6 One-SidedzLimitszandzContinuity 30
CheckupzforzChapterz1 33
ReviewzProblems 36
Chapterz2zzz Differentiation:zBasiczConcepts 43
2.1 ThezDerivative 43
2.2 Techniqueszofz Differentiation 52
2.3 ProductzandzQuotientzRules;zHigher-OrderzDerivatives 57
2.4 ThezChainzRule 64
2.5 MarginalzAnalysis;zApproximationszUsingzIncrements 72
2.6 ImplicitzDifferentiationzandzRelatedzRates 75
CheckupzforzChapterz2 82
ReviewzProblems 84
Chapterz3zzz AdditionalzApplicationszofzthezDerivative 93
3.1 IncreasingzandzDecreasingzFunctions;zRelativezExtrema 93
3.2 ConcavityzandzPointszofzInflection 103
3.3 CurvezSketching 114
3.4 Optimization 124
3.5 AdditionalzAppliedzOptimization 132
CheckupzforzChapterz3 141
ReviewzProblems 148
Chapterz4zzz ExponentialzandzLogarithmiczFunctions 159
4.1 ExponentialzFunctions 159
4.2 LogarithmiczFunctions 165
4.3 DifferentiationzofzLogarithmiczandzExponentialzFunctions 173
4.4 AdditionalzExponentialzModels 182
CheckupzforzChapterz4 199
ReviewzProblems 205
iii
, iv Contents
Chapterz5zzz Integration 219
5.1 Antidifferentiation;zthezIndefinitezIntegral 219
5.2 IntegrationzbyzSubstitution 226
5.3 ThezDefinitezIntegralzandzthezFundamentalzTheoremzofzCalculus 233
5.4 ApplyingzDefinitezIntegration:zAreazBetweenzCurveszandzAveragezValue 238
5.5 AdditionalzApplicationsztozBusinesszandzEconomics 245
5.6 AdditionalzApplicationsztozthezLifezandzSocialzSciences 252
CheckupzforzChapterz5 259
ReviewzProblems 262
Chapterz6zzz AdditionalzTopicszinzIntegration 273
6.1 IntegrationzbyzParts;zIntegralzTables 273
6.2 IntroductionztozDifferentialzEquations 284
6.3 ImproperzIntegrals;zContinuouszProbability 292
6.4 NumericalzIntegration 300
CheckupzforzChapterz6 307
ReviewzProblems 312
Chapterz7zzz CalculuszofzSeveralzVariables 325
7.1 FunctionszofzSeveralzVariables 325
7.2 PartialzDerivatives 329
7.3 OptimizingzFunctionszofzTwozVariables 336
7.4 ThezMethodzofzLeastzSquares 346
7.5 ConstrainedzOptimization:zThezMethodzofzLagrangezMultipliers 353
7.6 DoublezIntegrals 362
CheckupzforzChapterz7 371
ReviewzProblems 375
