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
,[to be supplied by publisher]
,CONTENTS
Chapter Functions, DGraphs, Dand 1
D1 DLimits
1.1 Functions 1
1.2 The DGraph Dof Da DFunction
6
1.3 Linear DFunctions 14
1.4 Functional DModels 19
1.5 Limits 26
1.6 One-Sided DLimits Dand 30
DContinuity
Checkup Dfor DChapter D133
Review DProblems 36
Chapter D2 D D D Differentiation: DBasic DConcepts 43
2.1 The DDerivative 43
2.2 Techniques Dof D Differentiation 52
2.3 Product Dand DQuotient DRules; DHigher-Order DDerivatives 57
2.4 The DChain DRule 64
2.5 Marginal DAnalysis; DApproximations DUsing DIncrements72
2.6 Implicit DDifferentiation Dand DRelated DRates75
Checkup Dfor DChapter D282
Review DProblems 84
Chapter D3 D D D Additional DApplications Dof Dthe DDerivative 93
3.1 Increasing Dand DDecreasing DFunctions; DRelative DExtrema 93
3.2 Concavity Dand DPoints Dof DInflection103
3.3 Curve DSketching 114
3.4 Optimization 124
3.5 Additional DApplied DOptimization 132
Checkup Dfor DChapter D3141
Review DProblems 148
Chapter D4 D D D Exponential Dand DLogarithmic DFunctions 159
4.1 Exponential DFunctions 159
4.2 Logarithmic DFunctions 165
4.3 Differentiation Dof DLogarithmic Dand DExponential DFunctions173
4.4 Additional DExponential DModels 182
Checkup Dfor DChapter D4199
, Review DProblems 205
iii
iv Contents
Chapter D5 D D D Integration 219
5.1 Antidifferentiation; Dthe DIndefinite DIntegral 219
5.2 Integration Dby DSubstitution 226
5.3 The DDefinite DIntegral Dand Dthe DFundamental DTheorem Dof DCalculus 233
5.4 Applying DDefinite DIntegration: DArea DBetween DCurves Dand DAverage DValue 238
5.5 Additional DApplications Dto DBusiness Dand DEconomics 245
5.6 Additional DApplications Dto Dthe DLife Dand DSocial DSciences 252
Checkup Dfor DChapter D5 259
Review DProblems 262
Chapter D6 D D D Additional DTopics Din DIntegration 273
6.1 Integration Dby DParts; DIntegral DTables 273
6.2 Introduction Dto DDifferential DEquations 284
6.3 Improper DIntegrals; DContinuous DProbability 292
6.4 Numerical DIntegration 300
Checkup Dfor DChapter D6 307
Review DProblems 312
Chapter D7 D D D Calculus Dof DSeveral DVariables 325
7.1 Functions Dof DSeveral DVariables325
7.2 Partial DDerivatives 329
7.3 Optimizing DFunctions Dof DTwo DVariables 336
7.4 The DMethod Dof DLeast DSquares 346
7.5 Constrained DOptimization: DThe DMethod Dof DLagrange DMultipliers 353
7.6 Double DIntegrals 362
Checkup Dfor DChapter D7 371
Review DProblems 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
,[to be supplied by publisher]
,CONTENTS
Chapter Functions, DGraphs, Dand 1
D1 DLimits
1.1 Functions 1
1.2 The DGraph Dof Da DFunction
6
1.3 Linear DFunctions 14
1.4 Functional DModels 19
1.5 Limits 26
1.6 One-Sided DLimits Dand 30
DContinuity
Checkup Dfor DChapter D133
Review DProblems 36
Chapter D2 D D D Differentiation: DBasic DConcepts 43
2.1 The DDerivative 43
2.2 Techniques Dof D Differentiation 52
2.3 Product Dand DQuotient DRules; DHigher-Order DDerivatives 57
2.4 The DChain DRule 64
2.5 Marginal DAnalysis; DApproximations DUsing DIncrements72
2.6 Implicit DDifferentiation Dand DRelated DRates75
Checkup Dfor DChapter D282
Review DProblems 84
Chapter D3 D D D Additional DApplications Dof Dthe DDerivative 93
3.1 Increasing Dand DDecreasing DFunctions; DRelative DExtrema 93
3.2 Concavity Dand DPoints Dof DInflection103
3.3 Curve DSketching 114
3.4 Optimization 124
3.5 Additional DApplied DOptimization 132
Checkup Dfor DChapter D3141
Review DProblems 148
Chapter D4 D D D Exponential Dand DLogarithmic DFunctions 159
4.1 Exponential DFunctions 159
4.2 Logarithmic DFunctions 165
4.3 Differentiation Dof DLogarithmic Dand DExponential DFunctions173
4.4 Additional DExponential DModels 182
Checkup Dfor DChapter D4199
, Review DProblems 205
iii
iv Contents
Chapter D5 D D D Integration 219
5.1 Antidifferentiation; Dthe DIndefinite DIntegral 219
5.2 Integration Dby DSubstitution 226
5.3 The DDefinite DIntegral Dand Dthe DFundamental DTheorem Dof DCalculus 233
5.4 Applying DDefinite DIntegration: DArea DBetween DCurves Dand DAverage DValue 238
5.5 Additional DApplications Dto DBusiness Dand DEconomics 245
5.6 Additional DApplications Dto Dthe DLife Dand DSocial DSciences 252
Checkup Dfor DChapter D5 259
Review DProblems 262
Chapter D6 D D D Additional DTopics Din DIntegration 273
6.1 Integration Dby DParts; DIntegral DTables 273
6.2 Introduction Dto DDifferential DEquations 284
6.3 Improper DIntegrals; DContinuous DProbability 292
6.4 Numerical DIntegration 300
Checkup Dfor DChapter D6 307
Review DProblems 312
Chapter D7 D D D Calculus Dof DSeveral DVariables 325
7.1 Functions Dof DSeveral DVariables325
7.2 Partial DDerivatives 329
7.3 Optimizing DFunctions Dof DTwo DVariables 336
7.4 The DMethod Dof DLeast DSquares 346
7.5 Constrained DOptimization: DThe DMethod Dof DLagrange DMultipliers 353
7.6 Double DIntegrals 362
Checkup Dfor DChapter D7 371
Review DProblems 375
