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

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




Prepared4by4Devi
lyna4Nichols4Pur
due4University

,[to4be4supplied4by4publisher]

,CONTENTS




Chapter41 Functions,4Graphs,4and4Limits 1
1.1 Functions 1
1.2 The4Graph4of4a4Function 6
1.3 Linear4Functions 14
1.4 Functional4Models 19
1.5 Limits 26
1.6 One-Sided4Limits4and4Continuity 30
Checkup4for4Chapter41 33
Review4Problems 36


Chapter42444 Differentiation:4Basic4Concepts 43
2.1 The4Derivative 43
2.2 Techniques4of4 Differentiation 52
2.3 Product4and4Quotient4Rules;4Higher-Order4Derivatives 57
2.4 The4Chain4Rule 64
2.5 Marginal4Analysis;4Approximations4Using4Increments 72
2.6 Implicit4Differentiation4and4Related4Rates 75
Checkup4for4Chapter42 82
Review4Problems 84


Chapter43444 Additional4Applications4of4the4Derivative 93
3.1 Increasing4and4Decreasing4Functions;4Relative4Extrema 93
3.2 Concavity4and4Points4of4Inflection 103
3.3 Curve4Sketching 114
3.4 Optimization 124
3.5 Additional4Applied4Optimization 132
Checkup4for4Chapter43 141
Review4Problems 148


Chapter44444 Exponential4and4Logarithmic4Functions 159
4.1 Exponential4Functions 159
4.2 Logarithmic4Functions 165
4.3 Differentiation4of4Logarithmic4and4Exponential4Functions 173
4.4 Additional4Exponential4Models 182
Checkup4for4Chapter44 199
Review4Problems 205
iii

, iv Contents




Chapter45444 Integration 219
5.1 Antidifferentiation;4the4Indefinite4Integral 219
5.2 Integration4by4Substitution 226
5.3 The4Definite4Integral4and4the4Fundamental4Theorem4of4Calculus 233
5.4 Applying4Definite4Integration:4Area4Between4Curves4and4Average4Value 238
5.5 Additional4Applications4to4Business4and4Economics 245
5.6 Additional4Applications4to4the4Life4and4Social4Sciences 252
Checkup4for4Chapter45 259
Review4Problems 262

Chapter46444 Additional4Topics4in4Integration 273
6.1 Integration4by4Parts;4Integral4Tables 273
6.2 Introduction4to4Differential4Equations 284
6.3 Improper4Integrals;4Continuous4Probability 292
6.4 Numerical4Integration 300
Checkup4for4Chapter46 307
Review4Problems 312

Chapter47444 Calculus4of4Several4Variables 325
7.1 Functions4of4Several4Variables 325
7.2 Partial4Derivatives 329
7.3 Optimizing4Functions4of4Two4Variables 336
7.4 The4Method4of4Least4Squares 346
7.5 Constrained4Optimization:4The4Method4of4Lagrange4Multipliers 353
7.6 Double4Integrals 362
Checkup4for4Chapter47 371
Review4Problems 375