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

Purdue 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
University
nm

,CONTENTS




Chapter Functions, Graphs, n m 1
and
n m

1 Limits
1.1 Functions 1
1.2 The Graph
n m of a n m n m

Function6
n m

1.3 Linear Functions 14
n m

1.4 Functional Models 19 n m


1.5 Limits 26
1.6 One-Sided Limits and
n m n m 30
Continuity
Checkup for Chapter
n m n m n m 1 n m 33
Review Problems 36
n m




Chapter n m 2 Differentiation: Basic Concepts 43 n m n m nm

2.1 The Derivative 43
n m

2.2 Techniques of Differentiation 52
n m n m


2.3 Product andn m Quotient Rules;
n m Higher-Order Derivatives57
n m n m n m


2.4 The Chain
n m Rule 64 n m n m n m

2.5 Marginal Analysis;
n m Approximations Using Increments72
n m n m n m


2.6 Implicit Differentiation
n m and Related n m n m


n Rates75 Checkup
m nm for Chapter 2 n m n m n m

82
n m


Review Problems 84
n m




Chapter n m 3 Additional Applications of
nm nm the Derivative 93 nm nm nm nm nm nm

3.1 Increasing and Decreasing
n m Functions;
n m Relative Extrema93 n m n m n m

3.2 Concavity and Points
n m of Inflection103
n m n m n m


3.3 Curve Sketching 114
n m


3.4 Optimization 124
3.5 Additional Applied n m Optimization132 n m


Checkup for Chapter
n m 3 141
n m n m n m


Review Problems 148
n m




Chapter nm nm4 Exponential and Logarithmic
n m nm nm nm nm Functions159
4.1 Exponential Functions 159
n m


4.2 Logarithmic Functions 165
n m


4.3 Differentiation of Logarithmic
n m and n m n m n m Exponential n m Functions173

, 4.4 Additional Exponential
n m n m Models182
Checkup for Chapter
n m n m 4 199
n m n m


Review Problems 205
n m


iii

iv Contents




Chapter nm nm5 Integration 219
5.1 Antidifferentiation; the Indefinite Integral 219
n m n m n m n m

5.2 Integration by Substitution
n m 226
n m


5.3 The n mDefinite Integral and
n m the Fundamental Theorem
n m of Calculus
n m 233n m n m n m n m


5.4 Applying Definite
n m Integration: Area Between
n m Curves and Average
n m Value 238 n m n m n m n m n m


5.5 Additional Applications
n m to Business and Economics 245
n m n m n m n m


5.6 Additional Applications
n m to the Life and Social
n m Sciences
n m 252 n m n m n m n m

Checkup for n m Chapter 5 259
n m n m n m


Review Problems 262
n m




Chapter Additional
Topics in n m n m nm 273
n m6 Integration nm

6.1 Integration by Parts; n mIntegral n m n m

Tables273 n m

6.2 Introduction to Differential
n m Equations
n m n m

284
n m

6.3 Improper Integrals;
n m Continuous n m

Probability 292
n m n m

6.4 Numerical Integration 300
n m


Checkup for n m Chapter 6 307
n m n m n m

Review Problems 312
n m




Chapter Calculus n m of Several
n m Variables n m n m 325
n m7 Functions of n m n m Several Variables
n m 325 n m

7.1
7.2 Partial Derivatives 329
n m


7.3 Optimizing Functions n mof Two Variables 336 n m n m n m nm

7.4 The Method
n m of Least Squares346
n m n m n m

7.5 Constrained Optimization:n m The Method of n m n m n m n m Lagrange 353
Multipliers
n m

7.6 Double Integrals 362
n m


Checkup for Chapter
n m 7 371
n m n m n m

Review Problems 375
n m

, Chapter 1 n m




Functions, Graphs, and Limits nm nm nm




9. 1
1.1 Functions f (t ) nm nm n m = n m (2t − n m 1)−3/2 n m n m
=
,
√
( 2t − n m 1)3
1
1. f(x) n m n m = n m 3x f √
=
nm nm

n m n m + n m 5, n m (1 n m


)
f (0)
n m n m =
n m
= [ n m 2(1) n m − 1,
3(0)
n m n m +
n m
1]3
5 = n m n m 5
f (−1) =
= ( 5√) =1 = =1 1 ,
n m n m
5 3(−1)
n m
n m
n m + f n m n m
nm nm


rw 2 rw
n m


f (2)
n m n m n m = [ — 1]
2(5)
3 nm [√nm
3 27
9]
+
nm
3(2)
n m n m n m n m 5
= n m 11 1
1 1
f n m (13) n m n m = nmrw n m√ = √ =
[ nm nm 2(13) n m n m − n m 1]3 [ nm
125
nm 25]3 .
nm



3. f(x) n m n m = n m 3x2 n m n m + 11. f(x) n m n m = n m x n m n m − n m |x n m n m − n m 2|,
n m 5x − n m 2,
f n m (0) nm nm = n m 3(0)2 nm nm + 2 f (1)
n m = 1 − |1 − n m2|= n m n m n m n m n m n m


n m 5(0) n m n m − n m 1 −|− n m nm nm


= n m −2, 1|= 1 − 1 = 0, f
n m (2) n m n m n m n m nm n m nm


= 2 − |2
= —
nm n m n m n m
f n m (−2) nm nm n m 3(−2)2
— 2|= 2 − |0|=
n m 2, n m n m n m 1 2.
+
n m
5(−2)
=
n m n m

f (3) = 3 − |3 − 2|= n m

=
n m n m n m n m n m n m n m n m
2 n m 0,n m

n m − |1|=
3 3 n m − n m n m n m

13. −2x + 4 if
=
n m n m n m
f (1) n m 3(1)2 2
≤
n m n m

h(x) = x 1 n m n m n m

+ −
n m n m
5(1)
+
n m n m n m
x2 1
n m if
n m x n m n m n m n m n m

= n m 6. > 1 n m n m n m n m


h(3) = (3)2 +
n m 1 =
n m n m n m n m n m n m n m 10

1
5. =
,g(x) n m h(1) nm nm = n m −2(1) nm nm + n m 4 n m = n m 2
n m x n m +
x n m
h(0) = −2(0) + 4 = 4
1 n m n m n m n m n m n m n m n m n m


g(−1) = n m −1 h(−3) = −2(−3) + 4 = 10
+
nm nm
nm nm n m n m n m n m n m n m
n m

= −2, −1 x
n m
15. g(x) nm .
1

g(1) n m = nm +