A-76 Answers
54. (A) Average g(x)≈2.
5
3 (B) 4
g(x) 5 x 1 1
f
f
73. (A)
100
210 130
51. (A) Average
f
(t)=2
(B)
10
f(t) 5 3t2 2 2t
85. 1
3
(–200t+600)dt =300 86. 1
I(t)
dt =600 units
A-78 Copyright © Pearson Education, Inc.
Chapter 13
Lb
a
[0 –h1x2]dx. 15. 24 16. 40 17. 51 18. 15 19. 42 20. 144
21. 6 22. 12.75 23. 2.350 24. 1.718 25. 1 26. 1 27. Mexico;
c
d
Lb
a
b
c
b
c
ANSWERS
39. Find the intersection points by solving
f1
x
2
=g
1
x
2
on the inter-
2
1
2
f1
2
1
2
40. Find the x intercepts b and c by solving
f1
x
2
=0. Then observe
f1
2
2
f1
2
a
b
c
41. 4 42. 0.5 43. 21.333 44. 2.667 45. 13 46. 12.667 47. 15
56. 1.763 57.
1
3
–
3
29–x2 dx; 14.137 58.
L
5
–
5
225 –x2dx;
39.270
59.
1
4
0
216 –x2 dx; 12.566 60.
6
0
236 –x2dx;
28.274
10
70. 7.360 71. 48.136 72. 184.741 73. 1.251 74. 4.600 75. 4.41
76. 2.64 77. 1.74 78. 2.17 79. Total production from the end of the
fifth year to the end of the 10th year is 50 +100 ln 20 –100 ln 15 ≈79
1
81. Total profit over the 5-yr useful life of the game is 20 –30e–1.
5
≈13.306,
or $13,306. 82. The total profit over the useful life of the game is
0
.
9
was more equally distributed in 1972. 85. 1963: 0.818; 1983: 0.846; total
f1
2
90. Total demand for wood from 2005 to 2010 is 102.25 billion cubic feet.
91. Average number of words learned from
t
=2 hr to
t
=4 hr is
17. 0.5
20.01
20. 0.03
20.01
21. (A) .75 (B) .11 (C) f(x)
22. (A) 0.75 (B) 0.15 (C) f(x)
1
A-80 Answers
Exercises 13.3
x
4
4+
Lg1x2
u
x
x
x
x
t
37. The integral represents the area between the graph of y=
l
n 2x and the
x axis from
x
=1 to x=3.
y
x
4
Exercises 14.2
dx
dx
x
dx
2
2
2
2
2
Chapter 14
26. 30p≈94.2 27. 118 28. 11.26 29. 6.2 30. 1 31. f
1
x
2
=x
–7
2
ANSWERS
Answers A-85
15.
f
x1x,
y2=yex–3;
f
y
1x,
y2=ex+4; the function
fy
1x,
y2 never has the
fy
f
f1
2
f1
2
f1
f1
f1
f1
f1
3
2
fy
fy
fy
fy
fy
f
f1
2
2
f
f1
f1
f1
f1
78. x=2.042 and y=2.085 79. (A) –
13
3
(B) The function
f1
0, y
2
, for
13
A-86 Answers
Exercises 14.6
2
4
2p
p
2p
(B) 3x
2
8. (A) 4y
3
x
3
+E
1
y
2
(B) 36y
3
9. (A) 2x
2
+6xy +5x+E
1
y
2
(B) 35 +30y 10. (A)
1
4x+5
2
y+3y
2
+C
1
x
2
(B) 12x+60
13. (A)
l
n x
l
n y
+C1x2 (B)
2
l
n x
14. (A) 1ln x22
+E1y2 (B)
1
26. e
–e–e
+1≈5,120.41 27. 16 28.
9 29. 49
1
26. Fx=3x
2
+6l=0, F
y
=6y
2
–2l=0, Fl=
6
x–2y–1=0 have
31. 60 of model A and 30 of model B will yield a minimum cost of $32,400 per
week. 32. $29,000 spent on labor and $31,000 spent on materials will yield
units 34. (A) 6,000 units of labor and 2,000 units of capital; max
1. 10 2. 38 3. 98 4. 30 5. 380 6. 100
A-88 Answers
Copyright © Pearson Education, Inc.
≈
8.37; marginal productivity of capital ≈
1.
6
7; management should
capital; max N
1
x, y
2
=N
1
80, 40
2
≈696 units; marginal productivity of
29. Tx170, 172=–0.924 min>f
t
increase in depth when V=70 ft
and
1
2
2
31. 50,000 (14.1) 32.
y
=
2x+48; y=68 when x=40 (14.5)
2
2
1
1
Exercises A.1
1
1
19. T 20. T 21. F 22. F 23. T 24. T 25. T 26. T 27. No
28. Ye s 29. (A) F (B) T (C) T 30. (A) T (B) F (C) T 31.
2
2 and p
1
21
1
3
1
1
1
1
1
1
1
1
1
1
34. 2y
1
y–3
21
y–8
2
35.
x
1
2y–3
22
36.
y
1
4x–1
22
1
1
2
1
43.
1
2x–3y
21
4x
2
+6xy +9y
22
44.
5
1
x+2y
21
x
2
–2xy +y
22
2
2
1
ANSWERS
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Answers A-91
65. 1
66.
x
–
y
many choices. 69. x=y=1 is one of many choices.
87. x+
6
2
2
43. x
2
1x–32
1
x–1
2
3x
4
1x+52
1
x+3
2
21x–12
x
x1x+62
1
x+3
2
47. 2.4 *10
; 24,000,000,000 48. 3*10–
; 0.0003 49. 3.125 *10
;
62. (A) 3 *10–
(B) 0.000 000 03 (C) 0.000 003% 63. 1,194,000
64. 91.3 people per square mile