of 84
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Answers to Exercises
and Pre/Post Tests
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604 Section 0.10.2 Answers to Exercises and Pre/Post Tests
Pretest 0.1
1. 1
2.
3. 3
4. 7
5.
6.
7. 20
8. 45
9. 4/3
10.
Posttest 0.1
1. 1
2. 2
3.
4. 15
5. 17/2
6.
7. 2/9
8.
9.
10. 6 ft
Exercise Set 0.1
1. 16
2.
3. 0
4. 0
5. 8/3
6. 4
7.
8. 26/11
9. 59/21
10. 2
11.
12.
13. 12
14. 15
15. 8/15
16. 10
17.
18. 29/7
19. 19/18
20. 65/84
21. 755/9
2.119 + 2y2/5
-33
-14/11
-3/7
-2/9
-6
13x - 92/4-270/109 L -2.47706
-32/7
-3
12x - 52/3
59/158 L 0.37342
-2/3
-3
23.
24.
25.
26.
27.
28.
29.
30.
31.
32. 84
33.
34. 12 cm
35.
36.
37. (a) 2 hrs
(b) 160 mi, 120 mi
38. 4 hrs
39. 4 hrs
40. 25
41. 150
42. 36
43. 5/14
44. 12/15
45. $6,480
46. 3 yrs.
47. 4%
Pretest 0.2
1. 0, 5/4
2. 0, 4
3.
4.
5.
6.
7.
8.
9.
10.
Posttest 0.2
1. 0, 3/7
2. 0, 9/2
3.
4.
5.
6.
7. ;26
4
;225i;1
;3/2
;9/4
5 ; 2252
5 ; 323i5 ; 322; 222
3
;222i2, -13/6
;232
;7/3
517, 19, 216531, 32, 336
w = 5, l = 13
J = 16, M = 21
M = 19, L = 12
RW/1W - R212A - ah2/hV/1pr225/91F - 3221c - ax2/b1c - by2/a15x - 192/2
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Section 0.20.3 Answers to Exercises and Pre/Post Tests 6
8.
9.
10.
Exercise Set 0.2
1.
2.
3.4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
2.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.39.
40.
41.
42.
43. 4 ; 4i
-3 ; 3i
1 ; 2223
3 ; 2262
- 4 ; 2255
7 ; 3224
-4/3, 4
-2, 5
-2, 10
-8, 2
-5/2, 3
-4, 5
-1, 5
;226i;2230
10
;217010
;4
22i
;223;323i;322i;4i
;222i;225i;4i
;3i
;7i
;2i
;6i
;5i
;226;223;222;322;3
;3
;8
;5
;3
;8
;7;2
;6
;5
- 4 ; 2235
5 ; 223i-3 ; 226 44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
Pretest 0.3
1. 16
2. 9/4
3.
4.
5.
Posttest 0.3
1. 36
2. 25/4
3.
4.
5.
Exercise Set 0.3
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17. -3 ; 223, -6.464, 0.4643 ;26, 0.551, 5.4491 ;211, -2.317, 4.317-3 ;26, -0.551, -5.449-1 ;211, -4.317, 2.3171x + 9/2
22 - 81/4
1x - 7/222 - 49/41x + 5/222 - 25/41x - 5/222 - 25/41x - 3/222 - 9/41x + 3/222 - 9/41x + 622 - 361x - 522 - 251x - 422 - 161x - 322 - 91x + 322 - 91
x + 222 - 4
2 ;26- 3 ; 325
2
6 ; 2210
6 ; 4233
- 5 ; 3252
5 ; 2
27
15 ; 2215i6
15 ; 22159
- 7 ; 322i2
-7 ; 3223 ; 225i
2
- 4 ; 525i10
2 ; 2
23
3
-3 ; 3222 ; 223i
3
5 ; 322i3
3 ; 226i2
- 7 ; 6i4
2 ; 5i3
5 ; 223i
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606 Section 0.30.4 Answers to Exercises and Pre/Post Tests
18.
19.
20.
21.
2.
23.
24.
25.
26.
27. 1, 1/6
28.
29.
30.
31.
32.
33.
34.
35.
36.37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52. 2.34 sec
53. 16.2 m by 6.2 m
Pretest 0.4
1.
2.
3.
4.
5. 1.664 or 198.336 sec.
Posttest 0.4
1.
2.1 ;233
4
3 ;2418
3 ;23i3
4 ;2349
2 ;252 ;214
2
b = 8, h = 5
5 ; 32510
, -0.171, 1.171
- 2 ;272
, -2.323, 0.323
15 ;
2393
12 , -0.402, 2.902
9 ;232112
, -0.743, 2.243
-5 ;221, -9.583, -0.4175 ;2103i
8
- 5 ;255i4
-5/2, -4/3
-3/4, 4/3
-3/2, 2/3
-2, 3/2
- 4 ;2142
, -3.871, -0.129
- 5 ;215i2
3 ;23i2-3 ; 2
23i
2 ; 223, -1.464, 5.4644 ; 225i5 ; 5i
6 ; 223i3 ;214i- 1 ;2119i
12
- 5 ;239i2
-1 ; 227, -6.29, 4.29
-7, 5
-2, 5
-1 ; 3i
- 3 ;2132
, -3.303, 0.303
3 ;2132
, -0.303, 3.303
5 ; 3252
, -0.854, 5.854
- 5 ; 3252
, -5.854, 0.854
6 ; 2210, -0.325, 12.3254 ; 225, -0.472, 8.472 3.
4.
5. 7.129 sec.
Exercise Set 0.4
Answers in 115 are in the form (a, b, c)
1.
2.3.
4.
5.
6.
7.
8.
9. (5, 0, 11)
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
2.
23.
24.
25.
26.
27.
28.
29. 1, 1/6
30.
31.
32.
33.
34.
35.
36.
37.38.
39.
40.
41.
42. -2, 3/2
- 4 ;2142 , -3.871, -0.129
- 5 ;215i2
3 ;23i2
-3 ; 223i2 ; 2
23, -1.464, 5.464
4 ; 225i-5 ; 5i
6 ; 223i3 ;214i- 1 ;2119i
12
- 5 ;239i2
-1 ; 227, -6.29, 4.29
-7, 5
-2, 5
-1 ; 3i
3 ;2132 , -0.303, 3.303
5 ; 3252
, -0.854, 5.854
- 5 ; 3252
, -5.854, 0.854
6 ; 2210, -0.325, 12.3254 ; 225, -0.472, 8.472-3 ; 223, -6.464, 0.4643 ;26, 0.551, 5.4491 ;211, -2.317, 4.317-3 ;26, -0.551, -5.449-1 ;211, -4.313, 2.31714, 5, -212160, -152, 71218, -14, -22213, -2, -13214, -9, 0217, -3, 02
12, 0, -10215, 10, -14219, -4, 4215, 27, -10213, 7, -10215, -8, -12213, 7,
-82
11, 4, -112
5 ;223i8
-1, 5/4
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Section 0.5 Answers to Exercises and Pre/Post Tests 6
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53. 5,6, 7, or
54. 11, 13, 15, or
55. 16.971 in
56. 13.416 in
57. (a) 0.195 sec or 4.805 sec (b) 5 sec (c) 5.807 sec
58. (a) 3.062 sec (b) 3.536 sec (c) 3.953 sec
59. 4ft
60. 82 and 94 miles
61. (a) 3.584ft (b) 12.832ft by 16.832 ft
62. 10 and 12 mph
63. 4 hr
64. (a) 50, 150 (b) 100 (c) 5000
65. (a) 18, 47 (b) 15, 50
66.
67.
68. 6/13, 4
69.
70.
71. 512, 19683
72.
Pretest 0.5
1.
2.
3.
4.
5.
Posttest 0.5
1.
2.
3.
4.
5.
Exercise Set 0.5
1.
2. x 3/2
x 7 3/2
-5/3 6 x 0 or 2/3 x 6 5/3 or x 5/2
-4/5 6 x 6 3
-3/2 6 x 5/2
3/4 6 x 6 1
x -3/2 or x 2/5
x 6 -4 or 0 x 1 or 2 x 6 4
-11/4 6 x 6 4/3
x 3/2 or x 7 5
x 6 0
x -4 or x 2/3
;32 +1102
= ;34 + 22102
23122
,23 36
3
;2
-17/2, 3
-4/3, 8
-15, -13, -11
-7, -6, -5
5 ; 32510
, -0.171, 1.171
- 2 ;272
, -2.323, 0.323
15 ;
239312 , -0.402, 2.902
9 ;232112
, -0.743, 2.243
-5 ;221, -9.583, -0.417- 5 ;2103i
8
- 5 ;255i4
-5/2, -4/3
-3/4, 4/3
-3/2, 2/3 3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
2.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50. x 6 1 or x 7 3
1 6 x 3
-3 6 x 6 4
x 6 -3 or x 4
3 6 x 8
x 6 3 or x 7 8
0 6 x 6 3/2 or 3/2 6 x 6 4
x 0 or x = 3/2 or x 7 4
2/3 x 5/2
x 6 2/3 or 5/2 6 x 6 4 or x 7 4
-2 6 x 6 1 or x 7 3
x -2 or 1 x 6 3
-11/20 6 x 6 1
x -11/20 or x 1
x -17/6 or x 2
-17/6 6 x 6 2
-5/2 6 x 6 4x -5/2 or x 4
x 6 -1 or x 7 1
-4 x 4
x 6 -5 or 0 6 x 6 5
-5 x 0 or x 5
x 6 -4 or 0 6 x 6 4
-4 x 0 or x 4
-5/4 6 x 6 5/6
x -5/4 or x 5/6
-3/2 6 x 6 4/5
x -3/2 or x 4/5
x 6 -4/3 or x 7 3/2
-4/3 x 3/2
x 6 -7 or x 7 6
2 6 x 6 5
x -4 or x -3
x -3/2 or -1 x 5/3
-5 x -1 or x 2
x -3 or 0 x 2
x 3/2
x = -2 or x 3
0 6 x 6 5/2
x 0 or x 5/2
x 2/3 or x 3/4
-4 6 x 6 5/2
-5 6 x 6 3/5
x -5 or x 3/5
x 6 -5/3 or x 7 7/4
-5/3 x 7/4
-4 6 x 6 3
x -4 or x 3
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608 Section 1.1 Answers to Exercises and Pre/Post Tests
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
Pretest 1.1
1.
2. 5/2
3.
4. 9/5
5.
6.
7.
8.
9.
10.
Posttest 1.1
1.2.
3. 12/7
4. 6
5.
6.
7.
8.
9.
Exercise Set 1.1
1.
2.
3.
4.
5.
6.
7. -12, 19/2, 02, 10, 9/423/4, 14, 02, 10, -32y =
1
4x + 3
y = 12x + 1/4
y = -2y
= -3x
y = 2x + 4
2x + 5y = 5
x + 11y = 47
x = 5
y = 6
-3x + 2y = 38
-2/7y = 3x - 3
2x + 3y = 27
3x - 2y = 8
5x - 2y = 16
y = 2
x = 5
y = 3x - 11
-9/2
y = 2x + 5
- q 6 x 6 q
2 - 325 x 2 + 325x 6 2 - 325 or x 7 2 + 325x 1 -22 or x 1 +221 -22 6 x 6 1 +22x 6 -222 or x 7 222-222 x 222-9/2 6 x 6 -1/2 or -1/2 6 x 6 0 or 0 6 x 6 7/4 or x 7 2
x 6 -9/2 or 7/4 x 6 2 or x = 0
-3 6 x 6 -4/3 or -4/3 6 x 6 0 or 0 6 x 6 12or x 7 2
x -3 or x = 0 or 12 6 x 2
-6 6 x 6 -5 or 5 6 x 6 6
x -6 or -5 6 x 6 5 or x 6
x 6 3
x 7 3 8. 5/4, (0,3)
9.
10. 0,
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
y = 8
x = 12
y = 2x + 4
y = -6
x = -1
y = 4.1x - 12.3
y = 14x + 143/10
y =1
6x
y = 12x + 1
y = -3x + 11
10, -19/42-13/47, 1-112/13, 02, 10, -112/472
1-12/5, 02,
2.
23.
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8/13/2019 Applied Calculus Zanswers
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610 Section 1.1 Answers to Exercises and Pre/Post Tests
32. 36.
y
x= 12
(12, 0) x
x= 1
33.
34.
35.
37.
39.
38.
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Section 1.1 Answers to Exercises and Pre/Post Tests 6
40. 54. 24
55.
56. 0
57. no slope
58. 4/7
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72. (a)
(b)
73. (a)
(b)
74. (a) 3
(b)
75.
76.
77. (a)
(b)
78. (b) no
(c) examine the slopes
79.
80. 130
81. 166
82.
t = -0.05x + 4000
` CAB
2A2 + B2291/5
y = -5x ; 20
5y + 2x = 20, 5y - 2x = 20.
C2
2 AB
7x - 3y = 16
3x + 7y = -18
5x + 2y = -18
2x - 5y = 16
y = 3x - 8
y =4
7x + 4
x = 12
y = -5
y = -2x
y = 24x - 9
14x + 2y = 3
y = 12x + 3
x = 12
y = 4
8x + 5y = 0.
7x - 5y = 59
x = 1
-2
41. (a) 2/5, (3,0),
(b) y =2
5 x +37
5
10, -6/52
(0, 37/5)
(0, -6/5)
42. (a)
(b) y = - 37x - 2
-3/7, 1-14, 02, 10, -62
43. (a)
(b)
44. (a)
(b)
45.
46.
47. no slope
48. 7/549.
50. 0
51. no slope
52.
53. -7
12
-8/5
x = 8, x = -4
y = 1, y = -7
x = -14
y = -6
x = 3
y = -6/5 (c)
(a)
(b)
(d) They are horizontal translations of each other. Each graph may be ob-
tained from (a) by moving it 3 units to the left or right.
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612 Section 1.11.2 Answers to Exercises and Pre/Post Tests
83. 11.
12.
13.
14.
15.
16.
17. (a)
(b)
(c) 1
(d)
(e)
18. (a)
(b) 7
(c) 1
(d)
(e)
19. (a)
(b) 0
(c) 4/3
(d)
(e)
20. (a) 0
(b) 0
(c) 12
(d) 48
(e)
21. 3
2. 5
23. m
24.
25.
26.
27.
28.
29.
30.
31.
32.
33. (a)
(b)
(c) - q 6 y 6 q
- q 6 x 6 q
212x + 2h - 1 +12x - 1
11x + h + 3 +1x + 3
- 41x - 321x + h - 32
- 2x1x + h23x2 + 3xh + h210x + 5h - 4
4x + 2h + 3
2x + h + 3
2x + 2h - 5
4x22x + 1
1x + h + 12/12x + 2h - 3212x + 12/14x - 32
-1/3
2x2 + 4xh + 2h2 - 1
18x2 - 1
-1
3x + 3h - 5
6x - 5
-8
-5
D =51, 2, 3, 46R =556D =54, 5, 96R =5-22, 2, 3, 76D =52, 3, 5, 66R =5-16D =53, 7, 96R =5-5, 2, 5, 116D =5-3, 2, 5, 196R =53, 5, 76D =53, 4, 7, 116, R =5-5, 11, 196
(b)
(a)
(c)
(d) They are vertical translations of each other. Each graph may be obtained
from (a) by moving it 4 units Up or down.
(d)
(e)
(a) (b)
(c)
84.
(f) They are each obtained from (a) by moving it 4 units up or down and si-
multaneously moving it 3 units to the left or right.
85. The second line is obtained from the first by moving it h units horizontally
and kunits vertically.
87. (a)
(b)
(c)
88. (25/14, 46/7)
89.
Exercise Set 1.2
1. Is a function
2. Is a function
3. Is a function
4. Is a function
5. Is not a function
6. Is a function
7. Is not a function
8. Is a function
9.
10. D =52, 3, 5, 76, R =5-5, 4, 9, 116D =5-1, 1, 2, 126, R =53, 5, 9, 236
B - b
2m2 + 1
4x + 3y = 2
2x - y = 4
2x + y = 6
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614 Section 1.2 Answers to Exercises and Pre/Post Tests
59. (a)
(b)
(c)
(d)
60. (a)
(b)
(c)
(d)
61. (a)
(b)
(c)
(d)
62. (a)
(b)
(c)
(d)
63. (a)
(b)
64. (a)
(b)
65. (a)
(b)
66. (a)
(b)
67. (a)
(b)
68. (a)
(b)
69. (a)
(b)
70.
71.
72.
f1d2 = g1b25x xis in the domain of fand f(x) is in the domain of g6
x x -3/2 x - q 6 x 6 qx x -1 x - q 6 x 6 qx - q 6 x 6 qx - q 6 x 6 qx - q 6 x 6 qx - q 6 x 6 q121x - 32
x + 2x Z -2, 3
12 + 2x
12 - 3x x Z 0, 4x
2 + 2 - q 6 x 6 q
x + 2 x 1
4x2 + 12x + 12 - q 6 x 6 q
2x2 + 9 - q 6 x 6 q
3x - 6
4x + 2 x Z ;2
12x + 6
1x + 2221x - 22
-1x + 82x2 - 4
7x - 4
x2 - 4
2x2 + 10
x + 1 x Z -1
121x3 + x2 + 5x + 52x2 - 12x + 9/2
x2 + 12x + 11/2
3x + 7
2x2 - 3 x Z ;26
2
6x3 + 14x2 - 9x - 21
-2x2 + 3x + 10
2x2 + 3x + 4
2x - 2
x2 x Z 0
2x3 - 3x2- x2 + 2x - 3
x2 + 2x - 3 73.
3
2
1
321
74.
75.
76. (a) 5(b)
(c) 5
(d)
77. (a) 5
(b)
(c) 6
(d)
78.
-5
-5
-6
-5
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Section 1.21.3 Answers to Exercises and Pre/Post Tests 6
79. 92. (a) 864
(b) 1600
(c)
(d)
(e)
(f)
(g)
(h)
93. (a) 218
(b)
(c)
(d)
(e)
Exercise Set 1.3
1. (a) $166.67
(b)
(c) $266.67
2. It reduces to $80
3. $5004. $27
5. $33
6.
7.
8. $30 and $3800.
9.
(b) $3.90 per item
10.
11. 5.26 yrs.
12.
13.
14.
(Either end points may have equality in 14 and 15.)
15. f1x2 =c 1 x -1- x -1 6 x 12x - 3 x 7 1 f1-22 = 1,f11.52 = -1.5,f152 =f1-12 = -3,f11.52 = 1,f142 = 3
f1x2 =c 2x - 1 x 11 1 6 x 2x - 1 x 7 2
= 2,f152 = 8
f1x2 =d -7x - 3
2 x 6 1
2 1 x 6 3
6x - 22 x 3
f1-22 = 11/2,f102 = -3/2,f122
Land = $10,000House = $90,000,
A1t2 = -950t + 10,000,p = -0.006x + 22.8
R1x2 = 2.25xC1x2 = 0.75x + 4500,
Marginal cost = $0.80overhead = $1000,C1x2 = 0.8x + 1000,C1x2 = 0.4x + 2000, R1x2 = 1.2x, P1x2 = 0.8x - 2000, x = 2500
15x - 2500
C1x2 = 2500 + 30x, R1x2 = 45x,
-6y3z - 3y3l + 2z + l
-4xy - 2kx - 9y2z2 - 9kyz2 - 3z2k22x + h - 2y2-8
16x3y, 48x3
24x2y2, 96y2
48x3 + 8x3k
96y2 + 48hy2 + 8y2h216x3y2 + 8x3k
24x2y2 + 24xy2 + 8y2h2
80. For non integer values,
81.
Ceil1x2 = flr1x2 + 1
82.
83.
84.
85.
86.
87.
8
88.
89.
91. (a) 3,
(b)
(c)
(d)
(e)
(f)(g)
(h) -4xy - 9y2, -4x - 9
2x - 2y2, 4 - 2y2-4x - 2xk - 9 - 9k - 3k
2
4 + h - 2y2-4xy - 2xk - 9y2 - 9yk - 3k22x - 2y2 + h
-15
x L 16 miles
x L 4 miles.
r = x +1xv = x +1r,v = x +2x +1x,w = x +1v,3x +2x +1x,
f1u2 =1u, u =4x +3x +2x +1x, u =1ww = x +f
1x
2 =23 x, g
1x
2 = x4 - 7x2 + 3x - 2
f1x2 =1x, g1x2 = x2 - 3g1x2 = 2x8 - 11x5 - 2x + 19f1x2 = x54,
g1x2 = 3x2 - 2x + 23f1x2 = x18,
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616 Section 1.31.4 Answers to Exercises and Pre/Post Testss
16. 3, 0-2,
24.
rather earn $19,999
Exercise Set 1.4
1. (b) (c) -1-1
T119.9992 = $116.99, T120.0012 = $123.51
T1x2 =d 6.5x - 19.5 x 6 106.5x - 13 10 x 6 206.5x - 65 20 x 6 30
6.5x x 30
17. 2,2,3,6,6
18. 1, 1, 3, 1-1,
19. (a) one intersection at (2, 1)
(b) two intersections at (0, 2) and (10, 6)
20. Three; (1/5, 3/5), (7/3, 5/3), (11/3, 7/3)
21.
22.
23. C1x2 =c 0.08x x 1002 + 0.06x 100 6 x 100022 + 0.04x x 7 1000
T1x2 =f 0.10x 0 6 x 14,0000.15x - 700 14,000 6 x 56,8000.25x - 6,380 56,800 6 x 114,6500.28x - 9,819.50 114,650 6 x 174,7000.33x - 18,554.50 174,700 6 x 311,950
0.35x - 24,793.50 x 7 311,950
V1t2 =e- 300,000t + 1,000,000 0 t 20-20,000t + 800,000 20 6 t 40
C(x)
x
2. (b) 2 (c) 2
3. (b) 3 (c) 3
4. (b) (c) -3-3
5. (b) 1 (c) 1
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Section 1.4 Answers to Exercises and Pre/Post Tests 6
6. (b) (c) -1-1 12. (b) (c) --1, 5
7. (b) 1 (c) 1
8. (b) (c) -2, 0-2, 0
9. (b) None (c) None
10. (b) 1.4, 4.6 (c)6 ;210
2
11. (b) (c)- 8 ;214
2-5.9, -2.1
13. (b) (c) -2 ;2-5.2, 1.2
14. (b) None (c) N
15. (b) (c)- 2 ;
2-3, 4, 1.4
16. (b) (c) --5, 1
17. (b) (c) 1 ;-1.2, 3.2
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Section 1.5 Answers to Exercises and Pre/Post Tests 6
3. C1-4, 32r = 4 6. C1-3, -22r = 3
(4,-1)
(3, -7)
4. C13, -22r = 5
5. C1-1, -42r = 2
7. C
10, 0
2r = 2
8. C10, 02r = 5
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620 Section 1.5 Answers to Exercises and Pre/Post Tests
9. C1-3, 52r = 5 12. C13/2, 5/22r = 2
10. C11, -22r = 2
11. C1-4, 32r = 4
13. C12/3, -4/32r = 11/3
14. C13/2, -1/42r = 2
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Section 1.5 Answers to Exercises and Pre/Post Tests 6
15.12/3, -5/62r = 3 32.
16. Contradiction
17. Contradiction18. Contradiction
19. Circle
20. Point
21. Point
22. Contradiction
23. point
24. Point
25. Circle
26. (a)
(b)
(c)
(d)
27. (a)
(b) 4
(c)
28. (a)
(b)
(c)
29. (a)
(b)
(c)
30. (a)
(b)
(c)
31. (a)
(b)
(c) 8
(d) 2
5 - 2265 + 2263 -
27
3 - 2253 -2153 +273 + 2253 +215-223-4
-223223
223b2 + c2-4ad 6 0
a = 0, bc Z 0,
b2 + c2-4ad = 0
b2 + c2-4ad 7 0
(c)
(a)
(b)
33. (a)
34. (a)
35. (a) 33 (b) 34. (b) 35 (b) the y-values on the tangent li
and on the circle near the point of tangency are almost the same
36.
y =12
5x -
169
5
y =3
4x
-25
4
y = 5/12xz +169
12
36.
37.
(d) They are translations of the same circle
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622 Section 1.51.6 Answers to Exercises and Pre/Post Tests
39.
42. (a)
(b)
(c)
(d)
43.
-626
5
6265
-3221
5
32215
38.
40.
41.
44.
Exercise Set 1.6
1. (a) Demand,x = 16, p = 4
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Section 1.6 Answers to Exercises and Pre/Post Tests 6
2. (a) Supply,p = 8 6. (a) Supply,p = 10
3. (a) Demand,x = 12, p = 6
4. (a) Demand,x = 110/7, p = 21
5. (a) Supply,p = 40
2p+x300 = 0
Demand
Supply
8p x200 = 0
p+14x-490 = 0
Demand
Supply
-5p+ 2x+ 70 = 0
7. (a) Demand x =22, p = 4
8.
(c) (200, 50),
(d)
(e) 10,000
R1x2 = - 12x2 + 150x
9.
(c) (105/4, 94)
(d)
(e) 2,444
R1x2 = -14/5x2 + 98x
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624 Section 1.6 Answers to Exercises and Pre/Post Tests
10. 17.
18.
19. 73.33 million, which would exceed population of NYC
(and capacity of system)
p = -1.5x + 110,
p = -20/3x + 80, x = -3/20p + 12
x + 500p = 20000
Supply
7p+ 2x+ 7= 0
Demand
Supply
Demand
x2+8x+220 -11p = 0
Supply
Demandx2+ 6x384 + 12p = 0
(c) (7, 3)
(d)
(e) 21
R1x2 = x216 - x
11.
(c) (11, 5)
(d)
(e) 55
R1x2 = x236 - x
12.
(c) (5.491, 26,742),
(d)
(e) 146.84
R1x2-1/121x3 + 6x2 - 84x2,
20. (13/4, 107/8)
21. (140/9, 760/9)
2. (2, 9)
23. (50, 350)
24. (17/3, 35/3)
25. (3, 48)
26.
27. $4800
28. (a) 2300
(b) 12,000
(c) 196
(d)
(e) 120
(f) 1.5, 2297.75
29. (a) 5040
(b) 99.18
(c)
(d) 100.80
(e) 4.5, 894
30. (a)
(b)
(c) $220
(d) 25, $12,500
31. (a)
(b)
(c) 35.73
(d) 267, 11940
32. 345, $345
33. (a)(b)
(c) 4
(d) 10
34. n =400 - x
3
P1x2 = 201x - 5x - 10R1x2 = 201
x
0 x 400
R1x2 = x22000 - 5x
0 x 50
R = -20x2 + 1000x
c1x2 = 100 + 2000/
x
c1x2 = x - 3 + 2300/x
2x + 4p = 21
13. (a) $40
(b) $65
(c) Perhaps everyone has a radio.
14. (a) 60 cords
(b) $25
15.
16. 7x - 600p + 2400 = 0
2x - 5p + 15 = 0
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Section 1.7 Answers to Exercises and Pre/Post Tests 6
Exercise Set 1.7
1. 4-3,
5. 0, 3-3,
2. 4, - 3
3. No zeros
4. 2-2,
6. 0, 2-2,
7. 0, 3/2, 3-3/2,
8. 0, 2
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626 Section 1.7 Answers to Exercises and Pre/Post Tests
9. -3 25. Both
26. y-axis
27. Both
28. Origin
29. Origin
30. (a) violates vertical line test
(b) Exercises 25 and 27
31.
32.
33.
34.
35.
36.
37.
38. None.
39.
40.
41.
42.
43. None
44.
45.
46.
47.
y = 0
y = 0
y = 2
y = 3/2
y = 0
y = 0
y = 2
x = -2
x = 2
x = 5/2
x = ;22x = -3
x = 3
x = 5
10. -3, 3
11. 0, 1
12. Even
13. Even
14. Neither
15. Odd
16. Neither
17. Neither
18. Odd
19. Odd20. Even
21. Odd
22. Even
23. Odd
24. Origin
48.
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Section 1.7 Answers to Exercises and Pre/Post Tests 6
49. 53.
50.
51.
52.
54.
(b) twice,x L -4.1106 and 6.2186
55.
56.
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628 Section 1.7 Answers to Exercises and Pre/Post Tests
57. (a) (b)
(c) (d)
(e) (f)
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Section 1.7 Answers to Exercises and Pre/Post Tests 6
(c) (d)
58. (a) (b)
(e) (f)
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630 Section 1.7 Answers to Exercises and Pre/Post Tests
59. (a) (b)
(c) (d)
(e) (f)
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Section 1.7 Answers to Exercises and Pre/Post Tests 6
60. (a) (b)
(c) (d)
(e) (f)
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632 Section 1.71.8 Answers to Exercises and Pre/Post Tests
61. (a)
(b)
x Z -1, 3/2 Exercise Set 1.8
1. (a)
(c) or
(d)
62. Observe
64.
65. Yes, also symmetry with respect to thex-axis.
67. See Section 3.4, Theorem 2.
68. No
69.
f1x2 = 02x - 4
x + 3 = 2 -
10
x + 3
11/4, -8/252 y 7 0y -8/25
x = 5/2 y= 2x 11
70.
y= 4x2
x= 3
x= 3
(b)
(c) 4267.7
2. (a)
(b)
y= 1108x+ 10442
y= 688x+ 6092
(c)
(d) Widening
(f) $9,810
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Section 1.8 Answers to Exercises and Pre/Post Tests 6
3. (a) 7. (a)
(b) 1.608
(c) It is widening
4. (a)
(b)
(c) It was unattractive in the 1980s.
R = 0.985237
5. (a)
(b)
(c) 0.976633
(d) 7.2
6. From the data, there is certainly some correlation between number of wins
and bating average.
(b) The money spent on each form of advertising grows changes the same
way.
(c) It is unclear, the different forms of advertising could be reaching diffe
consumers.
8. (a)
(b) 1077.3
(c) 1997
9. For 1977 to 1982,
For 1983 to 1986
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634 Section 1.8 Answers to Exercises and Pre/Post Tests
10. (a) It changes after 1980
(b)
(c) Riding became safer (perhaps because of helmet usage, or some other rea-
son.
f1x2 =e 36x + 428 if x 211100 if x 23
1x = 212 (c)
11. (a)
(b)
(c) The divorce rate in the 1980s decreased.
f1x2 =e 0.207x + 3.44 x 10-0.067857x + 5.996 x 11
13.
14. (a)
(b)
12. (a)
(b) Something in the country resulted in the decrease, perhaps better health
care. (There is a lot of information on the web regarding this topic.)
f1x2 =e 4.28x + 137.6 x 4-
5.75x +
179.75 x
5
(d)
15.
16.
Chapter Review
1.
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Chapter 1 Review Answers to Exercises and Pre/Post Tests 6
2. 14. Allxexcept 2/3 and 3/2
15. or (3, 4) or
16. (a)
(b)
17. 24
18. 105
19. (a) The first is a supply and the second a demand function
(b) [2, 8]
(c)
20. (a) $790
(b) $330
21. x Z 3
A5, 23 B
5 - 8x
3 - 2x, x Z 3
2
5 - 2x
4 - 3x, x Z 3
4
[4, q2[-5/2, 32y= 4
x = 2 x= 4
y = 1
3.
4.
5. (a) (7/2, 0),
(b)
10, -7/32y = -12x - 3
y =2
3x +
16
3
6. y = 5/4x 12
7.
8. (a)
(b)
9. No, samexcorresponds to differenty
10. (a)
(b) 7
(c) 3
11. (a)
(b)
(c) 3/2,
(d) 3/2
12. (a)
(b)
(c)
(d) same as before.
13. (a)
(b)
x 3/4
4x + 2h - 3
5 + 2h
9 + 2h
-2,
-4/3
x + 2
-6x2 + x + 12
3x2 + 10x + 8
3 - 2x
-5/3
4x + 3y = 6
3x - 4y = 17
2x - 3y = 6
(c) y 0
2. available
x 0 1 2 3 4 5
f(x) 3 4 1 4 7 9
(a) NA NA 3 4 1 4
(b) 1 4 7 9 NA NA
(c) 5 6 0 3 6 9 11
(d) 0 0 3 5(e) NA NA 6 7 1 0 4 7
(f) 2 1 5 8 11 13 NA NAf1x + 22 + 4f1x - 22 + 3 -3-7-6-1f1x2 - 4
-1f1x2 + 2-3-2f1x + 22
-3-2f1x - 22-3-2
-1-2
NA = not
23. (a) V1-1, 102
(b)
(c) -2.4, 0.34, -1 ;22-3.2, 1.2, -1 ;25
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636 Chapter 1 Review Answers to Exercises and Pre/Post Tests
24. 50, 100
25. (a) 194
(b)
26. x2 + y2 -4x + 6y - 3 = 0.
2x - 200 + 600/x, 1.94
33. (a)
27. C12, -32r = 5
28. it is a point.
29. (a)
(b) on Tan. 11.995833 on Circle 11.995844
30.x2
16 +
y2
25 = 1
y = 5/12 x + 169/12
C12, 32r = 0,
31.
32.
T
T
T
Note: y-values are positive on
(b) Turning points are indicated in sketch by T. (There is also one in the inter-
val 1-3, -2.521-3, -2.52
34.
x = -1 x= 1
y= 2
Zeros:x= 4, 3/2
35. (a) odd
(b) even
(c) even
(d) odd
(e) even
36. (a)
(b)
(c)
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Section 2.1 Answers to Exercises and Pre/Post Tests 6
Exercise Set 2.1
1.
2. 3/4
3.
4. (a)
-4/3
-1
10. (a)
Q 4.99 4.999 4.9999 5.0001 5.001 5.01
.166713 .166710 .166710 .166710 .166662 .1666204
(b) 1/6
11. (a)
Q 1.001 1.00001 0.9999 0.999
.299895 .30000 .300011 .3001051
(b) 0.3
12. 6
13. 0
14. 2
15.
16. 1/4
17. 12
18.
19.
20.
21. (a) 0
(b) The TL is the line itself which has slope 0.
22. m
23.
24.
25.
26. and
27. Connect the segments.
28. (a)
(b)
(c)
29. (a)
(b)
(c) (4, 16)
30. (a) (0, 0)
(b) does not exist
31. (a)
1-4, -162,13, -921-3, 92,12, -1621-2, 162,
11, -4213, -4
2
12, -72
1
21x + 2/x22/x2
-3/x2
-6x + 7
1
21x2x - 7
-5
mPQ
mPQ
(1, 4)
(2, 1)
(c) 2
5. (a)
(c)6.
-5
(3,2)
(c) 1/4
7. (a)
(2, 8)
(1, 0) y= 0
(c) 12
8. (a)
(c) 0
9. (a)
Q 0.99 0.999 0.9999 1.0001 1.001 1.01
1.99 1.999 1.9999 2.0001 2.001 2.01
(b) 2
mPQ(b) 4
(c) 1
(d) does not exist.
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638 Section 2.12.2 Answers to Exercises and Pre/Post Tests
32. (a)6.
7.
8.
9.
10.
11. 2x
12.
13.
14.
15.
16.
17. (0, 3),
18.
19.
20. (a) or
(b)
21. (a) (64, 24),
(b) (0, 0)
22.
23.
24. (a)
(b)
25. (a) 2.828
(b) 0.162
(c)
(d) 0.177
(e) 0.708
26.
27.
28.
29.
30. 1, 114, 112
31. 1/12
32. (a)
(b) 15.866667
(c) 15.866387
33. 3.9995
34. (a) 4
y =4
3x +
16
3
1
21x
-2
x3
2
3x1/3
57x56
x = -p
22
2 + 322
y = -16x + 81, y = 4x + 1
y = 6x + 4, y = -6x + 16
y = -6x + 13, y = 6x + 13
Area = 2k
x 6 -6
0 6 x-6 6 x 6 0
y = -1
11x +
79
11
a- b2a
,4ac - b2
4a b
12, -1321-2, -132,13, -10721-3, 1092,
y =7
2x + 1
y =25
12x -
56
3
y =145
3x -
575
3
y = 88x - 129
-5
12 -5
u2
-32t + 256
8
v3/4 +
32
v3 + 14v
1
323 x2 -1
424 x3 + 7 + 128x3
14x6 +12
x5 -
21
4x7/4
(b) 2x
(c) 1
(d) Does not exist
33. (a) (5/2, 0)
(b)
(c) 2
34. (a)
-2
(b)
(c) 9
(d) 9
35. and (2, 8)
36.
h .0001 .001 .01 .1
4.6416 21.544 100.00 464.16 464.16 100.00 21.544 4.6416
.0464 0.1 0.2154 0.4642
in the slope is becoming infinite as h approaches zero for
it approaches 0.
38. (a) 0
(b) m
(c)
(d)
Exercise Set 2.2
1. 10
2. 2
3.
4.
5.6x5 + 7x2 - 6
3x4
15x4 - 3x1/2 +5
x6
2
x1/3 - 12x3 -
4
x2
2/x2
-3/x2
x4/3f1x2 =f1x2 = x1/3,
- .0464-0.1-0.2154-0.4642mPQ
mPQ
- .0001- .001- .01- .1
1-4, -642
2x + 7
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Section 2.4 Answers to Exercises and Pre/Post Tests 6
19. 1/4
20. (a)
(b)
(c)
(d)
y = 2
x = 1
x = 0
(d)
21. (a)
(b)
(c)
(d)
y = -1
x = -1
x = 2
22. (a)
(b)
(c)
(d)
y = 2
x = 1
x = 3/2
23. (a)
(b)
(c) y = 2
x = 3
x = -12
24. (a)
(b)
(c)
(d)
y = -2
x = 4
x = -2
25. (a)
(b)
(c)
(d)
y = 12
x = 3/2
x = 0
26. (a)
(b)
(c)
(d)
y = 0
x = ;1
x = 0
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642 Section 2.4 Answers to Exercises and Pre/Post Tests
27. (a)
(b) none
(c)
(d)
y = 0
x = 0 31. (a) 2
(b)
32. (a) 1
(b)
33. (a)
(b)
(c)
(d)
y = 12/5
x = 0, 3/5
x = -3/2, 2/3
-1
-2
34. (a)
(b) none
(c)
(d)
y = ;2
x = 0
35. (a)
(b)
(c)
(d)
y = ;2
x ; 1x = 0
28. (a)
(b) none
(c)
(d)
y = 4
x = 0
29. (a)
(b)
(c)
(d)
y = 4
x = ;2
x = 0
30. (a)
(b)
(c)
(d)
y = 3
x = -1
x = 0
36. (a)
(b)
(c) y = 1/8
x = -1, 3/2
x = -2, 1, 3
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Section 2.42.5 Answers to Exercises and Pre/Post Tests 6
(d) 44.
38. (a)
(b)
(c)
(d)
y = 2
x = 1,1 ;217
8
x = 0.83585
39. (a)
(b)
(c)
(d)
y = 0
x = -1.23297
x = ;215
5
41.
42.
43.
y = 3x - 2
y = 2x + 3
45. Let evaluate for large values ofx.
46.
47.
Exercise Set 2.5
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 3/17
14.
15.
16. (a)
(b)
17. (a)
(b) (1, 2)
18. (3/2, 625/16), (4, 0)
19. (a)
(b)
23. (a)
(b)
(c)
25. (a)
28. (a) 12
(b) 4
f1x2 = 21x + 321x - 121x - 52x1x - 221x + 22x = -2
y = - x - 2
y = x, y = 12, y = 0.12x + 0.64, y = 0.08x + 0.54
1 - x2
1x2 + 1221-1, 02,
A1, 12 BA -1, - 12 B , A1, 12 B1-1, -22, 11, 22
y = 6x - 2
y = 52/3x - 84/5
y = -3x + 1
2x5 - 3x2 + 16
3x5
4x5 - 2x2 - 3
4x2
-6/x3
4x12x3 - 21x - 5212x2 + 722
-18/1x + 3222x/1x2 + 122-13/13x - 222x5120x4 - 21x + 2422x
13x4 + 4x2 - 7
2
2x3150x6 + 135x2 + 8221x217x4 - 92
x L -17.33, -1.577, 0.9851, 2.424
x L -0.7590, 0.6738
f1x211 + 0.07/x25x,
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644 Section 2.52.6 Answers to Exercises and Pre/Post Tests
29. fand g have derivative zero at the samex-values, and the
y-values are reciprocals.
Exercise Set 2.6
1. (a)
(b)
2. (a)
(b)
3. (a)
(b)
4. (a)
(b)
5. (a) 1/x
(b) 1/x
6. (a)
(b)
7. (a)x
(b)x
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.r135r2 - 262
32r2 - 115r2 - 221/3
-11x - 123/22x + 1
41x2 - 321x2 + 2x + 82715x3 + 6x2 - 4x - 122
12x11x2 - 1221x2 + 124
2x51x2 - 927111x2 - 272
-100u
15u2 + 923/2
312x2 + 12222x3 + 3x + 2
-13t + 1213t2 + 2t23/2
3110x - 72415x2 - 7x + 221/417
12x + 3
21x2 + 3x + 1
216
f1x2 = 42x2 + 4, g1x2 = xf1x2 = x3 + 5x + 5, g1x2 = 2x - 1f1x2 = x3, g1x2 = 2x + 3
2x - 4
f1x2 = x3/5, g1x2 = 5x3 - 7x + 3g1x2 = 3x7 - 7f1x2 = x9,
2x9 - 3x3 + 712x3 - 3x + 723
-1x + 426
3 - 2x
4x - 3
x + 1
x + 21x + 11
3x - 2
3 - 2x
x
1x + 522x2 + 5
g1x2 = -f1x21f1x222, 23.
24.
25.
26.
27.
28.
29.
30. (a)
(b)
(c)
31. (a)
(b)
(c)
32.
33.
34.
35.
36.
37.
38.
39.
40. (a)
(b) (1, 0), (2, 0)
(c) has horizontal tangents at the zeros offand at the horizontal tan-
gents off.
41. (a)
(b)
(c)
42.
43.
44.
45.1668964526
32
2 +
3 +1
1x2
23x + 2
1x
232x +23x + 21x
412x + x4211 + 2x323x2
6x2S212x32f1g1h1x22g1h1x22h1x25x551x2 - 423 +1x2 - 42102-1/2131x2 - 422 + 21x2 - 4292
f1x2 = x1/2, g1x2 = 5x3 - x10, h1x2 = x2 - 4[f1x2]N13/2, -1/42; 13/2, -1/4152,10, -42; 10, 4102, 1;2, 02
1
111x6 + 5211
12
131x4 + 5213
13x3 + 9232xS21x22
2x
x2 + 1
2xE1x223x2ax6 - 1
x6 + 1b
2x1x4 - 1230y1y + 221y3 + 3y2 + 429dy
dx
13y2 + 6y2dydx
3y2 + 6y
71x5 + 12y6dydx
+ 5x4y7
7y6dy
dx
7y6
y = -13
6x + 16
y = -296x + 8
y = 12x
y = 108x - 189
823 4t1t + 3231t + 421/3
5t2 - 3
31t2 - 122/3313t2 + 121t3 - 6t + 126125t4 - 59t2 + 4t - 142
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Section 2.62.7 Answers to Exercises and Pre/Post Tests 6
Exercise Set 2.7
1. (a)
(i) 1060.10
(ii) 1070
(b)
(i) 9.90
(ii) 9.90
(c) 0.002
(d) 10.70
2. 654, 656 (or 652)
3. (a)
(i) 240
(ii) 241.90
(b) 1.90
(c) 1.80 (or 2.00)
(d) 0.10 (or 0.20)
4. (a)
(b)
(c)
R
1x
2 =
-5
4
x2 + 7x, R
1x
2 =
-5
2
x + 7
p = -5
4x + 7
(f) 200, max. Profit
7. (a) 80
(b) 16
(c) 64
8. (a) 112(b) 16
(c)
9. (a)
(b) 112 ft/sec
(c)
(d)
(e)
(f) (I) 144 ft/sec
(ii) 80 ft/sec
(g) 5.5 sec, time to reach maximum height
(h) 484 ft
10. (a) 576 ft
(b) 12 sec
(c)
11. (a) in 200 sec.
(b) 640,000ft
12.
13. 5.66 sec,
14. Each answer is 3, the rate is the slope.
15. m see 14.
16. 3
17. 20
18. 3
19. m
20. 5
21.
22. -9
-5/48
-181.02 ft/sec
-128.996 ft/sec
-208 ft/sec
-32t + 176
-32t - 16h + 176
-32th - 16h2 + 176h
s = -16t2 + 176t
-48
At is maximized
(d) $3.50, 2.8 million
5. (a)
(b) 2000
(c)
(d) 35
5(e)
P = -1/10x + 30
P1x2 = - 120 x2 + 30x - 500
x = 14/5, R
6. (a)
(b) 2000
(c)
(d) 50
(e)
P = -1/5x + 40
P1x2 = - 110
x2 + 40x - 1000
R(x) = -5/4x2+7x
R'= -5/2x+ 7
5(f) 300, maximum profit
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Section 2.92.11 Answers to Exercises and Pre/Post Tests 6
(b)
(c) (13/3, 11/3)
17. (16/5, 36/5)
18.
21. (a)
(b) (5, 17/3)
Exercise Set 2.10
1. 27
2. 6
3.
4. 256/767
5.
6. 1/6
7.
8. (a)
(b) 50mph
9. (a)
(b) in either case at
10.
11. (a) 1/12 in/min
(b)
12.
13. 24/13 ft/sec
14. 5/6 ft/min
15.16. (a) decreasing at 1/6 lb per week
(b) $0 per week
17. (a) 49/6, 121/12 million
(b) 92/25, 828/3721, 3312/21025 million per year
18. (a)
(i) 820, 620, 320
(ii) 410, 15190/3, 9680/3
(b) 4690,
19. 80,000 psi/sec
20. (a)
(b) It will increase by 10 km
21.
22.
23. 32/3 ft/sec
24. 8/3 ft/sec, shorter
25. Longer side is increasing at 14/3 cm/sec, shorter decreasing at 5/3 cm.sec
26. Both increase, shorter side at 4 m/sec, larger at 2 m/sec.
4/p L 1.2732 ft/sec
-35 units/sec
3p/5000 cubic km/day
-11019, -8155/18
12,
48p L 150.796 sq ft/sec
decr.10
16pL 0.1989 ft/sec
2212
L 0.1179 in/min
-2 in/sec
2p L 6.28 in/hr
8p L 25.133 sq. in/hr
dz
dt
=
xdx
dt + y
dy
dt
z
dx/dt = -3, dy/dt = 3
;5/2
-4
y = -2
3x +
7
3, x = 5, y = -
1
6x +
13
2
xm = nx1 + mx2
m + n, ym =
ny1 + my2
m + n
241, 229, 52227. (a)
(b)
8.
Exercise Set 2.11
1. (a) so a root is in (1, 3)
(b) 2.3
(c) 2.2511896
(d) 2.443357
(e) 2.258259
2. 1.626577
3. 1.903654
4. 1.164035
5. 0.879385
6. (a) 0.3399, 2.2207
(b)
8. method will not work. If iterates converge to larger r
If they converge to smaller root.
9. They are the same.
10.
11.
13.
Chapter Review
1. (a)
(b)
(c)
2. (a)
(b)
3. (a)
(b)
4. (a)
(b)
5. (a) 2
(b) 25/6
6. (a)(b)
7. (a)
(b)
8. (a)x1x3 + 402
21x3 + 1023/2y = 20x - 28
x17x3 + 4222x3 + 1-4/3
1
2
y = -68
3x +
95
3
-20
x5 -
8
3x2/3
y =25
2x -
35
2
8x3 - 6x +1
21x +10
x3
y = -1
4x +
7
4
-4
1x + 1221-1, 72y = -4x + 7
-2x - 2
r = 7.56%
f122 = 0; 3.259921f132 = 0; -0.174802
x0 6 2
x0 7 2,f122 = 0,f1x2 L 51x + 1.814321x + 0.146121x - 0.339921x - 2.22072-1.8143, -0.1461,
-2.532089, -1.347296,
-1.4526269,
y = 13.203564x - 29.8174032,
y = 13.87x - 31.334,
y = 10x - 23,
f112 6 0,f13) 7 0
y = -8
5x +
11
5
-2x
3y2
dy
dx =
dy
dt
dx
dt
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648 Chapter 2 ReviewSection 3.1 Answers to Exercises and Pre/Post Tests
(b)
9. (a)
(b)
10. $24
11. (a)
(b) $3.60
12. (a)
(b)
(c)
13. (a) 1320 ft
(b) 1332.25 ft
(c)
14. 16 ft
15. (100/13, 172/13)
16. 3 ft/min
17. 5 ft/sec
18.
19. (a)
y =
5
4
x -
9
2
-292 ft/sec
0 6 t 6 12
t = 0, 12; s = 614
6t - 12t2
-3
5x2 + 12x
213x + 4251x2 - 124124x2 + 20x - 92
9x2
212x3 + 523/22x3 + 1
y = -13
18x -
7
18
21. (a)
(b)
(c)
(d)
20. (a)
f1-32 = -1/6-3, 3
-3, 3
(b) 1
(c) 1
(d) f112 = 1
(b) everywhere continuous
(c) not differentiable at
2.
23. 1.25307
Exercise Set 3.1
1.
y =7
24x +
25
8
x = 1
2.
3.
4.
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650 Section 3.2 Answers to Exercises and Pre/Post Tests
16. N(0, 0)
17. is a m if is a M if
18.
19. m(3/2, 45/4), M(2/3, 335/27)
20.
21.
22. m(0, 2)
23. M(0, 5),
24.
25.
M1-9/7, 137.5112, m11, 02, N1-3, 02m1;1, 32
m A0, 223 BM10, -72, m111/4, -899/1282, m21-1, -82
m15, -2702, M1-2, 732a 6 0a 7 0A - b2a , 4ac - b24a B
29.
26.
27.
28.
30.
31.
32.
33.
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652 Section 3.3 Answers to Exercises and Pre/Post Tests
34. CD on
35. CD on
36. Always CU
37. CD if or CU if and (243, 27)
38. Always CU
39. CU if
40. m(1, 2)
41. m(3/2, 45/4), M(2/3, 335/27)
42.
43.
44.
45.
m1-3/2, -1/42, M13/2, 1/42m1-3, 02, M1-1, 162, m11, 02m1-3, 1012, M1-2, 1082, m11, -272
x Z 0
0 6 x 6 243 I10, 02x 7 243x 6 0
-3 6 x 6 3
x 6 3 49.
46.
47.
Additionalx-intercepts at
48.
;223
50.
M A6 - 2233 , 16239 B , m A 6 + 2233 , - 16239 B
51.
52.
mat
A;223, -144
B
53.
mat A ;223, -119B
54.
other zeros x = ;2155
I1 A - 32210 , 567225000B , I3A32210 , - 567225000 B
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Section 3.3 Answers to Exercises and Pre/Post Tests 6
55. 59.
56.
57.
other zeros:
58.
x = ;222
I1 A- 3232 , -238 B , I3 A3232 , 238B
60.
m A -83, - 16239 B
I2(4/5, 2048/3125)
61.
62.
Note: Vertical tangent line at (0, 0), zero at Inflection at (243, 27x = 32
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654 Section 3.33.4 Answers to Exercises and Pre/Post Tests
63. 69.
64.
65.
66. (7 ,f(7))
(-1,f(-1))
(5,f(5))
67.
(2,7)(0,5)
(-4,3) (-1,1) (5,2)
m(-2,-2)
68. M(1,f(1))
(2,f(2))
m(3,f(3))
M(2,f(2))
(0,f(0))
m(-2,f(-2))
70. M(-1,f(-1)) M(1,f(1))
(-.5,f(-.5)) (.5,f(.5))
m(0,f(0))
71. (a) neither
(b) m(2, 0)
(c) M(2, 0)
(d) neither at (1, 0),
73. (a)
(b)
76. (a)
75. 3
80.
Exercise Set 3.4
1.
3. (50, 50)5.
7. (a)
(b)
8. (a)
(b)
9. 2400 ft.
10.
11.
12.
13.
14.
15. (a)
(c) doesnt look sleek.
16.
17. 2 cm
18. (0, 0), (6, 0), (0, 10)
d = 3p
1/3, h =24
p1/3
h = 2r; r = 323p
5 * 5 * 2
6 * 6 * 3
radius = height of rectangle, x =30
p + 4, y =
60
p + 4
x = 20, y = 24
x = 60, y = 40
2022 * 202220 * 40
100 * 100
100 * 200
15 * 15
36 * 36
a0 = 1, a1 = 5, a2 = 10, a3 = 10, a4 = 5, a5 = 1
b2 - 3ac 7 0
2f1x2f1x2
M1-3, 02, m1-5/7, -137.5112
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Section 3.43.6 Answers to Exercises and Pre/Post Tests 6
19.
20.
21. (a) and
(b) 3 miles
(c) 1 mile from A
22. (61/25,2/25)
23. (a) (4, 0),
(b)
(c)
24. (1, 1)
25. (a)
26. (a)
(b)
27.
29. 125 ft.
Exercise Set 3.5
1. (a) 25
(b) 97/4
2. 11
3. 212
4. (a) No max
(b) 33.60
(c) 1406.25
(d) 50
(e) not a demand equation
(f) 25
5. 60.4
6. (a)
(b)
(c) 4
7. 80
8.
9. (a)
(b) 8/3, $32/9, $256/27
10. 75
11. 350 trees
12. (a)
(b)
(c) or
13. (a)
(b)
(c) 0
(d)
(e)
(f)
14. 17.8 thousands
15. Decreases by 4750
-8/5
-12
-1
-23/2
-1
- 2pp + 1
-2 +1x5
-1100 - x22
2x2 or -
p21100 - p2
- 200 + x4
or4p
200 + 4p
2 x 4
623 - 1
C = 2000x + 2500, P = -1000x2 + 8000x - 2500
p = -1000x + 10,000
48
p + 4in. for square,
12p
p + 4in for circle
222 * 3222
222 *22A 6213, 9213 B , A - 6213, - 9213 BA 8213, 12213 B , A - 8213, - 12213 BA
12
210, 4
210 B , A - 12210, - 4210 B1-4, 02
48 * 24 * 24
15 * 10 16. $49.50 per thous.
17. $4,000 per coat.
Exercise Set 3.6
1. (a)
(b)
2. (a)
(b)3.
4. (a)
(b)
(c) yes,fis not differentiable at
5. (a) 6.05
(b) 2.93
(c) 6.05 is better because the 1 is closer to 1.01 than is 0
6. (a)
(b)
(c) 3.08 using (b)
7. (a) 4.00125 large,
(b) 3.9975 large
8. (a) 3.037 large
(b) 2.963 large
9. (a) 256.256 small
(b) 1.015 small
10. (a) 253.44 small
(b) 8.006 large
11. (a) 2.9963 large
(b)
12. (a)
(b)
(c)
(d) (i) 100, 105, 5
(ii) 0.1, 0.1005, 0.05
13. (a)
(b)
(c)
(d) (i) 900, 993, 93
(ii) 0.09, 0.090903, 0.0903
(iii)
14. (a)
(b)
(c)
15. (a)
(b)
(c)
(d) (i) 14, 16, 2
(ii) 0.14, 0.1402, 0.02
2 x
14x + 22x + 21x22dy =14x + 22dx
+1x25 + 15x21x23130x + 15x4
21x
2 + 20x3
1x
22 + 6x
1x
24 + 10
1x
22
+ 101x23 +1x26 + 15x21x246x21x3 + 52x +130x + 15x421x22 + 20x31x23 + 6x1x256x21x3 + 52dx
-0.09, -0.089103, -0.0897
9xx + 31x229x2x + 9x1x22 + 31x239x2dx
5 x
10xx + 51x22dy = 10xdx
-3.00741 large
y =5
6x +13
6
y = 54x + 2
-1
y =224 x + 3224y = 1 + 12x
y =1
3x + 1
y = -15
y = 12x - 3
y = 10x - 7
y = -2x + 5
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656 Section 3.6Chapter 3 Review Answers to Exercises and Pre/Post Tests
16. (a)
(b)
(c)
17. (a)
(b)
(c)
18. (a)
(b) small
19. At most
20. 0.0001 in
21. (a) 5.75
(b) 0.1997%
22. 60%/r
23. (a)
(b)
24. (a)
(b)
25. (a)
(b)
26. (a)
(b)
27.
(b) D
(c)
28. (a)
(b)
(c) and
(d)
2ss
2ss +1s22D =
dy
dx
x + Px
11x + x22 + 423 -1x2 + 4233x41x2 - 92717x2 - 152dx
- 100u
15u2 + 923/2du
312x2 + 12232x3 + 3x2 + 2dx
- 7
12x - 3
22dx
2x
1x2 + 122dx
- 21x2 + 3x + 221x2 - 222 dx
x5120x4 - 21x + 242dx2x13x5 + 4x2 - 72dx
0.24 in3
10.24p L 32.1699 cm3
11x + x23 + 521.7 -1x3 + 521.7x
- 5.1x21x3 + 520.711x + x23 + 521.7 -1x3 + 521.7dy = 5.1x21x3 + 120.7dx12x + 2 x + 120.6 -12x + 120.6
x - 1.212x + 12-0.4
12x + 2 x + 120.6 -12x + 120.6dy = 1.212x + 1020.4dx (b)
s s ss2
ss (s)2
s s
29. (a)
(b)
31. (b)
32. (b)
(c) 8.7
Chapter Review
1. (a)
T1x2 = 1121x - 92 + 1
40
T = 2 + 1712
x
3s2s
3s2s + 3s1s22 +1s23
M(-2,f(-2))
(-3,f(-3)) (7,f(7))
(- f()) (2,f(2))
m(,f())
2. (a) M(-1.3.5)
(-2,f(-2))
(2 .f(2))
m(0,1)
(b)M(1.2)
M(3, 4)
(-4,f(-4))
(4 ,f(4))
m((0, -5)
3. (a)
(b) (0, 0),
(c)
4. (a)
(b) (0, 0),
5. (1/27, 2/9),
(b) (1, 0), (2/5, 108/3125), (0, 0)
6. (a) (0, 0),
(b) (0, 0),(1, 1/3)
7. (a)
(b) (0, 0)
8. (a)
(b)
(c)
9. (a)
(b)
(c)
(d)
10. See Exercise 16
11. See Exercise 17
12. See Exercise 28
13. See Exercise 27
14. (a) none
(b)
(c) (0, 0)15. (a)
(b)A ; 263 , - 209B12, -122
14, -1282
M = 8, m = -4
M = 2, m = -22
M = 0, m = -4
M = -10, m = -30
m = 0, M = 155
M = 0, m = -648
M = 16, m = -5.125
1-2, -3/42, 12, 3/42
1-2, -42
1-1/27, -2/92A ;22, -4 B , 10, 02
11, -102, 13, -14212, -162, 1-2, 1621
-4, 32213, -6
2
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Chapter 3 Review Answers to Exercises and Pre/Post Tests 6
16. (a) (c)
(b)
(c)
17. (a)
(b)
inflection points A; 263 , - 209Bm1 A -22, -4 B , m2 A22, -4 B
Zeros at
(d)
x = ;239
Inflection points at and
18. (a)
A4 +2610 , 0.01862 BA4 -2610 , 0.0145 B
(b)
(c)
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658 Chapter 3 ReviewSection 4.1 Answers to Exercises and Pre/Post Tests
(d)
19. (a)
(b) 256
20. (a)
(b)
(c) 16
(d) 3
21. (a)
(b)
22. (a) (i) 10, 10 (ii) none
(b) (i) 40/3, 20/3 (ii) none
23. 5ft. high, 3 1/3 ft. wide
24. (6, 6)
25. 12, 64
26. (a) 250
(b) 325/4
27. (a)
- 768
12x + 12512x - 60x-6
t = 0, 3; t = 0, 2
v = 12t2 - 4t3a = 24t - 12t2
v = -32t + 64, a = -32
(b)
I1 A -223, - 3238 B , I210, 02I3 A223, 3238B
Inflection points A; 2233 , 14 B
28. (a)
(b)
29. (a)
(b) 1.0015
30. (a)
(b)
(c)
31. (a) 4.96
(b) 0.2496
Exercise Set 4.1
1. Yes
2. Yes
3. Yes
4. Yes
5. No
6. No
7. Yes
8. Yes
9. Yes
10. Yes
11. Increasing
12. Decreasing
13. Increasing
14. Decreasing
15. Neither
16. Neither
17. Increasing
18. Decreasing
19. Increasing
20. Increasing
21. No
22. Yes
23. Yes
24. No
25. Yes
26. Yes
27. No
28. Yes
- 212x2 + 3x - 1221x2 + 622 dx
x411 - x22315 - 13x22dx114x - 15x22dx
12x + 1
I1 A1 - 3255 , -0.42155B , I2A1 + 3255 , 0.30586 B
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Section 4.1 Answers to Exercises and Pre/Post Tests 6
29. (a)
(c)
(f)
(g)
(h) f-11x2 =1x + 32/21- q , q21- q , q21- q , q21- q , q2 33. (a)
(c)
(f)
(g)
(h) f-11x2 =1xy 0
x 0
y 0
x 0
(e)
(b)
30. (a)
(c)
(f)
(g)
(h) f-11x2 =17 - x2/31- q , q21- q , q21- q , q21- q , q2
(b)
(e)
31. (a)
(c)
(f)
(g)
(h) f-1
1x
2 =
1x2 + 8
2/2
y 4
x 0
y 0
x 4
(e)
(b)
32. (a)
(c)
(f)
(g)
(h) f-11x2 =16 - x22/2y 3
x 0
y 0
x 3
(b)
(e)
(b)
v.
34. (a)
(c)
(f)
(g)
(h) f-11x2 =22x - 22
y 0
x 1
y 1
x 0
(b)
(e)
35. (a)
(b)
(f)
(g)
(h) f-11x2 = -27 - x2
y 0
x 7
y 7
x 0
(b)
(e)
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660 Section 4.1 Answers to Exercises and Pre/Post Tests
36. (a)
(c)
(f)
(g)
(h) f-11x2 =13 x2
1- q , q21- q , q21- q , q21- q , q2 42. (a) 7/3
(b) 14/3
43. (a)
(b)
44. (a)
(b)
45.
46.
47.
48.
49.
50.
51.
52.
61.
62.
63.
64.
65.
66. (a)
(b) 1/27
67. (a)
(b) 1/21
69. It is one-to-one
f1x2 = 15x4 + 6x2 7 0
f1x2 = 6x2 + 3 7 0f1x2 = 1912x + 522 7 0f1x2 = 2
3x2/3 7 0
f1x2 = -8x 6 0f1x2 = - 116 - 2x 6 0f1x2 = 2 7 0f-11x2 = 11 - 5x
3 + 2x
f-11x2 = 3x + 79x - 2
f-11x2 = 5 - x24
, x 0
f-11x2 = x2 - 32
, x 0
f-11x2 = -215 - 5x5
f-11x2 =22x - 62
f-11x2 = x - 12
f-1
1x
2 =
x + 9
5
-15/7
-9/11
-3/5
-12
(b)
(e)
37. (a)
(c)
(f)
(g)
(h) f-11x2 = x3
8
1- q , q21- q , q21- q , q21- q , q2
(b)
(e)
38. (a)
(c)
(f)
(g)
(h) f-11x2 = x13 + 11- q , q21- q , q
2
1- q , q21- q , q2
(e) (b)
39. (a) 3
(b) 440. (a) 7/3
(b) 4/3
41. (a) 1
(b) 5
70. It is one-to-one
2
71. No, see exercises 69 and 70.
72. Yes, see Exercise 57
73. (a) No
(b) only if they are one-to-one
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Section 4.14.2 Answers to Exercises and Pre/Post Tests 6
74.
(b) No, it is not one-to-one
76.
fis fis g is
increasing Concave Upwards Concave Downwards
increasing Concave Downwards Concave Upwards
decreasing Concave Upwards Concave Upwards
decreasing Concave Downwards Concave Downwards
Exercise Set 4.2
1. 1.67789
2. 0.0069593
3. 0.242273
4. 7.99142
5. 0.126485
6.
7.
8. 7.10299
9. 0.06156706343
10. 1.632527
11. 0.00179239
12. 0.003607
13.
-32165728.94
-3912.9874
f1x2 = - 41x2 + 921x2 - 922 6 0 16.
14.
15.
17. See Exercise 14.
18. See Exercise 15.
19.
20.
21.
22.
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662 Section 4.2 Answers to Exercises and Pre/Post Tests
23. 33.
24.
25.
26.
27.
28.
29. y = 3x -2 - 3
y = 3x -2 + 3
y = 3x - 2
y = 3x + 2
y = 3x +2y = 3x -2
30.
31.
32.
34.
35.
36.
37.
38. 13/22
39. 7/13
40. 2/3
41. 4/21
42. 19/2
43.
44. 11/4
45. They are symmetric about they-axis
-18/7
-3/4
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Section 4.24.3 Answers to Exercises and Pre/Post Tests 6
46. They are symmetric about they-axis 64.
65.
66.
67. 508.541 million
68. (a)
(b)
(c) (i) (ii) better information,
ter treatment, contraception, among other reasons.
Exercise Set 4.3
1. 20.0855
2. 0.1353
3. 10.6974
4. 4.1133
5. (a) 716.02
(b) 716.64
(c) 716.67
6. (a) 2110.66
(b) 2112.99(c) 2113.07
7. (a) 20,081.64
(b) 20,166.07
(c) 20,168.96
8. (a) 2,642.90
(b) 2,645.92
(c) 2,646.02
9. (a) 8041.95
(b) 8029.35
(c) 8028.92
10. (a) 1480.92
(b) 1479.88
(c) 1479.84
11. (a) 736.50
(b) 736.18
(c) 736.17
12. (a) 664.33
(b) 662.17
(c) 662.09
13.
55732.2088x-0.3533;67438.53710.83842x119.983x2.4257
366.07111.55552x11.14774711.2227092x,138.88710.722x/20 L 138.88710.9837092x23.529410.852x/8 L 23.529410.979892x4.9062513.22x/10 L 4.9062511.123352x
47. They are symmetric about they-axis
48. They are symmetric about they-axis
49. (a) 1261
(b) 530
(c) 223
50. (a) 1140
(b) 289
(c) 19
51. (a)
(b) 396.918
(c) 263.973
52. (a) $52,167.33
(b) $70,108.53
53. (a)
(b) 9.839 million
(c) 10.241 million
54. (a) 27.9203 lb
(b) 4.8615 lb
55. (a) 9.12673 lb
(b) 8.07983 lb
(c) 4.01007 lb
56. (a) 31.6875 lb
(b) 1.00971 lb
57. (a) $1628.89
(b) $3386.35
58. (a) 2
(b) 2
59. (a)
(b)
(c)
60. (a) 3x
(b)(c) 3x
61. Power function
62. Linear(or power) function
63. 9.2307711.32x/5 L 9.2307711.0538742x
3122x/2 L
311.4142x
y = 5x0.485427
25
7A75 Bx2x + 3
10.13910.9952t
296.611.062t
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664 Section 4.3 Answers to Exercises and Pre/Post Tests
14. 19.
15.
16.
17.
18.
20.
21.
22.
23.
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Section 4.34.4 Answers to Exercises and Pre/Post Tests 6
24. 30. (a) 479 gm
(b) 326 gm
(c) 6.9 gm
32. 1.09861
33.
Exercise Set 4.4
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24. (a) inc on dec on
(b) CD on CU on
(c)
(d)
(1/3, 4e-1/3)
x 7 2/3x 6 2/3,
x 7 1/3x 6 1/3,
y = e316x - 52y = x
y = e-11-2x + 32y = 2x - 5
y = - x + 1
y = x + 1
9x2 + 2 - 6x4y2e2x3y2 - 2xe2x
3y2 + 2ex - 3e2y
4x5ye
2x3y
2
+ 6e2y
+ 8y + 3
x11 + ex22y11 + ey22
2x - ex + 2y
2ex + 2y
- 1
12x2 - 2x + 62e2xaxeaxxex
2x[12x2 + 12e2x2 - 1]1x2 + 122
4
1ex + e-x22
2ex
1ex + 122
1x2 - 2x - 12ex - 2x1x2 - 122
xex1x + 22x3e-3x1-3x + 422xe2x1x + 122axeax
2
-e-x-3e-3x2e2x
-0.693147
25.
26.
27.
28.
(e) Max at inflection at 12/3, 8e-2/3211/3, 4e-1/32,
29. (a) 98.8 gm
(b) 29.8 gm
(c) 4.9 gm
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666 Section 4.44.5 Answers to Exercises and Pre/Post Tests
25. (b) dec for inc for
(c) CU for allx
(d) rel min at (0, 1)
(f) (0, 1) is the minimum point.
29. (b) inc for allx
(c) CU for CD for
(d) none
(e)
x 6 0x 7 0,
x 7 0x 6 0,
M(1/4, e /2)-1
I(, e )-2
26.
M(1, e )-2
2I
1I
m(0, 0)
Note:
27.
I1a1 -222
, .293b , I2a1 +222
, 1.707b
M(3/2, 27e /8)-3
3I
2I
1I(0, 0)
Note:
28.
I2a 3 -232
, 0.0717b , I3a 3 +232
, 0.1167b
(e)
(f) none (0, 0) is an inflection point
30. 1/a
32.
Exercise Set 4.5
1.
2.
3.
4.
5.
6.
7.
8.
9.10.
11.
12.
13.
14.
15.
16.
17. 2
18. 2/3
19. 4
20.
21.
22. 5
23. 3
24. 3/2
25. 2
26. 1/16
-2/3
-3
12/324 = 16/8111223 = 1/833 = 27
102 = 100
10-2 = 1/100
b0 = 1
8-4/3 = 1/162
3
= 8
log9/1627/64 = 3/2
log1/31/9 = 2
log168 = 3/4
log61 = 0
log812 = -1/3
log216 = 4
log31/9 = -2
log381 = 4
A2
ae
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Section 4.5 Answers to Exercises and Pre/Post Tests 6
27. 81
28. 8
29. 5
30. 1/8
31. (a) 11.5 base
(b) 3.6 acid
32. (a) 4.4 acid
(b) 5.1 acid
33. (a) 7.2 base, almost neutral
(b) 6.9 acid, almost neutral
34. (a) 7.1 base, almost neutral
(b) 8.6 base
35. (a) 10.3 base
(b) 4.1 acid
36.
40.
37.
38.
39.
41.
42.
43.
44.
45. 1/x46. 1/x
47. 1/x
48. 3/x
49. 5/x
50. -3/x
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668 Section 4.54.6 Answers to Exercises and Pre/Post Tests
51. n/x
52.
53.
54.
55.
56.
57.58.
59.
60.
y = e-21-7x + 112y = 2x - 2
1
xln x
e2x + x2 + 1 - 2xln x1e2x + x2x1e2x + x2 + 122
e-2x11 - 2xln x2x
51ln x24x
5x4
x5
+ 12
6x
4 + 3x2
64. (a)
(b) 2.11866
65. (a)
(b) 0.075,
Exercise Set 4.6
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 0.6020
14. 115. 1.3010
16. 1.398
17. 1.204
18. 2.6020
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31. 3.58496
32. 1.77124
33. 1.729716
34. -1.63093
log3x + 1
1x - 128
lnB x7
1x + 127
ln241x + 32324 x + 1
2x + 5
logx513 y
z1725 w2
ln14x23 y2z3
w425 v2
logx41z
y223 w2
log1xy2
z3
lnx2
y4
ln x3y2
log516
log645
log38
5 log6x + 1/3 log6y + 5 log6z -12log6w - 5 log6v - 9 log6r
10 log4x + 1/3 log4y - 1/4 log4z
5 ln x + 3/4 ln y
12log x + 3/2 log y
12ln x + 2 ln y
3 ln x + 4 ln y + 5 ln z
3 ln x + 4 ln y - 5 ln z
1 + 2 log x + 3 log y
log x + 2 log y
log2x + 2 log2y
log32 - log
3y
log 3 + log x
-2.96076
0.075 - 1.4599 ln x
-0.023609,
-0.023609 + 1.030215 ln x
m(1/e, -1/e)
61.
m(2, 2-2ln 2)
62.
x= 0 is V.A.
63.M(1.7632, 0.0973)
I(2.552, .07299)
x= 0 is V.A.
y= 0 is H. A.
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Section 4.6 Answers to Exercises and Pre/Post Tests 6
35. 1.86135
36. 3
37. 2
38. 2
39. 3/4
40.
41.
42. 5
43.
44. 2.26178
45. 3.15465
46.
47. 1.04317
48. 0.74901
49. 3
50. 1
51. 0.635777
52. 15y 3m 22d
53. 13y 3m 7d
54. 10y 6m 16d
55. 3y 10m 18d
56. (a) 6y 5m 21d
(b) 6y 4m 20d
(c) 6y 3m 29d
(d) 6y 3m 19d
(e) 6y 3m 19d
57. (a) 13y 8m 24d
(b) 17y 3m 29d
58. 7.44%
59. 3.65%
60. 5.62%
61. 6.10%
62.
-0.231544
211
-1
-3/7
64.
63.
65.
67. 1/x
68. 1/x
69. 6/x
70. 9/x
71. 6/x
72. 5/x
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95. y = -8
53x +
69
53
y = 1
y =15
4x - 7
ex11 + xln x2xex -1211 + ln x2x2xA
24
3x - 2 + 2
4x - 1 - 2x
x2
+ 1 B A 13x - 228
24x - 1
x2
+ 1 BA 8x
x2
+ 5+ 5
215x + 72 B A1x2 + 52425x + 7 B7
x + 60x
3x2
+ 8+ 2x
2x2
+ 5- 50x
4
2x5
+ 9- 3x
213x2 + 12
3
x + 8
2x + 1 - 5x
5x2
+ 4
3
x + x
x2
+ 4- 2x
3x2
+ 7
-18x2 + 92xln 214x2 + 32
-112x2 + 252x13x2 + 52
1 + ln xxln x
4111x2 + 4525x12x2 + 92
317x + 222x13x + 12
- 2x4-2x2121x2 + 12ln 4 + 12
1x2
+12
2
x242x12xln 4 + 326xln 2123x222 ln 3132x2
5
xln 7
2
xln 3
5
315x + 72
1
2x + 1
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670 Section 4.7Chapter 4 Review Answers to Exercises and Pre/Post Tests
Exercise Set 4.7
1. (a) 10,919,630
(b) 0.549 hours
2. 5.74 hours
3. 9.04 billion
4. (a)
(b) 2016
5. (a) 3.59 billion
(b) 4.46 billion
(c) 2.51 billion
(d) 1.02 billion
6. 2535.69
7. (a) 5040.60
(b) 5.96 years
8. 8.54%
9. (a)
(b) 17.6 kilograms
10. (a) 9.1796 1grams
(b) 1620 years
11. 79.45%
13. 19,030 years
14. 28,980 years
15. 11.85%
16. 43,220 years
17. 5.98 years
18. 1.096 years
19. After 10.3 weeks
20. 11.4 days
21. 4.03 weeks
22. 5.6
23. 6.324. 4.6
25. 5.1
26.
27.
28.
29.
30.
31.
32. 178 times
33. 1000 times
34. 5623 times
35. 177,828 times
36. (a) 3.468 billion
(b) 4.01 billion
(c) 5.68 billion
(d) 2.24 billion
3.55 * 1024ergs
5.01 * 1018ergs
3.16 * 1017ergs
7.08 * 1021ergs
5.62 * 1022ergs
2.82 * 1019ergs
-0.01474781
P1t2 = 149000e0.0155109t
(e) 0.527 billion
(f)
38. (a) 170.8F
(b) 23.3 minutes
Chapter Review
1. (I) (a)
(b)(d)
- q 6 x 6 q ; - q 6 y 6 q
1 - 1
7.9 * 109billion
(e)
(II) (a)
(b)
(d)
- q 6 x 6 q ; - q 6 y 6 q
1 - 1
f-11x2 = 12x - 5/2
(e)
(III) not dec when inc when
(IV) not dec for inc for
(V) not dec for inc when
(VI) (a)
(b)
(d)
x 0, y -2
1 - 1
x 7 0x 6 0,1 - 1,
x 6 0x 7 0,1 - 1,
x 7 0x 6 0,1 - 1,
f-11x2 =Ax - 42 B1/3
(e)
2. (a)
(b)
(c) 1/8
-1
f1x2 7 01
2 2x + 2
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Chapter 4 ReviewSection 5.2 Answers to Exercises and Pre/Post Tests 6
3. (a) 941.95
(b) 2341.61
4. Call
(a)
(b) 8.95
(c) 6.39
5.
6. $1057.94
7. 5.21%
8.
9.
y = -3e-21x + 22
f1x2 = 4.3546511.224742x
P1t2 = 7.211.0222004t = 0,
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
32. (a)
(b)
(c)
33. (a) ln x
(b) lnx
34.
35. They differ by a constant
Exercise Set 5.2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. 3ex + x2 - 6x - 2
-2 ln x - 16x
2 +143 x -
19924
+ 2 ln 2
x3
6 - x2 + 3x - 19
6
x2 + 2
3x - 2 ln x + x33 +53
2x + 5 ln x + 1
3ex + 2x
+ x + 4 - 3e22ex - 4x3/2 + 2x + 2
x3
3 - x2 + 9x + 2
x2 - 3x + 7
1
a + bx
- 14 e-4x + c
-e-x + c
12e2x + c
x4 - 9ex + 8 ln x - 5x + c
2et -3t5
5 + 7 ln t - 12t + c
5 ln x - 2ex + 7x + c
2et + c
7ex + c
2 ln x + c
4 ln x + c
2t7 - 2t4 - 12
4t2 + c
- 4x
+ 73x
3 -1
2x4 + c
2223
x3/2 + c
t5
5 + 2t
3
3 + t + c
4x3
3 + 2x2 + x + c
27x4
4 + c
5
3x3 + 4
3 x3/2 - 3x + c
r4
2 + 3
r + 4r + c
- 14w
2 + c
t8
4 + c
3x1/3 + c
4
9x9/4 + c
2
5s5/2 + c
72w2/7 + c
4
7x7/4 + c
21x + c4
5t5/4 + c
3
4x4/3 + c
2
3t3/2 + c
2
3x3/2 + c
- 1
2x2 + c
M(1/3, 2e /3)-1
I(2/3, 4e /3)-2
y= 0 is H.A.
10.
11.
12.
e-x2 A 55x + 2 - 2xln12 + 5x2 B
3x212x2 +13x2 + 12ln13x2 + 1223x
2+ 1
I
m(e /2, e /8)- -1
I( e /2 ,-3e /8)-3/2 -3
13. 1.892789
14.
15.
16.
17.
18. 5,380 yrs
19. 4.89
20. (a) basic (11.42)
(b) acidic (3.54)
Exercise Set 5.1
1.
2. x4/4 + c
3x + c
12 + ln x2x1x -12
2
-4x5-2x2
ln 5
A 123x - 2 - x21x2 + 92 B A 13x - 22424 x2 + 9Bln 8 L 2.079442
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Section 5.35.5 Answers to Exercises and Pre/Post Tests 6
25.
26.
27.
28.
29.
30.
31.
32.
33.
34. when
35. (a)
(b)
(c) They differ by a constant.
36.
37. If and
38. (a)
(b)
(c) they differ by a constant
Exercise Set 5.4
1. (a) 0.5
(b) 0.2
(c) 0.02
2. (a) 0.75
(b) 0.3
(c) 0.03
3.
4.
5. 5.75
6. 7.75
7. 6.625
8. 8
9. 10
10. 11
11. (a) 3.125
(b) 3.875
(c) 3.5
12. (a) 2.25
(b) 1.75
(c) 2
13. (a) 19.21875
(b) 21.46875
(c) 20.32812514. (a) 13.953125
(b) 18.703125
(c) 16.210938
15. 10.75
53, 3.5, 4, 4.5, 5650, 0.5, 1, 1.5, 26
x - ln1ex + 12 + c2- ln11 + e-x2 + c1
am Z 0n = m - 1
625
17x17 +
250
7x14 +
150
11x11 +
5
2x8 +
x5
5 + c
1
612x + 323 + C
43x
3 + 6x2 + 9x + c
N Z -11ln x2N + 1N + 1
+ c
ln ln x + c
54x2
4 ln 5 + c
42x
2 ln 4 + c
1ln x244
+ c
1
aeax + c
1
aln ax + b + c
x2
2 - x + ln x + 1 + c
4x -1
2 ln1x2 + 12 + c
-18 A3 + 2x B4 + c 16. (a) 3.3125
(b) 3.6875
(c) 3.5
17. (a) 2.125
(b) 1.875
(c) 2
18. 19.773438
(b) 20.898438
(c) 20.332031
19. 10.6875
20. (a) 3.40625
(b) 3.59375
(c) 3.5
21. (a) 2.0625
(b) 1.9375
(c) 2
22. (a) 20.052734
(b) 20.615234
(c) 20.333008
23. (a) 0.32779589
(b) 0.31579589
(c) 0.32172789
24. (a) 20.288350
(b) 20.37835
(c) 20.333325
25. (a) 0.0833
(b) 0.0833
(c) 0.08335
26. (a) 6.3253785
(b) 6.4531596
(c) 6.3889496
27. (a) 2.5243268
(b) 2.5659156
(c) 2.5452056
28. 10
29. 3.5
30. 2
31. 20.34375
Exercise 5.5
1.
2.
3.
4. a5
i = 1
15i - 42a19
i = 1
1
2i
a
23
i = 212i + 12
a20
i = 1
1
i
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674 Section 5.55.6 Answers to Exercises and Pre/Post Tests
5. or
6.
7.
8.
9. 105
10. 32
11. 3457/840
12. 8
13. 240
14. 228
15. 8270
16. 850,745
17. 791,910
18. 292,320
19. (a) 62
(b) 2,097,150(c)
20.
21.
22. (a) 50
(b) 500
(c)
23. 81,159,640
24.
25.
26. 1
27. 1
28. 20/3
29. 75/4
30. Region bounded by and
31. Region bounded by and
32. Region bounded by and
33. Region bounded by and
34. 8
35. 2/3
36. 1/4
37. (a) 11/2
(b) 5/6
(c) 10/3
38. 14/3
39. (a) 15/4
(b) 1/4
(c)
(d) 17/4
12
x = 2y = 5x3, y = 0, x = 1
x = 1y = 6 + 2x2, y = 0, x = 0
x = 1y = 4x3, y = 0, x = 0
x = 1y = 3x2, y = 0, x = 0
-19,961,022
-358,192,305,872
n + 12
an + 1 - a1 + an - a0
an + 1 - a1
2n + 1 - 2
an
i=
1
xi
i
an
i =1ari - 1
a12
i =1
2i - 1
a5
i = 1
i
2i + 3a6
i =2
i - 1
2i + 140.
41.
44. (a)
(b)
(c)
47. Consider the interval [0, 1], with the partition
48. (a) 2/3
(b)
49. (a) 3/4
(b)
Exercise Set 5.6
1. 10
2. 20
3.
4. (a) 15/2
(b)
5. (a) 6
(b)
6.
7. 38/3
8. 195/4
9. 18
10. 11/2
11. 8/3
12. 1793/12
13. 3
14. 11/5
15. 14/3
16. 7/9
17. (a) ln 2
(b) ln 2
(c) ln 2
18. (a)
(b)
19.20.
21.
22.
23. 13/2
24. 13/3
21e2 - e2e-2 - e-4
2
e - 1
1
21ln 5 - ln 22
ln b/a
ln b/a
-2
-6
-15/2
k1b - a2
limn:qa
n
i = 1Ain B 1/31n
limn:qa
n
i = 1Ain B 1/21n
1/10 + 2 # 9/110n2, 1/10 + 3 # 9/110n2, , 1650, 1/10, 1/10 + 9/110n2,
n21n + 12212n2 + 2n - 1212
n1n + 1216n3 + 9n2 + n - 1230
an1n + 122
b2lim
n:qan
i = 1
ln A1 + in B 1nlim
n:qan
i = 1ei/n
1
n
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Section 5.6 Answers to Exercises and Pre/Post Tests 6
25. (a)
(b) 7
26. (a)
(b) 22/3
27. (a)
(b) 32/2
28. (a)
(b)
29. (a)
(b) 4 ln 3
30. (a)
(b)
31. 81/2
32.
33.
34.
35.
3 5
112x3 - 3x2 + 12dx = 192
3 3
2exdx = e3 - e2
3 2
1x2dx = 7/3
e-1 - e-2
3 2
1e-xdx
3 3
14
xdx
8 A22 - 1 B3 2
14
x1/2dx
3
2
-2 14 - x22dx
3 3
21x2 + 12dx
3 2
114x + 12dx
37.
y= 5
x=1 A x=3
36.
x= 4 A x= 9
A
38.
A
39.
A
40.
A
41.
A
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676 Section 5.65.8 Answers to Exercises and Pre/Post Tests
42.9.
10.
11. 0
12. 0
13. 6
14. 0
15. 0
16. 9
17. 0
18. 9/2
19. 956/15
20. 26/5
21. 16/3
22.
23. ln 10
24. ln 5
25.
26. (a) 0
(b) 0
27. (a)
(b)
28. (a) 1/3
(b)
29. (a)
(b) 1.52846
30. (a)
(b) 0.262997 or 1.287403
31. $6082.69
32. $1107.01
33.
34.
35.
36.
37.
39.
42.
43.
44.
Exercise Set 5.81. 9
2. 32
3. 32/3
4. 9
3x5
x6
+ 1- 2e
4x
e4x
+ 1
2x2x4 + 1f1v1x22v1x2 - f1u1x22u1x2;0.674537
a11 + x2224 - x2 - 2x3 x
024 - t2dtb
11 + x222
32x
5
x423 1 - x221 - x2
x2
1 - e-4
4
12ln 5/2
113
121a + b2m1a + b2 + 2d
2
12ln 17
1 - e-1
1
2ln1e2 + 12
1ln 2222
43.
A
44. 63/2
45. 9
46. 18
47. 9
48. 2 ln 3
49. 2 ln 3
50.
51.
52.
53. 8
54. 28/3
57. (a)
(b) 0.24535037
(c)
58. (a)
(b) 0.56226116
(c)
60.
61.
65. 0.32174914 (using )
Exercise Set 5.7
1. 1/5
2. 38/15
3. 1
4. 0
5.
6.
7. 0
8. e2 - e-2
6
12ln 5/2
-2 ln 3
n = 100
-0.517999
;0.466221
ln A A25 + 2 B A22 - 1 B B L 0.562262
ln 2
22 6 A 6 1ln13/426 + p2
318 L 0.254353
3/16 6 A 6 3/8
21e2 - e-2231e2 - 123 ln 2 + 4
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Section 5.8Chapter 5 Review Answers to Exercises and Pre/Post Tests 6
5. 9
6. 1331/750
7. 8
8. 32
9. 37/6
10. 1
11. 6
12. 9/2
13. 9
14. 27/2
15. 25.1771
16. (a) 10,000
(b) 2500
17. (a) 1260
(b) 180
18. (a) 11/3
(b) 7
19. (a) 17/3
(b) 6.59
20. (a) 16.75
(b) 21.02
21. (a) $63,138.58
(b) $77,892.69
22. (a) $93,174.11
(b) $309,348.92
23. (a) $12,969.09
(b) $23,613.00
24. (a) $152,996.22
(b) $278,777.29
25. $688,338.79
26. (b)
27. (b) 5/32
(c) 11/32
(d) 11/16
(e) 27/32 (f)
28. (b) 0.731059
(c) 0.268941
(d) 0.731059
29. (a)
(b) 19/32
30. 1.17157
31. 0
32. 0.2831133. 0
37.
38. T0 c e1j - r2t - 1
j - r d
A = T Cert - 1rD
12
12
12
40.
41.
Exercise Set 5.9
1.
2.
3. 1209/14
4.
5.
6.
7.
8.
9.
10.
11.
12.13.
14.
15.
16.
17.
18.
(b) 0.424367
(c) 0.575633
19.
(b) 0.353093
(c) 0.381282
20. 1.11537
21. 16/7
Chapter Review
1.
2. (a) 13/2
(b)
3.
4. (a) 204(b) 452
(c) 310
5. (a) 311.0592
(b) 320.9792
(c) 315.9904 exact area is 316
416 - 4
3 1
012x3 + 4x2 + 7x - 12dx
9n4 + 10n3 + 21n2 - 64n12
2 ln 2 - 3/4
e2 - 5e-2
4
e 1ln x22
2 + c if n = -1
xn + 1
n + 1 A ln x - 1n + 1 B + c if n Z -1
e2 - 5e-2
4
x2
2 A1ln x22 - xln x + 12 B + c
1
212x + 32ln12x + 32 - x + c2 ln 2 - 3/4
-1412x4 + 4x3 + 6x2 + 6x + 32e-2x + c
1
128132x3 - 24x2 + 12x - 32e4x + c
-1412x2 + 2x + 12e-2x + c
211 - 4e-329
3
412x - 12e2x + c
-40224/1105
1
10512x - 123/2115x2 + 6x + 22
22x - 11x + 42 + c2
151x + 123/213x - 22 + c
1xe - a2pe - 3 xe
aS1x2dx
3 xe
aD1x2dx -1xe - a2pe
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678 Chapter 5 ReviewSection 6.2 Answers to Exercises and Pre/Post Tests
6. 15
7. (a) 196 ft
(b)
8.
9.
10.
11.
12.
13.
14.
15.
16. (a) 0.0202
(b) 1.41683
17. 93/5
18. 32/315
19. (a) 0.8758057
(b) 4/3
20.
(b)(c) 0.836667
(d) 0.163333
21. (a) $329,226.55
(b) $1,269,966.90
22. (a) $167,957.60
(b) $557,638.86
23.
24.
Exercise Set 6.1
1. (a)
(b)2. (a) 3
(b)
3. (a) 800
(b) 5400
4. (a) 150
(b) 900
5. (a) 400
(b) 2400
6. (a) 4
(b)
7. (a) 432
(b) 800
8. (a) 143
(b)
9. (a) 3/2
(b) 2/3
-4
-2
-77
-20
-8
2x321 - x4x21 - x2
7214 -2248
45 - 327e-2
8
1ln 322 -1 ln 22221ln 3221ln 222
1
31ln 223
110
ln 4 - 2e-5u + c
3
4
A923 9 - 16
B
1
4011 + 4t223/216t2 - 12 + c
y = ; 131 - ln11 + x22
p =29 - x-112 ft/sec
(c)
10. (a) 10
(b) 10
(c)
11. (a) 0
(b) 0
(c)
12. (a)
(b)
13. 247,028
14. (a)
(b)
(c)
(d)
15. (a)
(b)
(c)
(d)
16. (a)
(b)
(c)
17.
Exercise Set 6.2
1.
(b)
2.
(b)
3.
(b)
4. (a)
(b)
5. (a)
(b)
6. (a)
(b)
7. (a)
(b)
8. (a)
(b)
9. (a)
(b)
10. (a)
(b)
11. (a)
(b) 4y12x3 - 3y42412x3 - 33y4260x2y212x3 - 3y4243x2y2e-4x
3y213 - 8x3y226xy3e-4x
3y211 - 6x3y222xe3xy13xy + 122ye3xy
13xy + 1
2
-32x2ye-2y2
16xe-2y2
12y212x2 + 3y42412x2 + 23y4280xy312x2 + 3y42424x3y1x2 + y2233x21x2 + y223111x2 + 3y22
4x2y
1x2 - y222
- 4xy2
1x2 - y222
- 4x2y
1x2 + y222
4xy2
1x2
+ y2
22
25x3y4 + 18y
9x2 - 16x3 + 15x2y5 - 7
-6y2 - 35x2y4 - 3
12x3 - 14xy5 + 16x
6y + 16x3y3 - 2
4x + 12x2y4 + 9
C1x, y, z2 = 5xy + 4xz + 4yz-4y3z + 2z
-6xy - 6y2z24x - 3y2-6 - 3x34 - 36y
-2y - 3x32x - 9x2y
2x - 9x22y - 12y32x - 9x2y22y - 6xy3
100243100
213
25 ln 2x2
10ex2 - y2 - 2yk - k2
x + hy
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680 Section 6.2 Answers to Exercises and Pre/Post Tests
36. 40.
37.
38.
39.
41.
42.
43. (3, 3)
44. (4, 4, 5)
45.
46. (a)
(b)
(c)
47. (a)
(b)
(c)
48. (a)
(b)
(c)
49. (a)
(b)
(c)
50. (a)
(b)
(c)
51. (a)
(b)(c)
52. (a)
(b)
(c) 120x2y12x3 - 3y42312x3 - 27y42412x3 - 3y42312079y8 - 432x3y4 + 4x62120x12x3 - 3y423114x3 - 3y42-64xye-2y
21-32x2
+ 128x2
y
2
2e-2y2
16e-2y2
240xy212x2 + 3y42312x2 + 19y4224y12x2 + 3y42314x4 + 192x2y4 + 759y82240y312x2 + 3y42316x2 + y42- 8xy1y2 - x22
1x2 + y223
4x213y2 - x221x2 + y223
- 4y213x2 - y221x2 + y223
-75x2y4100x3y3 + 18
18x - 48x2 + 30xy5
-70xy4-12y - 140x2y336x2 - 14y5 + 16
48x2y3
6 + 48x3y24 + 24xy4
112, - 12, -1/32
12, -22
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Section 6.26.5 Answers to Exercises and Pre/Post Tests 6
53. (a)
(