Idea Transcript
16314_19_ans_pA18-A42.qxd
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Answers to Selected Exercises Chapter 0 Section 0.1 1. −48 3. 2/3 5. −1 7. 9 9. 1 11. 33 13. 14 15. 5/18 17. 13.31 19. 6 21. 43/16 23. 0 25. 3*(2-5) 27. 3/(2-5) 29. (3-1)/(8+6) 31. 3-(4+7)/8 33. 2/(3+x)-x*y^2 35. 3.1x^3-4x^(-2)-60/(x^2-1) 37. (2/3)/5 39. 3^(4-5)*6 41. 3*(1+4/100)^(-3) 43. 3^(2*x-1)+4^x-1 45. 2^(2x^2-x+1) 47. 4*e^(-2*x)/(2-3e^(-2*x)) or 4*(e^(-2*x))/ (2-3e^(-2*x)) 49. 3(1-(-1/2)^2)^2+1
Section 0.2 5. 4/9 7. −1/8 9. 16 11. 2 13. 32 x6 z4 1 y 21. 15. 2 17. x 5 19. − 23. x 3 y 25. 3 27. 6 y y x x x 4 y6 3 3 6 2 29. 31. 4 33. 35. 1 − 0.3x − 37. 2 z4 x 4x 2/3 5x 39. 1/2 41. 4/3 43. 2/5 45. 7 47. 5 49. −2.668 √ 3 51. 3/2 53. 2 55. 2 57. ab 59. x + 9 61. x a 3 + b3 2y 65. 31/2 67. x 3/2 69. (x y 2 ) 1/3 71. x 3/2 63. √ x 3 3 2 1 4 1 73. x −2 75. x −1.2 − x −2.1 77. x − x 0.1 + x −1.1 5 2 3 3 2 3 √ √ 3 2 3 3 2 −3 −1/3 2 4 79. (x + 1) − (x + 1) 81. 2 83. x 4 √ √ 0.2 3 x 3 √ + √ 89. 85. 5 x 3 y 87. − √ 3 7 24 x x2 √ 3 93. 64 95. 3 97. 1/x 99. x y 91. 4 (1 − x) 5 y 1/3 103. ±4 105. ±2/3 107. −1, −1/3 101. x 109. −2 111. 16 113. ±1 115. 33/8 1. 27
3. −36
Section 0.3 1. 4x 2 + 6x 3. 2x y − y 2 5. x 2 − 2x − 3 7. 2y 2 + 13y + 15 9. 4x 2 − 12x + 9 11. x 2 + 2 + 1/x 2 13. 4x 2 − 9 15. y 2 − 1/y 2 17. 2x 3 + 6x 2 + 2x − 4 19. x 4 − 4x 3 + 6x 2 − 4x + 1 21. y 5 + 4y 4 + 4y 3 − y 23. (x + 1)(2x + 5) 25. (x 2 + 1) 5 (x + 3) 3 (x 2 + x + 4) √ 27. −x 3 (x 3 + 1) x + 1 29. (x + 2) (x + 1) 3 31. a. x(2 + 3x) b. x = 0, −2/3 33. a. 2x 2 (3x − 1) b. x = 0, 1/3 35. a. (x − 1)(x − 7) b. x = 1, 7 37. a. (x − 3)(x + 4) b. x = 3, −4 39. a. (2x + 1)(x − 2) b. x = −1/2, 2 41. a. (2x + 3)(3x + 2) b. x = −3/2, −2/3 43. a. (3x − 2)(4x + 3) b. x = 2/3, −3/4 45. a. (x + 2y) 2 b. x = −2y 47. a. (x 2 − 1)(x 2 − 4) b. x = ±1, ±2 A18
Section 0.4 2x 2 − 7x − 4 3x 2 − 2x + 5 3. 2 x −1 x2 − 1 x2 − 1 (x + 1) 2 2x − 3 7. 11. 9. 2 x (x + 2) 4 x y −(2x + y) 15. 2 x (x + y) 2 1.
x2 − x + 1 x +1 −1 13. (x 2 + 1) 3 5.
Section 0.5 1. −1
5. 13/4
3. 5
9. −1
11. (c − b)/a 5 19. −1 17. ± 2
7. 43/7
13. x = −4, 1/2
15. No solutions √ 1± 5 21. −1, 3 23. 25. 1 27. ±1, ±3 2 √ −1 ± 5 31. −1, −2, −3 33. −3 35. 1 29. ± 2 √ 1 43. −2, −1, 2, 3 37. −2 39. 1, ± 5 41. ±1, ± √ 2
Section 0.6 √
1. 0, 3 3. ± 2 5. −1, −5/2 7. −3 9. 0, −1, 1 11. x = −1 (x = √−2 is not a solution.) 13. −2, −3/2, −1 15. −1 17. ± 4 2 19. ±1 21. ±3 23. 2/3 25. −4, −1/4
Chapter 1 Section 1.1 1. a. 2 b. 0.5 3. a. −1.5 b. 8 c. −8 5. a. −7 b. −3 c. 1 d. 4y − 3 e. 4(a + b) − 3 7. a. 3 b. 6 c. 2 d. 6 e. a 2 + 2a + 3 f. (x + h) 2 + 2(x + h) + 3 9. a. 2 b. 0 c. 65/4 d. x 2 + 1/x e. (s + h) 2 + 1/(s + h) f. (s + h) 2 + 1/(s + h) − (s 2 + 1/s) 11. a. 1 b. 1 c. 0 d. 27 13. a. Yes; f (4) = 63/16 b. Not defined c. Not defined 15. a. Not defined b. Not defined c. Yes, f (−10) = 0 17. a. h(2x + h) b. 2x + h 19. a. −h(2x + h) b. −(2x + h) 21. 0.1*x^2-4*x+5 x
0
1
f(x)
5
1.1 -2.6 -6.1 -9.4 -12.5 -15.4 -18.1 -20.6 -22.9 -25
2
3
4
5
6
7
8
9
10
23. (x^2-1)/(x^2+1) x
0.5
1.5
2.5
3.5
4.5
5.5
6.5
7.5
8.5
9.5
10.5
h(x) -0.6000 0.3846 0.7241 0.8491 0.9059 0.9360 0.9538 0.9651 0.9727 0.9781 0.9820
25. a. P(5) = 117, P(10) = 132, and P(9.5) ≈ 131. Approximately 117 million people were employed in the U.S. on July 1, 1995, 132 million people on July 1, 2000, and 131 million people
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Answers to Selected Exercises
on January 1, 2000. b. [5, 11]. 27. a. [0, 10]. t ≥ 0 is not an appropriate domain because it would predict U.S. trade with China into the indefinite future with no basis. b. $280 billion; U.S. trade with China in 2004 was valued at approximately $280 billion. 29. a. (2) b. $36.8 billion 31. a. 358,600 b. 361,200 c. $6.00 33. a. P(0) = 200: At the start of 1995, the processor speed was 200 megahertz. P(4) = 500: At the start of 1999, the processor speed was 500 megahertz. P(5) = 1100: At the start of 2000, the processor speed was 1100 megahertz. b. Midway through 2001 c: t
0
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9
P(t)
200
275
350
425
500
1100
1700
2300
2900
3500
35. a. (0.08*t+0.6)*(t=8) b: t C(t)
0
1
2
3
4
0.6 0.68 0.76 0.84 0.92
5
6
1
7
8
9
10
11
1.08 1.16 1.24 1.595 1.95 2.305
37. T (26,000) = $730 + 0.15(26,000 − 7300) = $3535; T (65,000) = $4090 + 0.25(65,000 − 29,700) = $12,915 39. a. $12,000 b. N (q) = 2000 + 100q 2 − 500q ; N (20) = $32,000 41. a. 100*(1-12200/t^4.48) b: t p(t)
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15. a. 1 b. 0 c. 1
1 1
2
4
1
x
(x^2)*(x