Answers to Selected Exercises - UTEP

[Pages:52]16314_19_ans_pA18-A42.qxd 7/17/06 11:54 PM Page 18

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

1. 27 3. -36 5. 4/9 7. -1/8 9. 16 11. 2

15. 2 17. x5

19. - y x

1 21.

x

23. x3 y

z4 25. y3

x 4 y6 29. z4

3 31. x4

3 33. 4x2/3

35. 1 - 0.3x2 - 6 5x

13. 32 x6

27. y6

37. 2

39. 1/2 41. 4/3 43. 2/5 45. 7 47. 5 49. -2.668 51. 3/2 53. 2 55. 2 57. ab 59. x + 9 61. x 3 a3 + b3

63. 2y 65. 31/2 67. x3/2 69. (x y2)1/3 71. x3/2 x

73. 3 x-2

75. 3 x -1.2 - 1 x -2.1

77.

2 x

-

1 x 0.1

+

4 x -1.1

5

2

3

32

3

79. (x2 + 1)-3 - 3 (x2 + 1)-1/3

81. 3 22

83. 3 x4

4

85.

5

x3 y

87. - 3

89. 0.2 + 3 x

24 x

3 x2

7

3 91.

93. 64 95. 3 97. 1/x 99. x y

4 (1 - x)5

101. y 1/3 103. ?4 105. ?2/3 107. -1, -1/3 x

109. -2 111. 16 113. ?1 115. 33/8

Section 0.3

1. 4x2 + 6x 3. 2x y - y2 5. x2 - 2x - 3

7. 2y2 + 13y + 15 9. 4x2 - 12x + 9 11. x2 + 2 + 1/x2

13. 4x2 - 9 15. y2 - 1/y2 17. 2x3 + 6x2 + 2x - 4

19. x4 - 4x3 + 6x2 - 4x + 1 21. y5 + 4y4 + 4y3 - y

23. 27.

(x + -x3(

x1)3(+2x1+)5x)

25. +1

(x2 + 1)5(x + 3)3(x2 + x + 4) 29. (x + 2) (x + 1)3

31. a. x(2 + 3x) b. x = 0, -2/3 33. a. 2x2(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. (x2 - 1)(x2 - 4) b. x = ?1, ?2

A18

Section 0.4

2x2 - 7x - 4

3x2 - 2x + 5

1.

x2 - 1

3. x2 - 1

x2 - 1 2x - 3

(x + 1)2

7. x

9. x2 y 11. (x + 2)4

-(2x + y) 15. x2(x + y)2

x2 - x + 1 5. x + 1

-1 13.

(x2 + 1)3

Section 0.5

1. -1 3. 5 5. 13/4 7. 43/7 9. -1 11. (c - b)/a

13. x = -4, 1/2

15. No solutions

17. ?

5 2

19. -1

21. -1, 3

1? 23.

5

25. 1

27. ?1, ?3

2

29. ? -1 ? 5 31. -1, -2, -3 33. -3 35. 1

2

37. -2

39. 1, ? 5

41. ?1, ? 1

43. -2, -1, 2, 3

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. a2 + 2a + 3 f. (x + h)2 + 2(x + h) + 3 9. a. 2 b. 0 c. 65/4 d. x2 + 1/x e. (s + h)2 + 1/(s + h) f. (s + h)2 + 1/(s + h) - (s2 + 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

01

234

5

678

9 10

f(x)

5 1.1 -2.6 -6.1 -9.4 -12.5 -15.4 -18.1 -20.6 -22.9 -25

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

16314_19_ans_pA18-A42.qxd 7/17/06 11:54 PM Page 19

ANSWERS TO SELECTED EXERCISES

Answers to Selected Exercises A19

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

01 2

34

5

6

7

8

9

P(t) 200 275 350 425 500 1100 1700 2300 2900 3500

35. a. (0.08*t+0.6)*(t=8) b:

t 0 1 2 3 4 5 6 7 8 9 10 11

C(t) 0.6 0.68 0.76 0.84 0.92 1 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 + 100q2 - 500q ; N (20) = $32,000 41. a. 100*(1-12200/t^4.48) b:

t 9 10 11 12 13 14 15 16 17 18 19 20

p(t) 35.2 59.6 73.6 82.2 87.5 91.1 93.4 95.1 96.3 97.1 97.7 98.2

c. 82.2% d. 14 months 43. t; m 45. y(x) = 4x2 - 2 (or f (x) = 4x2 - 2) 47. N (t) = 200 + 10t (N = number of sound files, t = time in days) 49. As the text reminds us: to evaluate f of a quantity (such as x + h) replace x everywhere by the whole quantity x + h, getting f (x + h) = (x + h)2 - 1. 51. False: Functions with infinitely many points in their domain (such as f (x) = x2) cannot be specified numerically.

Section 1.2 1. a. 20 b. 30 c. 30 d. 20 e. 0 3. a. -1 b. 1.25 c. 0 d. 1 e. 0 5. a. (I) b. (IV) c. (V) d. (VI) e. (III) f. (II)

7.

y

9.

y

11 1 1

x

-(x^3)

11.

y

11

x

x^4 13. a. -1 b. 2 c. 2

y

1 1x

1/x^2

2 4

x 4

x*(x=0)

15. a. 1 b. 0 c. 1 y

4

17. a. 0 b. 2 c. 3 d. 3 y

1

1

x

2

24

x 1

(x^2)*(x ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download