Applied Calculus Zanswers

8/13/2019 Applied Calculus Zanswers

1/84

Answers to Exercises

and Pre/Post Tests


2/84

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


3/84

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


4/84


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


5/84

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


6/84

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.


7/84


8/84


32. 36.

y

x= 12

(12, 0) x

x= 1

33.

34.

35.

37.

39.

38.


9/84


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.


10/84


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


11/84


12/84


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


13/84


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,


14/84

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


15/84


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


16/84


17/84


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


18/84


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


19/84


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


20/84


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


21/84


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


22/84


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


23/84


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


24/84


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.


25/84


49. 53.

50.

51.

52.

54.

(b) twice,x L -4.1106 and 6.2186

55.

56.


26/84


57. (a) (b)

(c) (d)

(e) (f)


27/84


(c) (d)

58. (a) (b)

(e) (f)


28/84


59. (a) (b)

(c) (d)

(e) (f)


29/84


60. (a) (b)

(c) (d)

(e) (f)


30/84


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


31/84


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


32/84


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.


33/84

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


34/84

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)


35/84


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.


36/84


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


37/84


38/84


39/84


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


40/84


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


41/84


(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,


42/84


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


43/84


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


44/84


45/84


(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


46/84

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.


47/84


48/84


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.


49/84


50/84


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


51/84


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


52/84


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


53/84


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


54/84

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


55/84

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)


56/84


(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


57/84


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)


58/84


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


59/84


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.


60/84


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


61/84


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



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


62/84


14. 19.

15.

16.

17.

18.

20.

21.

22.

23.


63/84


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


64/84


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


65/84


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


66/84


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.


67/84


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


68/84

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


69/84

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


70/84


71/84


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


72/84


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




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


73/84


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


74/84


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


75/84

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


76/84


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


77/84


78/84


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


79/84


53. (a)

(

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