A-14 INSTRUCTOR ANSWERS

Calculus and Its Applications, 2e Marvin Bittinger, David Ellenbogen, Scott Surgent, Gene Kramer

(Solutions Manual All Chapter)

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A-14 INSTRUCTOR ANSWERS

69.1-1 -1 -2 -3

-22345 678

5 4 76 3 2 1 x y g(x) = 2x - 5 x - 3

2, does not exist 70.1-1 -1

-2-3-4-5-6-723

5 4 3 2 9876 1 x y g(x) = 4x + 9 x + 2 4, does not exist

INSTRUCTOR ANSWERS: CHAPTER 1

Exercise Set 1.1, p. 112

• 0.3, xS0.3

-

• 1.7, xS1.7

+

• -3, xS-3

-

• -4.9, xS-4.9

+ 5.2 3, xS 1 2 32 - 6.4 3, xS 1 4 32 -

• 0.3, xS0.3

-

• 1.2, xS1.2

-

• 1, xS1

+

• 0, xS0

-

11. -2 12. 7 13.

limxS2 +

• limxS3
• limxS5 16. lim xS

1 2

• “the limit,

as x approaches 4, of f1x2” or “the limit of f1x2 as x approaches 4”

• “the limit, as x approaches 1, of g1x2” or “the limit of g1x2 as x

approaches 1” 19. “the limit, as x approaches 5 from the left, of F1x2” or “the limit of F1x2 as x approaches 5 from the left”

• “the limit, as x approaches 4 from the right, of G1x2” or “the

limit of G1x2 as x approaches 4 from the right” 21. (a) -3; (b) -3; (c) -3 22. (a) 1; (b) 2; (c) does not exist

• (a) -1; (b) -1; (c) -1 24. (a) 4; (b) 2; (c) does not

exist 25. 5 26. 4 27. Does not exist 28. 0 29. 2

30. 0 31. 2 32. 4 33. 1 34. 3 35. 4 36. -1

• 0 38. Does not exist 39. 0 40. 0 41. 0 42. 1
• 1 44. 1 45. 4 46. 2 47. 1 48. Does not exist
• 1 50. 1 51. -1 52. 1 53. 2 54. Does not exist
• Does not exist 56. 0 57. 0 58. 3 59. 2 60. 1

61.1-1 -1 -2 -3 -4 -5

-2-3-4-52345

5 4 3 2 1 x y f(x) = ƒxƒ 0, 2 62.f(x) = x 2 1-1 -1

-2-3-4-52345

5 4 3 2 9 8 7 6 1 x y 1, 0 77.H

12345-1-2-3-4-5

-5 -4 -3 -2 -1 1 2 3 4 5 x y does not exist, 2 78.G

24-2-4

2 4 6 8 x y 1, 9

• $3.50, $3.50, $3.50 80. $3.00, $3.50, does not exist
• $4.00, $4.50, does not exist 82. $1.00, $1.21, does not exist
• $1.21, $1.42, does not exist 84. $1.42, $1.42, $1.42
• Does not exist 86. $1.63 87. 10%, 12%, does not exist
• 12%, 12%, 12% 89. 22%, does not exist
• 10%, 10%, 10% 91. 12%, 22%, does not exist
• 22%, does not exist 93. 3 94. -3 95. -1
• (a) 0; (b) 2; (c) answers may vary.
• (a) 4; (b) 4, (c) 4; (d) 4; (e) 4; (f) no; (g) yes
• Does not exist, 2 99. 0, 0 100. Does not exist,

1 6 63.g(x) = x 2

• 5

1-1 -1 -2 -3 -4 -5

-2-3-4-52345

5 4 3 2 1 x y

-5, -4

64.1-1 -1 -2 -3 -4

-2-3-4-52345

5 4 6 3 2 1 x y g(x) = ƒxƒ + 1 4, 1 65.1-1 -5 -4 -3 -2 -1

-2-3-4-5-6-723

5 4 3 2 1 x y G(x) = 4 x + 2 4, does not exist 66.1-1 -5 -4 -3 -2 -1

-2 2345678

5 4 3 2 1 x y F(x) = 2 x - 3 does not exist, 2 67.1-1 -1 -2 -3 -4 -5 -6 -7

-2-3-4-52345

3 2 1 x y f(x) =

• - 2x

x -2, does not exist 68.1-1 -1 -2

-2-3-4-52345

5 4 6 7 8 3 2 1 x y f(x) =

• + 3x

x 3, does not exist 71.1-1 -1 -2 -3 -4 -5

-2-3-4-52345

5 4 3 2 1 x F y

3, 1, does not exist 72.1-1 -1 -2

-2-3234567

5 4 7 8 6 3 2 1 x G y 1, 3, does not exist 73.1-1 -1 -2 -3

-22345 678

5 4 76 3 2 1 x y g 1, 0, does not exist 74.

12345-1-2-3-4-5

-5 -4 -3 -2 -1 1 2 3 4 5 x y f

-1, -1, -1

75.F

12-1-2-3

-1 1 2 3 x y -1 76.G

12-1-2

-1 1 2 3 4 x y

1 2 / 4

INSTRUCTOR ANSWERS A-15

Exercise Set 1.3, p. 133

• The temperature rose 3 degrees/hr. 2. Jennifer hiked 3 mi/hr.
• Marcus delivered 7 packages/hr. 4. The population of Felton

grew by 100 people/yr. 5. Tanya scored 25 points/game.

• Chris grew 7.5 cm/yr. 7. Burnham Industries had

5,000,000 dollars/month in revenue. 8. Juan spent 2.25 dollars/gallon on gasoline. 9. Unemployment changed by -0.333 percentage point/month. 10. Shannon spent 3.1 dollars/ day on electricity for April. 11. 3 12. 5 13. 2

14. 6 15. -

1

32 16. -

3

5 17. 8 18. 8 19. 4.25

• 1.6 21. (a) 10x+5h; (b) 60, 55, 50.5, 50.05
• (a) 8x+4h; (b) 48, 44, 40.4, 40.04 23. (a) -10x-5h;

(b) -60, -55, -50.5, -50.05 24. (a) -8x-4h; (b) -48, -44, -40.4, -40.04 25. (a) 2x+h-1; (b) 11, 10, 9.1, 9.01 26. (a) 2x+h+1; (b) 13, 12, 11.1, 11.01

• (a) -

9 x1x+h2 ; (b) - 9 35 , -

3 10 , -

6 17 , -

60 167

• (a) -

2 x1x+h2 ; (b) - 2 35 , -

1 15 , -

4 51 , -

40 501

• (a) 2; (b) 2, 2, 2, 2 30. (a) -2; (b) -2, -2, -2, -2
• (a) 36x

2 +36xh+12h 2 ; (b) 1308, 1092, 918.12, 901.8012

• (a) -3x

2 -3xh-h 2 ; (b) -109, -91, -76.51, -75.1501

• (a) 2x+h-4; (b) 8, 7, 6.1, 6.01 34. (a) 2x+h-3;

(b) 9, 8, 7.1, 7.01 35. (a) 2x+h-3; (b) 9, 8, 7.1, 7.01

• (a) 2x+h+4; (b) 16, 15, 14.1, 14.01 37. 0.36 percentage

point/yr, -0.3 percentage point>yr, 0.09 percentage point/yr

• 1.7 percentage point/yr, -0.2 percentage point>yr,

0.66 percentage point/yr 39. 0.66 percentage point/yr, -0.15 percentage point>yr, 0.21 percentage point/yr

• -0.31 percentage point>yr, 0.1 percentage point/yr,

-0.08 percentage point>yr 41. 0.1 percentage point/yr, -0.04 percentage point>yr, 0.03 percentage point/yr

• -0.7 percentage point>yr, 0.46 percentage point/yr,

-0.05 percentage point>yr 43. 2.1 percentage points/yr, -4.3 percentage points>yr, -1.5 percentage points>yr

• 1 percentage point/yr, -0.43 percentage point>yr,

0.2 percentage point/yr 45. -+450>yr, $1266.67/yr, $580/yr

• $1.467 billion/yr, $0.4 billion/yr, $0.93 billion/yr
• (a) 70, 39, 29, 23; (b) answers may vary. 48. (a) 300,

180, 120, 100; (b) answers may vary. 49. (a) $26.62; (b) $31.16; (c) $4.54; (d) 0.7567, which means that prices increased by an average of about $0.76 per year 50. (a) $2391.24;

(b) $2693.71; (c) $302.47; (d) $151.24, which means the amount grew on average $151.24 per year for 2 yr 51. The average cost of production of between 300 and 305 holders is $19.75 per unit.

• The average revenue from sales of between 300 and 305 holders

is $149.40 per unit. 53. 17.62; the average rate of change in Amazon’s revenue between 2014 and 2017 was $17.62 billion per year.

• 41.35; the average rate of change in Panera Bread Co.’s income

between 2014 and 2017 was $41.35 million per year.

• (a) 1.49 hectares/g; (b) home range increases by 1.0902 hect-

ares per gram as the animal’s weight grows from 200 g to 300 g.

• (a) 50.33; the population grew by about 50 condors per year

between 2010 and 2017. (b) 42.064; the population increased by about 42 condors per year between 2007 and 2015. 57. (a) 1.25, 1.25, 0.625, 0, 0; (b) answers may vary. 58. (a) 29.4 mi/gal; (b) 0.034 gal/mi 59. (a) 256 ft; (b) 128 ft/sec

• (a) 184.05 mi, or the distance traveled from t=2

hr to t=5 hr; (b) 61.35 mi/hr 61. (a) 125 thousand people/yr; (b) answers

may vary; (c) A: 290 thousand people/year, -40 thousand people/yr,

-50 thousand people/yr, 300 thousand people/yr; Exercise Set 1.2, p. 124

• True 2. False 3. True 4. True 5. True 6. False
• False 8. True 9. 5 10. 3 11. -3 12. 7 13. 4

14. 4 15. 15 16. 10 17. 1 18. -4 19. 10

20. 6 21.

7

• 22.

3

2 23. -

13

• 24.

13

4 25. 3 26. -12

27. -6 28.

1 10 29. Does not exist 30. Does not exist 31.5

• 32.

7

• 33.

1

6 34. 3 35.

1

• 36.

1

2 37. 0

• 0 39. Does not exist 40. Does not exist 41. 3
• 27 43. Does not exist 44. Does not exist 45. 0
• 0 47. Not continuous 48. Not continuous
• Continuous 50. Not continuous 51. Not continuous
• (a) -2, -2, -2; (b) -2; (c) yes, the limit exists and equals

the function value; (d) does not exist; (e) -3; (f) no, the limit does not exist. 53. (a) -1, 2, does not exist; (b) -1; (c) no, the limit does not exist; (d) 3; (e) 3; (f) yes, the limit exists and equals the function value. 54. (a) 2; (b) 2; (c) yes, the limit exists and equals the function value; (d) 0; (e) 0; (f) yes, the limit exists and equals the function value. 55. (a) 2; (b) does not exist; (c) no, the function value does not exist; (d) -2; (e) -2; (f) yes, the limit exists and equals the function value. 56. (a) 0.25; (b) 0.25; (c) yes, the limit exists and equals the function value; (d) does not exist; (e) does not exist; (f) no, neither the limit nor t1-22 exists. 57. (a) 3; (b) 1; (c) does not exist; (d) 1; (e) no, the limit does not exist; (f) yes, the limit exists and equals the function value; (g) yes, the limit exists and equals the function value. 58. (a) 1; (b) -1; (c) does not exist; (d) 1; (e) no, the limit does not exist; (f) yes, the limit exists and equals the function value. 59. Yes, the limit exists and equals the function value at 4. 60. Yes, the limit exists and equals the function value at 5. 61. No, the limit does not exist and G is not defined at 0.

• No, F is not defined at -1. 63. Yes, the limit exists and

equals the function value at 4. 64. Yes, the limit exists and equals the function value at 3. 65. No, the limit does not exist at 3.

• No, the limit does not exist and G is not defined at 4.
• No, g is not defined at 4. 68. Yes, the limit exists and equals

the function value at 3. 69. No, the limit value does not equal the function value at 2. 70. No, the limit value does not equal the function value at 1. 71. Yes, the limit exists and equals the function value at 4. 72. Yes, the limit exists and equals the function value at 5. 73. No, the limit does not exist and the function is not defined at 5. 74. Yes, the limit exists and equals the function value at 3. 75. No, the limit does not exist and the function is not defined at 2. 76. Yes, the limit exists and equals the function value at 4. 77.Yes, because lim xSa g1x2=g1a2 for all a such that -46a64 78. Yes, because lim xSa F 1x2=F1a2 for all a such that -56a65 79. Yes, because lim xSa g1x2=g1a2 for all a such that 16a6`, and lim xS1

• g1x2=g112 80. Yes,

because lim xSa h 1x2=h1a2 for all a such that -36a6`, and lim xS -3

• h

1x2=h1-32 81. Yes, because lim xSa F1x2=F1a2 for all a such that -56a65, and lim xS -5

• F

1x2=F1-52 and lim xS5

• F

1x2=F152 82. Yes, because lim xSa G1x2=G1a2 for all a such that -36a63, and lim xS -3

• G

1x2=G1-32 and lim xS3

• G

1x2=G132 83. 30, 25, does not exist 84. 8, 6, does not exist 85. 120, 120, 120 86. Yes 87. Yes

• Yes 89. Yes 90. No 91. No 92. Yes 93. Yes
• 5 95. 2 96. (a) Does not exist; (b) -3 97. a=

19 4 , b=-3 98. c=9 99.1 2

100. 6 101.

1 2

102. -

1223 103.1 27 104.3 4

105. 0 106.

1

4 3 / 4

A-16 INSTRUCTOR ANSWERS

• (a) and (b)

f

12345-1-2-3-4-5

-10 -8 -6 -4 -2 2 4 6 8 10 x y

(-2, -8)

(1, 1)

x-axis is tangent to curve at (0, 0).(c) f91x2=3x 2 ; (d) 12, 0, 3

• (a) and (b)

f

2345-1-2-3-4-5

-10 -8 -6 -4 -2 2 4 6 8 10 x y

(-2, 8)

(1, -1)

x-axis is tangent to curve at (0, 0).(c) f91x2=-3x 2 ; (d) -12, 0, -3

• (a) and (b)

6 7 8

12345-1-2-3-4-5

-2 -1 1 2 3 4 5 x y f (c) f91x2=-2; (d) -2, -2, -2

• (a) and (b)

12345-1-2-3-4-5

-2 -1 1 2 3 4 5 6 7 8 x y f (c) f91x2=2; (d) 2, 2, 2

• (a) and (b)

12345678-1-2

-5 -4 -3 -2 -1 -6 1 2 3 4 x y f (c) f91x2= 1 2; (d) 1 2, 1 2, 1 2

• (a) and (b)

12345-1-2-3-4-5

-5 -4 -3 -2 -1 1 2 3 4 5 x y f (c) f91x2= 3 4; (d) 3 4, 3 4, 3 4

• (a) and (b)

(-2, 6)

(0, 0)

123-1-2-3

-2 -1 1 2 3 4 5 6 7 8 x y f

(1, 0)

(c) f91x2=2x-1; (d) -5, -1, 1 Exercise Set 1.4, p. 144

• (a) and (b)

f 1

(1, 1.5)

x-axis is tangent to curve at (0, 0).

(-2, 6)

2-1-2 -1 1 2 3 4 5 6 7 8 9 x y (c) f91x2=3x; (d) -6, 0, 3

• (a) and (b)

f

(-2, 2)

12-1-2

-1 1 2 3 x y )(1, 1 2 x-axis is tangent to curve at (0, 0).(c) f91x2=x; (d) -2, 0, 1

• (a) and (b)

1-1 f 2-2 -10 -8 -6 -4 -2 -18 -16 -14 -12 2 x y

(-2, -12)

(1, -3)

x-axis is tangent to curve at (0, 0).(c) f91x2=-6x; (d) 12, 0, -6

• (a) and (b)

f

12-1-2

-5 -4 -3 -2 -1 -9 -8 -7 -6 1 x y

(-2, -8)

(1, -2)

x-axis is tangent to curve at (0, 0).(c) f91x2=-4x; (d) 8, 0, -4

B: 125 thousand people/yr, 125 thousand people/yr, 125 thousand

people/yr, 125 thousand people/yr (d) answers may vary.

• -116; Payton County lost an average of 116 people per year

between the 5th and 8th years. 63. 825.46; Harbor University’s undergraduate population was increasing at the rate of 825.46 students per year between the 2nd and 6th years.

• m 65. 2ax+

b+ah 66. 3ax 2 +3axh+ah 2 +2bx+bh

• 4x

3 +6x 2 h+4xh 2 +h 3

• 5x

4 +10x 3 h+10x 2 h 2 +5xh 3 +h 4

• 5ax

4 +10ax 3 h+10ax 2 h 2 +5axh 3 +ah 4 +4bx 3

• 6bx

2 h+4bxh 2 +bh 3 70.-2x-h 1x+h2 2 x 2 71.1 11-x-h211-x2

• (a) Multiplying by 1;

(b) performing multiplication in the numerator; (c) combining like terms and simplifying; (d) when h is not 0, then h>h=1.

73.2 221x+h2+1+22x+1

74.-1 2x2x+h12x+2x+h2

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