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Deck 6: Techniques of Integration
Full screen (f)
Question
Use a table of integrals with forms involving 
to find the integral.
A) 
B) 
C) 
D) 
E) 
to find the integral.
A)
B)
C)
D)
E)
Question
Find the indefinite integral. 
.
A) 
B) 
C)
D)
E) 
. A)
B)
C)
D)
E)
Question
Find the indefinite integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use integration by parts to evaluate 
.
A) 
B) 
C)
D)
E) 
. A)
B)
C)
D)
E)
Question
Use a table of integrals to find the indefinite integral 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the indefinite integral. 
A)
B)
C)
D)
E) none of the above
A)
B)
C)
D)
E) none of the above
Question
Find the indefinite integral.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Identify u and dv for finding the integral using integration by parts. 
A) 
; 
B) 
; 
C) 
; 
D) 
; 
E) 
; 
A)
; B)
; C)
; D)
; E)
; Question
Find the integral below using an integral table.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Evaluate the definite integral 
Round your answer to three decimal places.
A) 11.381
B) 12.721
C) 3.645
D) 12.572
E) 1.538
Round your answer to three decimal places. A) 11.381
B) 12.721
C) 3.645
D) 12.572
E) 1.538
Question
Identify u and dv for finding the integral using integration by parts. 
A)
; 
B)
; 
C)
; 
D)
; 
E)
; 
A)
; B)
; C)
; D)
; E)
; Question
Use integration by parts to find the integral below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use integration by parts to evaluate 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A model for the ability M of a child to memorize,measured on a scale from 0 to 10,is 
, 
where t is the child's age in years.Find the average value predicted by the model for a child's ability to memorize between second and third birthdays.Round your answer to three decimal places.
A) 5.992
B) 4.892
C) 6.792
D) 3.992
E) 4.692
, where t is the child's age in years.Find the average value predicted by the model for a child's ability to memorize between second and third birthdays.Round your answer to three decimal places.A) 5.992
B) 4.892
C) 6.792
D) 3.992
E) 4.692
Question
Find the indefinite integral.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the definite integral. 
A)
B)
C)
D)
E) none of the above
A)
B)
C)
D)
E) none of the above
Question
Use integration by parts to find the integral below. 
,( 
, 
)
A)
B)
C)
D)
E)
,( , )
A)
B)
C)
D)
E)
Question
Find the indefinite integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Use integration by parts to evaluate 
Note that evaluation may require integration by parts more than once.
A) 
B) 
C)
D)
E) 
Note that evaluation may require integration by parts more than once. A)
B)
C)
D)
E)
Question
Approximate the definite integral "by hand," using the Trapezoidal Rule with 
trapezoids.Round answer to three decimal places. 
A) 13.716
B) 23.708
C) 11.854
D) 17.145
E) 18.966
trapezoids.Round answer to three decimal places. A) 13.716
B) 23.708
C) 11.854
D) 17.145
E) 18.966
Question
Use a table of integrals with forms involving 
to find 
A) 
B) 
C)
D) 
E) 
to find A)
B)
C)
D)
E)
Question
A body assimilates a 12-hour cold tablet at a rate modeled by 
, 
where 
is measured in milligrams per hour and t is the time in hours.Use Simpson's Rule with 
to estimate the total amount of the drug absorbed into the body during the 12 hours.
A)
mg
B)
mg
C)
mg
D)
mg
E)
mg
, where is measured in milligrams per hour and t is the time in hours.Use Simpson's Rule with to estimate the total amount of the drug absorbed into the body during the 12 hours. A)
mgB)
mgC)
mgD)
mgE)
mg Question
Decide whether the integral is proper or improper. 
A) The integral is improper.
B) The integral is proper.
A) The integral is improper.
B) The integral is proper.
Question
Use a table of integrals to find the indefinite integral 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use the Trapezoidal Rule to approximate the value of the definite integral 
, 
Round your answer to three decimal places.
A) 4.662
B) 6.764
C) 4.655
D) 2.793
E) 2.796
, Round your answer to three decimal places. A) 4.662
B) 6.764
C) 4.655
D) 2.793
E) 2.796
Question
The probability of recall in an experiment is modeled by 
, 
where x is the percent of recall.What is the probability of recalling between 50% and 80%? Round your answer to three decimal places.
A) 0.387
B) 0.221
C) 0.685
D) 0.173
E) 0.867
, where x is the percent of recall.What is the probability of recalling between 50% and 80%? Round your answer to three decimal places. A) 0.387
B) 0.221
C) 0.685
D) 0.173
E) 0.867
Question
Use Simpson's Rule to approximate the revenue for the marginal revenue function 
with 
Assume that the number of units sold,x,increases from 13 to 18.Round your answer to two decimal places.
A) 1346.14
B) 1230.4
C) 678.36
D) 1602.42
E) 1439.03
with Assume that the number of units sold,x,increases from 13 to 18.Round your answer to two decimal places. A) 1346.14
B) 1230.4
C) 678.36
D) 1602.42
E) 1439.03
Question
Determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate compounded continuously. 
, 
A) $210,000
B) $200,000
C) $220,000
D) $240,000
E) $230,000
, A) $210,000
B) $200,000
C) $220,000
D) $240,000
E) $230,000
Question
The rate of change in the number of subscribers S to a newly introduced magazine is modeled by 
, 
where t is the time in years.Use Simpson's Rule with 
to estimate the total increase in the number of subscribers during the first 6 years.
A)
subscribers
B)
subscribers
C)
subscribers
D)
subscribers
E)
subscribers
, where t is the time in years.Use Simpson's Rule with to estimate the total increase in the number of subscribers during the first 6 years. A)
subscribersB)
subscribersC)
subscribersD)
subscribersE)
subscribers Question
Use a table of integrals with forms involving 
to find 
A)
B)
C)
D)
E)
to find A)
B)
C)
D)
E)
Question
Use the table of integrals to find the average value of the growth function 
over the interval 
,where N is the size of a population and t is the time in days.Round your answer to three decimal places.
A) 1280.000
B) 3037.844
C) 1279.773
D) 2816.025
E) 2816.057
over the interval ,where N is the size of a population and t is the time in days.Round your answer to three decimal places. A) 1280.000
B) 3037.844
C) 1279.773
D) 2816.025
E) 2816.057
Question
Use a table of integrals to find the indefinite integral 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
The revenue (in dollars per year)for a new product is modeled by 
where t the time in years.Estimate the total revenue from sales of the product over its first 3 years on the market.Round your answer to nearest dollar.
A) $6,579
B) $3,291
C) $10,821
D) $15,830
E) $1,138
where t the time in years.Estimate the total revenue from sales of the product over its first 3 years on the market.Round your answer to nearest dollar. A) $6,579
B) $3,291
C) $10,821
D) $15,830
E) $1,138
Question
Use a table of integrals to find the indefinite integral 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate the definite integral 
Round your answer to three decimal places.
A) 7.499
B) 8.562
C) 5.896
D) 6.999
E) 6.236
Round your answer to three decimal places. A) 7.499
B) 8.562
C) 5.896
D) 6.999
E) 6.236
Question
Use the error formulas to find n such that the error in the approximation of the definite integral 
is less than 0.0001 using the Trapezoidal Rule.
A) 77
B) 78
C) 76
D) 74
E) 75
is less than 0.0001 using the Trapezoidal Rule. A) 77
B) 78
C) 76
D) 74
E) 75
Question
Approximate the integral using Simpson's Rule: 
, 
Round your answer to three decimal places.
A) 0.85
B) 1.017
C) 1.284
D) 1.161
E) 0.652
, Round your answer to three decimal places. A) 0.85
B) 1.017
C) 1.284
D) 1.161
E) 0.652
Question
A body assimilates a 16-hour cold tablet at a rate modeled by 
, 
where C is measured in milligrams and t is the time in hours.Use Simpson's Rule with 
to estimate the total amount of the drug absorbed into the body during the 16 hours.
A) 34.878
B) 46.878
C) 38.325
D) 54.325
E) 58.878
, where C is measured in milligrams and t is the time in hours.Use Simpson's Rule with to estimate the total amount of the drug absorbed into the body during the 16 hours.A) 34.878
B) 46.878
C) 38.325
D) 54.325
E) 58.878
Question
Evaluate the definite integral 
Round your answer to three decimal places.
A) 10.323
B) 31.66
C) 36.304
D) 23.314
E) 5.679
Round your answer to three decimal places. A) 10.323
B) 31.66
C) 36.304
D) 23.314
E) 5.679
Question
Evaluate the improper integral if it converges,or state that it diverges. 
A) 
B) 
C) 
D) 
E) diverges
A)
B)
C)
D)
E) diverges
Question
Question
Evaluate the improper integral if it converges,or state that it diverges. 
A) 
B) 1
C) 
D) 
E) diverges
A)
B) 1
C)
D)
E) diverges
Question
Find the capitalized cost C of an asset forever.The capitalized cost is given by 
where 
is the original investment,t is the time in years, 
is the annual interest rate compounded continuously,n is the total time in years over which the asset is capitalized,and 
is the annual cost of maintenance (measured in dollars).Round your answer to two decimal places.
A) $1,325,000
B) $1,075,000
C) $1,099,218.75
D) $908,333.33
E) $1,047,222.22
where is the original investment,t is the time in years, is the annual interest rate compounded continuously,n is the total time in years over which the asset is capitalized,and is the annual cost of maintenance (measured in dollars).Round your answer to two decimal places. A) $1,325,000
B) $1,075,000
C) $1,099,218.75
D) $908,333.33
E) $1,047,222.22
Question
Determine whether the improper integral diverges or converges.Evaluate the integral if it converges. 
A) converges to 0
B) converges to 5
C) converges to
D) diverges to
E) diverges to
A) converges to 0
B) converges to 5
C) converges to
D) diverges to
E) diverges to
Question
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Deck 6: Techniques of Integration
1
Use a table of integrals with forms involving to find the integral.
A)
B)
C)
D)
E)
to find the integral.
A)
B)
C)
D)
E)
2
Find the indefinite integral. .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
3
Find the indefinite integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Use integration by parts to evaluate .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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5
Use a table of integrals to find the indefinite integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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6
Find the indefinite integral.
A)
B)
C)
D)
E) none of the above
A)
B)
C)
D)
E) none of the above
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k this deck
7
Find the indefinite integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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8
Identify u and dv for finding the integral using integration by parts.
A) ;
B) ;
C) ;
D) ;
E) ;
A)
; B)
; C)
; D)
; E)
; Unlock Deck
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9
Find the integral below using an integral table.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Evaluate the definite integral Round your answer to three decimal places.
A) 11.381
B) 12.721
C) 3.645
D) 12.572
E) 1.538
Round your answer to three decimal places. A) 11.381
B) 12.721
C) 3.645
D) 12.572
E) 1.538
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11
Identify u and dv for finding the integral using integration by parts.
A) ;
B) ;
C) ;
D) ;
E) ;
A)
; B)
; C)
; D)
; E)
; Unlock Deck
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12
Use integration by parts to find the integral below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Use integration by parts to evaluate
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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14
A model for the ability M of a child to memorize,measured on a scale from 0 to 10,is , where t is the child's age in years.Find the average value predicted by the model for a child's ability to memorize between second and third birthdays.Round your answer to three decimal places.
A) 5.992
B) 4.892
C) 6.792
D) 3.992
E) 4.692
, where t is the child's age in years.Find the average value predicted by the model for a child's ability to memorize between second and third birthdays.Round your answer to three decimal places.A) 5.992
B) 4.892
C) 6.792
D) 3.992
E) 4.692
Unlock Deck
Unlock for access to all 46 flashcards in this deck.
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k this deck
15
Find the indefinite integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Find the definite integral.
A)
B)
C)
D)
E) none of the above
A)
B)
C)
D)
E) none of the above
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17
Use integration by parts to find the integral below. ,( , )
A)
B)
C)
D)
E)
,( , )
A)
B)
C)
D)
E)
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18
Find the indefinite integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
Present Value of a Continuous Stream of Income.An electronics company generates a continuous stream of 4t income of million dollars per year,where t is the number of years that the company has been in operation.Find the present value of this stream of income over the first 15 years at a continuous interest rate of 10%.Round answer to one decimal place.
A) $407.2 million
B) $176.9 million
C) $497.3 million
D) $1296.3 million
E) $324.1 million
A) $407.2 million
B) $176.9 million
C) $497.3 million
D) $1296.3 million
E) $324.1 million
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20
Use integration by parts to evaluate Note that evaluation may require integration by parts more than once.
A)
B)
C)
D)
E)
Note that evaluation may require integration by parts more than once. A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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21
Approximate the definite integral "by hand," using the Trapezoidal Rule with trapezoids.Round answer to three decimal places.
A) 13.716
B) 23.708
C) 11.854
D) 17.145
E) 18.966
trapezoids.Round answer to three decimal places. A) 13.716
B) 23.708
C) 11.854
D) 17.145
E) 18.966
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22
Use a table of integrals with forms involving to find
A)
B)
C)
D)
E)
to find A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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23
A body assimilates a 12-hour cold tablet at a rate modeled by , where is measured in milligrams per hour and t is the time in hours.Use Simpson's Rule with to estimate the total amount of the drug absorbed into the body during the 12 hours.
A) mg
B) mg
C) mg
D) mg
E) mg
, where is measured in milligrams per hour and t is the time in hours.Use Simpson's Rule with to estimate the total amount of the drug absorbed into the body during the 12 hours. A)
mgB)
mgC)
mgD)
mgE)
mg Unlock Deck
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24
Decide whether the integral is proper or improper.
A) The integral is improper.
B) The integral is proper.
A) The integral is improper.
B) The integral is proper.
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25
Use a table of integrals to find the indefinite integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
26
Use the Trapezoidal Rule to approximate the value of the definite integral , Round your answer to three decimal places.
A) 4.662
B) 6.764
C) 4.655
D) 2.793
E) 2.796
, Round your answer to three decimal places. A) 4.662
B) 6.764
C) 4.655
D) 2.793
E) 2.796
Unlock Deck
Unlock for access to all 46 flashcards in this deck.
Unlock Deck
k this deck
27
The probability of recall in an experiment is modeled by , where x is the percent of recall.What is the probability of recalling between 50% and 80%? Round your answer to three decimal places.
A) 0.387
B) 0.221
C) 0.685
D) 0.173
E) 0.867
, where x is the percent of recall.What is the probability of recalling between 50% and 80%? Round your answer to three decimal places. A) 0.387
B) 0.221
C) 0.685
D) 0.173
E) 0.867
Unlock Deck
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Unlock Deck
k this deck
28
Use Simpson's Rule to approximate the revenue for the marginal revenue function with Assume that the number of units sold,x,increases from 13 to 18.Round your answer to two decimal places.
A) 1346.14
B) 1230.4
C) 678.36
D) 1602.42
E) 1439.03
with Assume that the number of units sold,x,increases from 13 to 18.Round your answer to two decimal places. A) 1346.14
B) 1230.4
C) 678.36
D) 1602.42
E) 1439.03
Unlock Deck
Unlock for access to all 46 flashcards in this deck.
Unlock Deck
k this deck
29
Determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate compounded continuously. ,
A) $210,000
B) $200,000
C) $220,000
D) $240,000
E) $230,000
, A) $210,000
B) $200,000
C) $220,000
D) $240,000
E) $230,000
Unlock Deck
Unlock for access to all 46 flashcards in this deck.
Unlock Deck
k this deck
30
The rate of change in the number of subscribers S to a newly introduced magazine is modeled by , where t is the time in years.Use Simpson's Rule with to estimate the total increase in the number of subscribers during the first 6 years.
A) subscribers
B) subscribers
C) subscribers
D) subscribers
E) subscribers
, where t is the time in years.Use Simpson's Rule with to estimate the total increase in the number of subscribers during the first 6 years. A)
subscribersB)
subscribersC)
subscribersD)
subscribersE)
subscribers Unlock Deck
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31
Use a table of integrals with forms involving to find
A)
B)
C)
D)
E)
to find A)
B)
C)
D)
E)
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Unlock Deck
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32
Use the table of integrals to find the average value of the growth function over the interval ,where N is the size of a population and t is the time in days.Round your answer to three decimal places.
A) 1280.000
B) 3037.844
C) 1279.773
D) 2816.025
E) 2816.057
over the interval ,where N is the size of a population and t is the time in days.Round your answer to three decimal places. A) 1280.000
B) 3037.844
C) 1279.773
D) 2816.025
E) 2816.057
Unlock Deck
Unlock for access to all 46 flashcards in this deck.
Unlock Deck
k this deck
33
Use a table of integrals to find the indefinite integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
34
The revenue (in dollars per year)for a new product is modeled by where t the time in years.Estimate the total revenue from sales of the product over its first 3 years on the market.Round your answer to nearest dollar.
A) $6,579
B) $3,291
C) $10,821
D) $15,830
E) $1,138
where t the time in years.Estimate the total revenue from sales of the product over its first 3 years on the market.Round your answer to nearest dollar. A) $6,579
B) $3,291
C) $10,821
D) $15,830
E) $1,138
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Unlock Deck
k this deck
35
Use a table of integrals to find the indefinite integral
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
36
Evaluate the definite integral Round your answer to three decimal places.
A) 7.499
B) 8.562
C) 5.896
D) 6.999
E) 6.236
Round your answer to three decimal places. A) 7.499
B) 8.562
C) 5.896
D) 6.999
E) 6.236
Unlock Deck
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Unlock Deck
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37
Use the error formulas to find n such that the error in the approximation of the definite integral is less than 0.0001 using the Trapezoidal Rule.
A) 77
B) 78
C) 76
D) 74
E) 75
is less than 0.0001 using the Trapezoidal Rule. A) 77
B) 78
C) 76
D) 74
E) 75
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38
Approximate the integral using Simpson's Rule: , Round your answer to three decimal places.
A) 0.85
B) 1.017
C) 1.284
D) 1.161
E) 0.652
, Round your answer to three decimal places. A) 0.85
B) 1.017
C) 1.284
D) 1.161
E) 0.652
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39
A body assimilates a 16-hour cold tablet at a rate modeled by , where C is measured in milligrams and t is the time in hours.Use Simpson's Rule with to estimate the total amount of the drug absorbed into the body during the 16 hours.
A) 34.878
B) 46.878
C) 38.325
D) 54.325
E) 58.878
, where C is measured in milligrams and t is the time in hours.Use Simpson's Rule with to estimate the total amount of the drug absorbed into the body during the 16 hours.A) 34.878
B) 46.878
C) 38.325
D) 54.325
E) 58.878
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40
Evaluate the definite integral Round your answer to three decimal places.
A) 10.323
B) 31.66
C) 36.304
D) 23.314
E) 5.679
Round your answer to three decimal places. A) 10.323
B) 31.66
C) 36.304
D) 23.314
E) 5.679
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41
Evaluate the improper integral if it converges,or state that it diverges.
A)
B)
C)
D)
E) diverges
A)
B)
C)
D)
E) diverges
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42
Suppose the mean height of American women between the ages of 30 and 39 is 64.5 inches,and the standard deviation is 2.7 inches.Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 feet 4 inches and 6 feet tall.
A) 0.5734
B) 0.5707
C) 0.8547
D) 0.9522
E) 0.4257
A) 0.5734
B) 0.5707
C) 0.8547
D) 0.9522
E) 0.4257
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43
Evaluate the improper integral if it converges,or state that it diverges.
A)
B) 1
C)
D)
E) diverges
A)
B) 1
C)
D)
E) diverges
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44
Find the capitalized cost C of an asset forever.The capitalized cost is given by where is the original investment,t is the time in years, is the annual interest rate compounded continuously,n is the total time in years over which the asset is capitalized,and is the annual cost of maintenance (measured in dollars).Round your answer to two decimal places.
A) $1,325,000
B) $1,075,000
C) $1,099,218.75
D) $908,333.33
E) $1,047,222.22
where is the original investment,t is the time in years, is the annual interest rate compounded continuously,n is the total time in years over which the asset is capitalized,and is the annual cost of maintenance (measured in dollars).Round your answer to two decimal places. A) $1,325,000
B) $1,075,000
C) $1,099,218.75
D) $908,333.33
E) $1,047,222.22
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45
Determine whether the improper integral diverges or converges.Evaluate the integral if it converges.
A) converges to 0
B) converges to 5
C) converges to
D) diverges to
E) diverges to
A) converges to 0
B) converges to 5
C) converges to
D) diverges to
E) diverges to
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46
A business is expected to yield a continuous flow of profit at the rate of $200,000 per year.If money will earn interest at the nominal rate of 2% per year compounded continuously,what is the present value of the business forever?
A) $10,100,000
B) $1,000,000
C) $10,000,000
D) $10,010,000
E) $1,100,000
A) $10,100,000
B) $1,000,000
C) $10,000,000
D) $10,010,000
E) $1,100,000
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