تكلم مع الذكاء الاصطناعي
Deck 10: Series and Taylor Polynomials
ملء الشاشة (f)
سؤال
Find the limit of the following sequence. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
Find the limit of the sequence 
A)
B) 1
C) 0
D)
E) The limit does not exist.
A)
B) 1
C) 0
D)
E) The limit does not exist.
سؤال
Write the first five terms of the sequence. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
سؤال
سؤال
Find the limit of the following sequence. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
Write an expression for the nth term of the sequence 
, 
, 
, 
,....
A) 
B) 
C) 
D) 
E)
, , , ,.... A)
B)
C)
D)
E)
سؤال
Give an example of a sequence that converges to 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
سؤال
Find the limit of the following sequence. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
سؤال
Find the limit of the following sequence. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
Write an expression for the nth term of the sequence 4,24,124,624,....
A) 
B) 
C) 
D) 
E)
A)
B)
C)
D)
E)
سؤال
Find the limit of the following sequence. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
Find the limit of the following sequence. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
Write an expression for the nth term of the sequence 
, 
, 
, 
,....
A) 
B) 
C) 
D) 
E)
, , , ,.... A)
B)
C)
D)
E)
سؤال
Write the first five terms of the sequence. 
A) 
B) 
C) 
D) 
E) none of the above
A)
B)
C)
D)
E) none of the above
سؤال
Determine the convergence or divergence of the sequence 
If the sequence converges,use a symbolic algebra utility to find its limit.
A)
B)
C)
D)
E) The sequence diverges.
If the sequence converges,use a symbolic algebra utility to find its limit. A)
B)
C)
D)
E) The sequence diverges.
سؤال
Find the limit of the following sequence. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
Find the limit of the following sequence. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
Find the limit of the following sequence. 
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
سؤال
Consider the sequence 
whose nth term is given by 
where P is the principal, 
is the amount of compound interest after n months,and r is the annual percentage rate.Write the first four terms of the sequence for 
and 
Round your answer to two decimal places.
A) 9,563.33, 9,637.22, 9,716.38, 9,755.88
B) 9,564.34, 9,637.22, 9,716.38, 9,789.25
C) 9,563.33, 9,627.09, 9,691.27, 9,755.88
D) 9,564.34, 9,637.22, 9,691.27, 9,755.88
E) 9,564.34,9,627.09,9,691.27,9,789.25
whose nth term is given by where P is the principal, is the amount of compound interest after n months,and r is the annual percentage rate.Write the first four terms of the sequence for and Round your answer to two decimal places. A) 9,563.33, 9,637.22, 9,716.38, 9,755.88
B) 9,564.34, 9,637.22, 9,716.38, 9,789.25
C) 9,563.33, 9,627.09, 9,691.27, 9,755.88
D) 9,564.34, 9,637.22, 9,691.27, 9,755.88
E) 9,564.34,9,627.09,9,691.27,9,789.25
سؤال
Determine the convergence or divergence of the series 
Use a symbolic algebra utility to verify your result.
A) The series diverges.
B) The series converges.
Use a symbolic algebra utility to verify your result. A) The series diverges.
B) The series converges.
سؤال
Determine the convergence or divergence of the p-series 
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
سؤال
A ball is dropped from a height of 14 feet,and on each rebound it rises to 
its preceding height.Write an expression for the height of the nth rebound.
A)
B)
C)
D)
E)
its preceding height.Write an expression for the height of the nth rebound.A)
B)
C)
D)
E)
سؤال
The annual spending by tourists in a resort city is 900 million dollars.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the resort city.If this pattern continues,write the geometric series that gives the total amount of spending generated by the 900 million dollars (including the initial outlay of 900 million dollars)and find the sum of the series.
A) The geometric series is
The sum of the series is $3600 million.
B) The geometric series is
The sum of the series is $67,500 million.
C) The geometric series is
The sum of the series is 3600 million.
D) The geometric series is
The sum of the series is $67,500 million.
E) The geometric series is
The sum of the series is $675 million.
A) The geometric series is
The sum of the series is $3600 million.B) The geometric series is
The sum of the series is $67,500 million.C) The geometric series is
The sum of the series is 3600 million.D) The geometric series is
The sum of the series is $67,500 million.E) The geometric series is
The sum of the series is $675 million. سؤال
Write the first five terms of the sequence of partial sums. 
A) 5 ,
, 
, 
, 
B) 5 ,
, 
, 
, 
C) 5 ,
, 
, 
, 
D) 5 ,
, 
, 321 , 
E) 5 ,
, 
, 
, 
A) 5 ,
, , , B) 5 ,
, , , C) 5 ,
, , , D) 5 ,
, , 321 , E) 5 ,
, , , سؤال
Determine the convergence or divergence of the following series 
Use a symbolic algebra utility to verify your result.
A) The series diverges.
B) The series converges.
Use a symbolic algebra utility to verify your result. A) The series diverges.
B) The series converges.
سؤال
Determine the convergence or divergence of the p-series 
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
سؤال
سؤال
Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] ![<strong>Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB1301/11ea8970_6ab4_8829_861b_bfe61db953a0_TB1301_11.jpg)
A) ![<strong>Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB1301/11ea8970_6ab4_882a_861b_75059c35e382_TB1301_11.jpg)
B) ![<strong>Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB1301/11ea8970_6ab4_882b_861b_75ca3cc57437_TB1301_11.jpg)
C) ![<strong>Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB1301/11ea8970_6ab4_af3c_861b_f7baeb8d1c3d_TB1301_11.jpg)
D)![<strong>Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB1301/11ea8970_6ab4_af3d_861b_6903e25bbe65_TB1301_11.jpg)
E) ![<strong>Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.] </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB1301/11ea8970_6ab4_af3e_861b_b786b725d2c5_TB1301_11.jpg)
A)
B)
C)
D)
E)
سؤال
Determine the convergence or divergence of the series 
Use a symbolic algebra utility to verify your result.
A) The series converges.
B) The series diverges.
Use a symbolic algebra utility to verify your result. A) The series converges.
B) The series diverges.
سؤال
Determine whether the series 
is a p-series.
A) 
is not a p-series.
B) 
is a p-series.
is a p-series. A)
is not a p-series.B)
is a p-series. سؤال
Determine the convergence or divergence of the series 
Use a symbolic algebra utility to verify your result.
A) The series diverges.
B) The series converges.
Use a symbolic algebra utility to verify your result. A) The series diverges.
B) The series converges.
سؤال
Find the sum of the convergent series.
A) 16
B) 8
C) 12
D) 4
E) 3
A) 16
B) 8
C) 12
D) 4
E) 3
سؤال
The repeating decimal 
is expressed as a geometric series 
Write the decimal 
as the ratio of two integers.
A) 
B) 
C) 
D)
E) 
is expressed as a geometric series Write the decimal as the ratio of two integers. A)
B)
C)
D)
E)
سؤال
Find the sum of the convergent series.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
سؤال
A deposit of $800 is made each month in an account that earns 8.4% interest,compounded monthly.The balance in the account after n months is given by 
Find the balance after 20 years by computing the 240th term of the sequence.Round your answer to two decimal places.
A) $696,946.54
B) $1,018,546.54
C) $24,073.84
D) $343,954.07
E) $1,125.60
Find the balance after 20 years by computing the 240th term of the sequence.Round your answer to two decimal places. A) $696,946.54
B) $1,018,546.54
C) $24,073.84
D) $343,954.07
E) $1,125.60
سؤال
A company produces a new product for which it estimates the annual sales to be 5000 units.Suppose that in any given year 10% of the units (regardless of age)will become inoperative.How many units will be in use after n years?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
سؤال
سؤال
Determine the convergence or divergence of the series 
Use a symbolic algebra utility to verify your result.
A) The series converges.
B) The series diverges.
Use a symbolic algebra utility to verify your result. A) The series converges.
B) The series diverges.
سؤال
Find the radius of convergence of the power series. 
A) -8
B) 1
C) 8
D) -1
E) 0
A) -8
B) 1
C) 8
D) -1
E) 0
سؤال
Determine the convergence or divergence of the p-series 
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
سؤال
Determine the convergence or divergence of the following series. 
A) diverges
B) converges
A) diverges
B) converges
سؤال
Find the radius of convergence of the series 
A) 16
B) 18
C) 1
D) 9
E) 8
A) 16
B) 18
C) 1
D) 9
E) 8
سؤال
Determine the convergence or divergence of the following series. 
A) diverges
B) converges
C) inconclusive
A) diverges
B) converges
C) inconclusive
سؤال
Use the Ratio Test to determine the convergence or divergence of the series. 
A) Diverges.
B) Converges.
C) Ratio Test is inconclusive.
A) Diverges.
B) Converges.
C) Ratio Test is inconclusive.
سؤال
Determine the convergence or divergence of the following series. 
A) converges
B) diverges
A) converges
B) diverges
سؤال
Write the first five terms of the power series 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
سؤال
Determine the convergence or divergence of the p-series 
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
سؤال
Determine the convergence or divergence of the following series. 
A) inconclusive
B) converges
C) diverges
A) inconclusive
B) converges
C) diverges
سؤال
Test the series 
for convergence for using any appropriate test.
A) converges
B) diverges
for convergence for using any appropriate test. A) converges
B) diverges
سؤال
Find the radius of convergence of the series 
A) 10
B) 2
C) 4
D) 13
E) 9
A) 10
B) 2
C) 4
D) 13
E) 9
سؤال
Find the radius of convergence of the power series.
A) 0
B) 10
C) 20
D) 100
E) 
A) 0
B) 10
C) 20
D) 100
E)
سؤال
Approximate the sum of the convergent series 
using four terms.Estimate the maximum error of your approximation.Round your answer to four decimal places.
A) The approximate value is 1.0286.
The maximum error of your approximation is 0.0084.
B) The approximate value is 1.0788.
The maximum error of your approximation is 0.0052.
C) The approximate value is 1.0108.
The maximum error of your approximation is 0.0217.
D) The approximate value is 2.0023.
The maximum error of your approximation is 1.0023.
E) The approximate value is 1.0812.
The maximum error of your approximation is 0.0069.
using four terms.Estimate the maximum error of your approximation.Round your answer to four decimal places.
A) The approximate value is 1.0286.
The maximum error of your approximation is 0.0084.
B) The approximate value is 1.0788.
The maximum error of your approximation is 0.0052.
C) The approximate value is 1.0108.
The maximum error of your approximation is 0.0217.
D) The approximate value is 2.0023.
The maximum error of your approximation is 1.0023.
E) The approximate value is 1.0812.
The maximum error of your approximation is 0.0069.
سؤال
Determine the convergence or divergence of the following series. 
A) diverges
B) converges
A) diverges
B) converges
سؤال
Use the Ratio Test to determine the convergence or divergence of the series. 
A) Diverges.
B) Converges.
C) Ratio Test is inconclusive.
A) Diverges.
B) Converges.
C) Ratio Test is inconclusive.
سؤال
Determine the convergence or divergence of the p-series 
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
سؤال
Determine the convergence or divergence of the following series. 
A) converges
B) diverges
A) converges
B) diverges
سؤال
Test the series 
for convergence or divergence using any appropriate test.
A) diverges
B) converges
for convergence or divergence using any appropriate test. A) diverges
B) converges
سؤال
Use the Ratio Test to determine the convergence or divergence of the series. 
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
سؤال
Find the third Taylor polynomial at 
for the given function.
A) 
B) 
C) 
D) 
E) 
for the given function.
A)
B)
C)
D)
E)
سؤال
Find the radius of convergence centered at 
for the following function. 
A) 4
B) 2
C) 0
D) 1
E) 
for the following function. A) 4
B) 2
C) 0
D) 1
E)
سؤال
Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4.
A) 
, 
, 
, 
B) 
, 
, 
, 
C) 
, 
, 
, 
D) 
, 
, 
, 
E) 
, 
, 
, 
A)
, , , B)
, , , C)
, , , D)
, , , E)
, , , سؤال
Find the radius of convergence of the series 
A) 1
B) 2
C) 3
D) 7
E) 9
A) 1
B) 2
C) 3
D) 7
E) 9
سؤال
Find the third degree Taylor polynomial centered at 
for the function.
A) 
B) 
C) 
D) 
E) 
for the function.
A)
B)
C)
D)
E)
سؤال
A Taylor polynomial approximation of 
is given below.Use a graphing utility to graph both functions. 
A) 
B) 
C) 
D) 
E) 
is given below.Use a graphing utility to graph both functions. A)
B)
C)
D)
E)
سؤال
Differentiate the series for 
to find the power series for the function 
A) 
B) 
C) 
D) 
E) 
to find the power series for the function A)
B)
C)
D)
E)
سؤال
Apply Taylor's Theorem to find the power series centered at 
for the function 
A) 
B) 
C) 
D) 
E) 
for the function A)
B)
C)
D)
E)
سؤال
A Taylor polynomial approximation of 
is given below.Use a graphing utility to graph both functions. 
A) 
B) 
C) 
D) 
E) 
is given below.Use a graphing utility to graph both functions. A)
B)
C)
D)
E)
سؤال
Find the power series for the function 
using the power series for 
A) 
B) 
C) 
D) 
E) 
using the power series for A)
B)
C)
D)
E)
سؤال
Find the radius of convergence centered at 
for the following function. 
A) 4
B) 2
C) 0
D) 1
E) 
for the following function. A) 4
B) 2
C) 0
D) 1
E)
سؤال
Use a symbolic differentiation utility to find the Taylor polynomials (centred at zero)of degrees (a)2,(b)4,(c)6,(d)8. 
A) 
, 
, 
, 
B) 
, 
, 
, 
C) 
, 
, 
, 
D) 
, 
, 
, 
E) 
, 
, 
, 
A)
, , , B)
, , , C)
, , , D)
, , , E)
, , , سؤال
Find the radius of convergence centered at 
for the following function. 
A) 4
B) 2
C) 0
D) 1
E) 
for the following function. A) 4
B) 2
C) 0
D) 1
E)
سؤال
Find the radius of convergence of 
where 
A) 1
B) ∞
C) 
D) 8
E) 16
where A) 1
B) ∞
C)
D) 8
E) 16
سؤال
Find the radius of convergence centered at 
for the following function. 
A) 4
B) 2
C) 0
D) 1
E) 
for the following function. A) 4
B) 2
C) 0
D) 1
E)
سؤال
Apply Taylor's Theorem to find the power series centered at 
for the function 
A) 
B) 
C) 
D) 
E) 
for the function A)
B)
C)
D)
E)
سؤال
Integrate the series for 
to find the power series for the function 
A)
B)
C)
D)
E)
to find the power series for the function A)
B)
C)
D)
E)
سؤال
Find the power series for the function 
using the power series for 
A) 
B) 
C) 
D) 
E) 
using the power series for A)
B)
C)
D)
E)
سؤال
A Taylor polynomial approximation of 
is given below.Use a graphing utility to graph both functions. 
A) 
B) 
C) 
D) 
E) 
is given below.Use a graphing utility to graph both functions. A)
B)
C)
D)
E)
سؤال
A Taylor polynomial approximation of 
is given below.Use a graphing utility to graph both functions. 
A) 
B) 
C) 
D) 
E) 
is given below.Use a graphing utility to graph both functions. A)
B)
C)
D)
E)
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ملء الشاشة (f)
Deck 10: Series and Taylor Polynomials
1
Find the limit of the following sequence.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
2
Find the limit of the sequence
A)
B) 1
C) 0
D)
E) The limit does not exist.
A)
B) 1
C) 0
D)
E) The limit does not exist.
0
3
Write the first five terms of the sequence.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Find the next three terms of the geometric sequence 8,40,200,....
A) 232, 264, 296
B) 1,000, 5,000, 25,000
C) 360, 520, 680
D) 205, 210, 215
E) 200,1,000,5,000
A) 232, 264, 296
B) 1,000, 5,000, 25,000
C) 360, 520, 680
D) 205, 210, 215
E) 200,1,000,5,000
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5
Find the limit of the following sequence.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
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6
Write an expression for the nth term of the sequence , , , ,....
A)
B)
C)
D)
E)
, , , ,.... A)
B)
C)
D)
E)
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7
Give an example of a sequence that converges to
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
Find the limit of the following sequence.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
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9
What are the next three terms in the arithmetic sequence -2,-6,-10,....
A) -14, -18, -22
B) 2, 6, 10
C) 56, -224, 896
D) -8, -10, -12
E) -10,-14,-18
A) -14, -18, -22
B) 2, 6, 10
C) 56, -224, 896
D) -8, -10, -12
E) -10,-14,-18
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10
Find the limit of the following sequence.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
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11
Write an expression for the nth term of the sequence 4,24,124,624,....
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Find the limit of the following sequence.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
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13
Find the limit of the following sequence.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
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14
Write an expression for the nth term of the sequence , , , ,....
A)
B)
C)
D)
E)
, , , ,.... A)
B)
C)
D)
E)
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15
Write the first five terms of the sequence.
A)
B)
C)
D)
E) none of the above
A)
B)
C)
D)
E) none of the above
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16
Determine the convergence or divergence of the sequence If the sequence converges,use a symbolic algebra utility to find its limit.
A)
B)
C)
D)
E) The sequence diverges.
If the sequence converges,use a symbolic algebra utility to find its limit. A)
B)
C)
D)
E) The sequence diverges.
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17
Find the limit of the following sequence.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
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18
Find the limit of the following sequence.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
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19
Find the limit of the following sequence.
A)
B)
C)
D)
E) The limit does not exist.
A)
B)
C)
D)
E) The limit does not exist.
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20
Consider the sequence whose nth term is given by where P is the principal, is the amount of compound interest after n months,and r is the annual percentage rate.Write the first four terms of the sequence for and Round your answer to two decimal places.
A) 9,563.33, 9,637.22, 9,716.38, 9,755.88
B) 9,564.34, 9,637.22, 9,716.38, 9,789.25
C) 9,563.33, 9,627.09, 9,691.27, 9,755.88
D) 9,564.34, 9,637.22, 9,691.27, 9,755.88
E) 9,564.34,9,627.09,9,691.27,9,789.25
whose nth term is given by where P is the principal, is the amount of compound interest after n months,and r is the annual percentage rate.Write the first four terms of the sequence for and Round your answer to two decimal places. A) 9,563.33, 9,637.22, 9,716.38, 9,755.88
B) 9,564.34, 9,637.22, 9,716.38, 9,789.25
C) 9,563.33, 9,627.09, 9,691.27, 9,755.88
D) 9,564.34, 9,637.22, 9,691.27, 9,755.88
E) 9,564.34,9,627.09,9,691.27,9,789.25
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21
Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.
A) The series diverges.
B) The series converges.
Use a symbolic algebra utility to verify your result. A) The series diverges.
B) The series converges.
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22
Determine the convergence or divergence of the p-series
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
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23
A ball is dropped from a height of 14 feet,and on each rebound it rises to its preceding height.Write an expression for the height of the nth rebound.
A)
B)
C)
D)
E)
its preceding height.Write an expression for the height of the nth rebound.A)
B)
C)
D)
E)
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24
The annual spending by tourists in a resort city is 900 million dollars.Approximately 75% of that revenue is again spent in the resort city,and of that amount approximately 75% is again spent in the resort city.If this pattern continues,write the geometric series that gives the total amount of spending generated by the 900 million dollars (including the initial outlay of 900 million dollars)and find the sum of the series.
A) The geometric series is The sum of the series is $3600 million.
B) The geometric series is The sum of the series is $67,500 million.
C) The geometric series is The sum of the series is 3600 million.
D) The geometric series is The sum of the series is $67,500 million.
E) The geometric series is The sum of the series is $675 million.
A) The geometric series is
The sum of the series is $3600 million.B) The geometric series is
The sum of the series is $67,500 million.C) The geometric series is
The sum of the series is 3600 million.D) The geometric series is
The sum of the series is $67,500 million.E) The geometric series is
The sum of the series is $675 million. فتح الحزمة
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25
Write the first five terms of the sequence of partial sums.
A) 5 , , , ,
B) 5 , , , ,
C) 5 , , , ,
D) 5 , , , 321 ,
E) 5 , , , ,
A) 5 ,
, , , B) 5 ,
, , , C) 5 ,
, , , D) 5 ,
, , 321 , E) 5 ,
, , , فتح الحزمة
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26
Determine the convergence or divergence of the following series Use a symbolic algebra utility to verify your result.
A) The series diverges.
B) The series converges.
Use a symbolic algebra utility to verify your result. A) The series diverges.
B) The series converges.
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27
Determine the convergence or divergence of the p-series
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
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28
A factory is polluting a river such that at every mile down river from the factory an environmental expert finds 15% less pollutant than at the preceding mile.If the pollutant's concentration is 600 ppm (parts per million)at the factory,what is its concentration 12 miles down river?
A) 180 ppm
B) 90 ppm
C) 85.35 ppm
D) 705.88 ppm
E) 100.41 ppm
A) 180 ppm
B) 90 ppm
C) 85.35 ppm
D) 705.88 ppm
E) 100.41 ppm
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29
Express the value of the given repeating decimal as a fraction.[Hint: Write as an infinite series.]
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.
A) The series converges.
B) The series diverges.
Use a symbolic algebra utility to verify your result. A) The series converges.
B) The series diverges.
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31
Determine whether the series is a p-series.
A) is not a p-series.
B) is a p-series.
is a p-series. A)
is not a p-series.B)
is a p-series. فتح الحزمة
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32
Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.
A) The series diverges.
B) The series converges.
Use a symbolic algebra utility to verify your result. A) The series diverges.
B) The series converges.
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33
Find the sum of the convergent series.
A) 16
B) 8
C) 12
D) 4
E) 3
A) 16
B) 8
C) 12
D) 4
E) 3
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34
The repeating decimal is expressed as a geometric series Write the decimal as the ratio of two integers.
A)
B)
C)
D)
E)
is expressed as a geometric series Write the decimal as the ratio of two integers. A)
B)
C)
D)
E)
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35
Find the sum of the convergent series.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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36
A deposit of $800 is made each month in an account that earns 8.4% interest,compounded monthly.The balance in the account after n months is given by Find the balance after 20 years by computing the 240th term of the sequence.Round your answer to two decimal places.
A) $696,946.54
B) $1,018,546.54
C) $24,073.84
D) $343,954.07
E) $1,125.60
Find the balance after 20 years by computing the 240th term of the sequence.Round your answer to two decimal places. A) $696,946.54
B) $1,018,546.54
C) $24,073.84
D) $343,954.07
E) $1,125.60
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37
A company produces a new product for which it estimates the annual sales to be 5000 units.Suppose that in any given year 10% of the units (regardless of age)will become inoperative.How many units will be in use after n years?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Bouncing Ball.A ball dropped from a height of 39 feet bounces to 0.6666666667 of its former height with each bounce.Find the total vertical distance that the ball travels.
A) 195 feet
B) 82 feet
C) 234 feet
D) 111 feet
E) 117 feet
A) 195 feet
B) 82 feet
C) 234 feet
D) 111 feet
E) 117 feet
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39
You accept a job that pays a salary of $60,000 the first year.During the next 49 years,you will receive a 6% raise each year.What would be your total compensation over the 50-year period? Round your answer to the nearest integer.
A) $17,420,154
B) $1,000,000
C) $56,400
D) $360,000
E) $3,600
A) $17,420,154
B) $1,000,000
C) $56,400
D) $360,000
E) $3,600
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40
Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.
A) The series converges.
B) The series diverges.
Use a symbolic algebra utility to verify your result. A) The series converges.
B) The series diverges.
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41
Find the radius of convergence of the power series.
A) -8
B) 1
C) 8
D) -1
E) 0
A) -8
B) 1
C) 8
D) -1
E) 0
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42
Determine the convergence or divergence of the p-series
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
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43
Determine the convergence or divergence of the following series.
A) diverges
B) converges
A) diverges
B) converges
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44
Find the radius of convergence of the series
A) 16
B) 18
C) 1
D) 9
E) 8
A) 16
B) 18
C) 1
D) 9
E) 8
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45
Determine the convergence or divergence of the following series.
A) diverges
B) converges
C) inconclusive
A) diverges
B) converges
C) inconclusive
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46
Use the Ratio Test to determine the convergence or divergence of the series.
A) Diverges.
B) Converges.
C) Ratio Test is inconclusive.
A) Diverges.
B) Converges.
C) Ratio Test is inconclusive.
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47
Determine the convergence or divergence of the following series.
A) converges
B) diverges
A) converges
B) diverges
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48
Write the first five terms of the power series
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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49
Determine the convergence or divergence of the p-series
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
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50
Determine the convergence or divergence of the following series.
A) inconclusive
B) converges
C) diverges
A) inconclusive
B) converges
C) diverges
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51
Test the series for convergence for using any appropriate test.
A) converges
B) diverges
for convergence for using any appropriate test. A) converges
B) diverges
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52
Find the radius of convergence of the series
A) 10
B) 2
C) 4
D) 13
E) 9
A) 10
B) 2
C) 4
D) 13
E) 9
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53
Find the radius of convergence of the power series.
A) 0
B) 10
C) 20
D) 100
E)
A) 0
B) 10
C) 20
D) 100
E)
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54
Approximate the sum of the convergent series using four terms.Estimate the maximum error of your approximation.Round your answer to four decimal places.
A) The approximate value is 1.0286.
The maximum error of your approximation is 0.0084.
B) The approximate value is 1.0788.
The maximum error of your approximation is 0.0052.
C) The approximate value is 1.0108.
The maximum error of your approximation is 0.0217.
D) The approximate value is 2.0023.
The maximum error of your approximation is 1.0023.
E) The approximate value is 1.0812.
The maximum error of your approximation is 0.0069.
using four terms.Estimate the maximum error of your approximation.Round your answer to four decimal places.
A) The approximate value is 1.0286.
The maximum error of your approximation is 0.0084.
B) The approximate value is 1.0788.
The maximum error of your approximation is 0.0052.
C) The approximate value is 1.0108.
The maximum error of your approximation is 0.0217.
D) The approximate value is 2.0023.
The maximum error of your approximation is 1.0023.
E) The approximate value is 1.0812.
The maximum error of your approximation is 0.0069.
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55
Determine the convergence or divergence of the following series.
A) diverges
B) converges
A) diverges
B) converges
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56
Use the Ratio Test to determine the convergence or divergence of the series.
A) Diverges.
B) Converges.
C) Ratio Test is inconclusive.
A) Diverges.
B) Converges.
C) Ratio Test is inconclusive.
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57
Determine the convergence or divergence of the p-series
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
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58
Determine the convergence or divergence of the following series.
A) converges
B) diverges
A) converges
B) diverges
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59
Test the series for convergence or divergence using any appropriate test.
A) diverges
B) converges
for convergence or divergence using any appropriate test. A) diverges
B) converges
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60
Use the Ratio Test to determine the convergence or divergence of the series.
A) The series converges.
B) The series diverges.
A) The series converges.
B) The series diverges.
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61
Find the third Taylor polynomial at for the given function.
A)
B)
C)
D)
E)
for the given function.
A)
B)
C)
D)
E)
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62
Find the radius of convergence centered at for the following function.
A) 4
B) 2
C) 0
D) 1
E)
for the following function. A) 4
B) 2
C) 0
D) 1
E)
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63
Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4.
A) , , ,
B) , , ,
C) , , ,
D) , , ,
E) , , ,
A)
, , , B)
, , , C)
, , , D)
, , , E)
, , , فتح الحزمة
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64
Find the radius of convergence of the series
A) 1
B) 2
C) 3
D) 7
E) 9
A) 1
B) 2
C) 3
D) 7
E) 9
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65
Find the third degree Taylor polynomial centered at for the function.
A)
B)
C)
D)
E)
for the function.
A)
B)
C)
D)
E)
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66
A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions.
A)
B)
C)
D)
E)
is given below.Use a graphing utility to graph both functions. A)
B)
C)
D)
E)
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67
Differentiate the series for to find the power series for the function
A)
B)
C)
D)
E)
to find the power series for the function A)
B)
C)
D)
E)
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68
Apply Taylor's Theorem to find the power series centered at for the function
A)
B)
C)
D)
E)
for the function A)
B)
C)
D)
E)
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69
A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions.
A)
B)
C)
D)
E)
is given below.Use a graphing utility to graph both functions. A)
B)
C)
D)
E)
فتح الحزمة
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70
Find the power series for the function using the power series for
A)
B)
C)
D)
E)
using the power series for A)
B)
C)
D)
E)
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71
Find the radius of convergence centered at for the following function.
A) 4
B) 2
C) 0
D) 1
E)
for the following function. A) 4
B) 2
C) 0
D) 1
E)
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72
Use a symbolic differentiation utility to find the Taylor polynomials (centred at zero)of degrees (a)2,(b)4,(c)6,(d)8.
A) , , ,
B) , , ,
C) , , ,
D) , , ,
E) , , ,
A)
, , , B)
, , , C)
, , , D)
, , , E)
, , , فتح الحزمة
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73
Find the radius of convergence centered at for the following function.
A) 4
B) 2
C) 0
D) 1
E)
for the following function. A) 4
B) 2
C) 0
D) 1
E)
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74
Find the radius of convergence of where
A) 1
B) ∞
C)
D) 8
E) 16
where A) 1
B) ∞
C)
D) 8
E) 16
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75
Find the radius of convergence centered at for the following function.
A) 4
B) 2
C) 0
D) 1
E)
for the following function. A) 4
B) 2
C) 0
D) 1
E)
فتح الحزمة
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76
Apply Taylor's Theorem to find the power series centered at for the function
A)
B)
C)
D)
E)
for the function A)
B)
C)
D)
E)
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77
Integrate the series for to find the power series for the function
A)
B)
C)
D)
E)
to find the power series for the function A)
B)
C)
D)
E)
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78
Find the power series for the function using the power series for
A)
B)
C)
D)
E)
using the power series for A)
B)
C)
D)
E)
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79
A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions.
A)
B)
C)
D)
E)
is given below.Use a graphing utility to graph both functions. A)
B)
C)
D)
E)
فتح الحزمة
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80
A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions.
A)
B)
C)
D)
E)
is given below.Use a graphing utility to graph both functions. A)
B)
C)
D)
E)
فتح الحزمة
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