تكلم مع الذكاء الاصطناعي
Deck 9: Infinite Series
ملء الشاشة (f)
سؤال
Use the Direct Comparison Test (if possible) to determine whether the series 
A) diverges
B) converges
A) diverges
B) converges
سؤال
Identify the graph of the first 10 terms of the sequence of partial sum of the series 
for 
.
A)
B)
C)
D)
E)
for .A)
B)
C)
D)
E)
سؤال
Find the fourth degree Maclaurin polynomial for the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Identify the most appropriate test to be used to determine whether the series 
converges or diverges.
A) Ratio Test
B) ρ-Series Test
C) Alternating Series Test
D) Telescoping Series Test
E) Root Test
converges or diverges.A) Ratio Test
B) ρ-Series Test
C) Alternating Series Test
D) Telescoping Series Test
E) Root Test
سؤال
Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used. 
A) converges; Integral Test
B) converges; Ratio Test
C) converges; Alternating Series Test
D) diverges; Ratio Test
E) diverges; Integral Test
A) converges; Integral Test
B) converges; Ratio Test
C) converges; Alternating Series Test
D) diverges; Ratio Test
E) diverges; Integral Test
سؤال
Use the Ratio Test to determine the convergence or divergence of the series 
.
A) converges
B) diverges
.A) converges
B) diverges
سؤال
True or false: The series 
converges.
converges. سؤال
Find the Maclaurin polynomial of degree 5 for the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used. 
A) diverges; Ratio Test
B) converges; both p-series and Integral Test
C) converges; p-series
D) converges; Integral Test
E) diverges; p-series
A) diverges; Ratio Test
B) converges; both p-series and Integral Test
C) converges; p-series
D) converges; Integral Test
E) diverges; p-series
سؤال
Use a graphing utility to graph 
and P1, a first-degree polynomial function whose value and slope agree with the value and slope of f at 
.
A) 
B) 
C) 
D) 
E) 
and P1, a first-degree polynomial function whose value and slope agree with the value and slope of f at . A)
B)
C)
D)
E)
سؤال
Use the Direct Comparison Test to determine the convergence or divergence of the series 
.
A) The series
diverges.
B) The series
converges.
.A) The series
diverges.B) The series
converges. سؤال
Match the sequence with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Approximate the sum of the series by using the first six terms. 
A) 0.723 < S < 0.743
B) 0.683 < S < 0.763
C) 0.733 < S < 0.738
D) 0.693 < S < 0.733
E) 0.73 < S < 0.736
A) 0.723 < S < 0.743
B) 0.683 < S < 0.763
C) 0.733 < S < 0.738
D) 0.693 < S < 0.733
E) 0.73 < S < 0.736
سؤال
Match the sequence with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Match the sequence with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the definition to find the Taylor series centered at 
for the function 
.
A)
B)
C)
D)
E)
for the function .A)
B)
C)
D)
E)
سؤال
Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x. 
A)
B)
C)
D)
E) The series diverges for all x.
A)
B)
C)
D)
E) The series diverges for all x.
سؤال
Use the Root Test to determine the convergence or divergence of the series. 
A) Root Test inconclusive
B) diverges
C) converges
A) Root Test inconclusive
B) diverges
C) converges
سؤال
True or false. The series 
is convergent.
is convergent. سؤال
Write the first three terms of the sequence. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the Maclaurin polynomial of degree 3 for the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. 
A) The sequence converges to 0.
B) The sequence diverges to -2.
C) The sequence converges to 1.
D) The sequence converges to -1.
E) The sequence diverges.
A) The sequence converges to 0.
B) The sequence diverges to -2.
C) The sequence converges to 1.
D) The sequence converges to -1.
E) The sequence diverges.
سؤال
Find a power series for the function 
centered at 0.
A)
B)
C)
D)
E)
centered at 0.A)
B)
C)
D)
E)
سؤال
Find the Maclaurin polynomial of degree 4 for the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Approximate the sum of the series by using the first six terms. 
A) 0.783 < S < 4.630
B) 2.066 < S < 3.348
C) 1.745 < S < 3.669
D) 0.569 < S < 4.844
E) 0.302 < S < 5.111
A) 0.783 < S < 4.630
B) 2.066 < S < 3.348
C) 1.745 < S < 3.669
D) 0.569 < S < 4.844
E) 0.302 < S < 5.111
سؤال
Write the first five terms of the sequence of partial sums. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine the convergence or divergence of the series. 
A) cannot be determined from the methods in the chapter
B) Diverges
C) Converges
A) cannot be determined from the methods in the chapter
B) Diverges
C) Converges
سؤال
Consider the function given by 
. Find the interval of convergence for 
.
A)
B)
C)
D)
E)
. Find the interval of convergence for .A)
B)
C)
D)
E)
سؤال
If the rate of inflation is 
per year and the average price of a car is currently $35,000, the average price after n years is 
. Compute the average price after 8 years. Round your answer to two decimal places.
A) $22,259.86
B) $53,714.03
C) $295,400.00
D) $46,685.40
E) $264,600.00
per year and the average price of a car is currently $35,000, the average price after n years is . Compute the average price after 8 years. Round your answer to two decimal places.A) $22,259.86
B) $53,714.03
C) $295,400.00
D) $46,685.40
E) $264,600.00
سؤال
Use the polynomial test to determine whether the series 
converges or diverges.
A) The series
converges.
B) The series
diverges.
converges or diverges.A) The series
converges.B) The series
diverges. سؤال
سؤال
Determine the convergence or divergence of the series. 
A) diverges
B) converges
C) cannot be determined
A) diverges
B) converges
C) cannot be determined
سؤال
Determine whether the series 
converges conditionally or absolutely, or diverges.
A) The series converges conditionally but does not converge absolutely.
B) The series converges absolutely but does not converge conditionally.
C) The series diverges.
D) The series converges absolutely.
converges conditionally or absolutely, or diverges.A) The series converges conditionally but does not converge absolutely.
B) The series converges absolutely but does not converge conditionally.
C) The series diverges.
D) The series converges absolutely.
سؤال
Consider the sequence 
whose nth term is given by 
where P is the principal, 
is the account balance in dollars after n months, and r is the interest rate compounded annually. Find the sixth term of the sequence if 
and 
. Round your answer to two decimal places.
A) $9,518.26
B) $10,061.16
C) $9,696.45
D) $9,342.82
E) $9,412.67
whose nth term is given by where P is the principal, is the account balance in dollars after n months, and r is the interest rate compounded annually. Find the sixth term of the sequence if and . Round your answer to two decimal places. A) $9,518.26
B) $10,061.16
C) $9,696.45
D) $9,342.82
E) $9,412.67
سؤال
Determine whether the series 
converges absolutely, converges conditionally, or diverges.
A) converges conditionally
B) diverges
C) converges absolutely
converges absolutely, converges conditionally, or diverges.A) converges conditionally
B) diverges
C) converges absolutely
سؤال
Suppose the winner of a $10,000,000 sweepstakes will be paid $200,000 per year for 50 years, starting a year from now. The money earns 6% interest per year. The present value of the winnings is 
Compute the present value using the formula for the nth partial sum of a geometric series. Round your answer to two decimal places.
A) $10,542,883.62
B) $3,323,509.25
C) $7,028,589.08
D) $2,556,671.23
E) $3,152,372.13
Compute the present value using the formula for the nth partial sum of a geometric series. Round your answer to two decimal places.A) $10,542,883.62
B) $3,323,509.25
C) $7,028,589.08
D) $2,556,671.23
E) $3,152,372.13
سؤال
Identify the interval of convergence of a power series 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Use the Ratio Test to determine the convergence or divergence of the series 
.
A) diverges
B) converges
.A) diverges
B) converges
سؤال
Approximate the sum of the series by using the first six terms. 
A) 5.398 < S < 5.404
B) 5.393 < S < 5.405
C) 5.381 < S < 5.416
D) 5.391 < S < 5.391
E) 5.297 < S < 5.501
A) 5.398 < S < 5.404
B) 5.393 < S < 5.405
C) 5.381 < S < 5.416
D) 5.391 < S < 5.391
E) 5.297 < S < 5.501
سؤال
Use a power series to approximate the value of the integral 
with an error less than 0.001. Round your answer to four decimal places.
A) 0.1063
B) 0.0900
C) 0.0982
D) 0.1071
E) 0.0985
with an error less than 0.001. Round your answer to four decimal places.A) 0.1063
B) 0.0900
C) 0.0982
D) 0.1071
E) 0.0985
سؤال
Write the next two apparent terms of the sequence 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Suppose the annual spending by tourists in a resort city is $100 million. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the same city, and so on. Summing all of this spending indefinitely, leads to the geometric series 
. Find the sum of this series.
A) $800 million
B) $401 million
C) $200 million
D) $801 million
E) $400 million
. Find the sum of this series.A) $800 million
B) $401 million
C) $200 million
D) $801 million
E) $400 million
سؤال
Write the first five terms of the sequence of partial sums. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
True or false: The series 
converges.
converges. سؤال
Sketch the graph of the sequence of partial sum of the series 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of 
at 
.
A)
B)
C)
D)
E)
at .A)
B)
C)
D)
E)
سؤال
Use the Limit Comparison 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
Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007. 
A) 5
B) 4
C) 2
D) 6
E) 3
A) 5
B) 4
C) 2
D) 6
E) 3
سؤال
Find the sum of the convergent series. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the binomial series to find the Maclaurian series for the function. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
سؤال
Use the Limit Comparison Test (if possible) to determine whether the series 
converges or diverges.
A) diverges
B) converges
converges or diverges. A) diverges
B) converges
سؤال
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the interval of convergence of the power series 
. (Be sure to include a check for convergence at the endpoints of the interval.)
A)
B)
C)
D)
E)
. (Be sure to include a check for convergence at the endpoints of the interval.)A)
B)
C)
D)
E)
سؤال
Find the fourth degree Taylor polynomial centered at 
for the function. 
A)
B)
C)
D)
E)
for the function. A)
B)
C)
D)
E)
سؤال
Use the polynomial test to determine whether the series 
converges or diverges.
A) The series
diverges.
B) The series
converges.
converges or diverges.A) The series
diverges.B) The series
converges. سؤال
Use a power series to approximate the value of the integral 
with an error of less than 0.01. Round your answer to two decimal places.
A) 0.74
B) 0.89
C) 0.88
D) 0.84
E) 0.81
with an error of less than 0.01. Round your answer to two decimal places. A) 0.74
B) 0.89
C) 0.88
D) 0.84
E) 0.81
سؤال
Suppose an electronic games manufacturer producing a new product estimates the annual sales to be 7,000 units. Each year 25% of the units that have been sold will become inoperative. So, 7,000 units will be in use after 1 year, 
units will be in use after 2 years, and so on. How many units will be in use after n years?
A)
units
B)
units
C)
units
D)
units
E)
units
units will be in use after 2 years, and so on. How many units will be in use after n years? A)
unitsB)
unitsC)
unitsD)
unitsE)
units سؤال
Use the Integral Test to determine the convergence or divergence of the series. 
A) diverges
B) converges
C) Integral Test inconclusive
A) diverges
B) converges
C) Integral Test inconclusive
سؤال
Use the power series 
to determine a power series centered at 0 for the function 
. .
A)
B)
C)
D)
E)
to determine a power series centered at 0 for the function . .A)
B)
C)
D)
E)
سؤال
State where the power series 
is centered.
A) 0
B) -3
C) 9
D) 3
E) -9
is centered.A) 0
B) -3
C) 9
D) 3
E) -9
سؤال
سؤال
Use the Direct Comparison Test (if possible) to determine whether the series 
converges or diverges.
A) converges
B) diverges
converges or diverges. A) converges
B) diverges
سؤال
Use the binomial series to find the Maclaurian series for the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
Explain how to use the geometric series 
to find the series for the function 
.
A) replace x with
B) replace x with
and multiply the series by 
C) replace x with
and divide the series by 
D) replace x with
and divide the series by 
E) replace x with
to find the series for the function .A) replace x with
B) replace x with
and multiply the series by C) replace x with
and divide the series by D) replace x with
and divide the series by E) replace x with
سؤال
Find the Maclaurin series for the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Determine whether the series 
converges conditionally or absolutely, or diverges.
A) The series converges absolutely.
B) The series diverges.
C) The series converges absolutely but does not converge conditionally.
D) The series converges conditionally but does not converge absolutely.
converges conditionally or absolutely, or diverges.A) The series converges absolutely.
B) The series diverges.
C) The series converges absolutely but does not converge conditionally.
D) The series converges conditionally but does not converge absolutely.
سؤال
Find the Maclaurin polynomial of degree 4 for the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the radius of convergence of the power series. 
A)
B)
C) 8
D)
E) 64
A)
B)
C) 8
D)
E) 64
سؤال
Use the definition to find the Taylor series centered at 
for the function 
.
A)
B)
C)
D)
E)
for the function .A)
B)
C)
D)
E)
سؤال
Use the power series 
to determine a power series for the function 
.
A)
B)
C)
D)
E)
to determine a power series for the function .A)
B)
C)
D)
E)
سؤال
Use the Direct Comparison 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
Determine the values of x for which the function 
can be replaced by the Taylor polynomial 
if the error cannot exceed 0.006. Round your answer to four decimal places.
A)
B)
C)
D)
E)
can be replaced by the Taylor polynomial if the error cannot exceed 0.006. Round your answer to four decimal places.A)
B)
C)
D)
E)
سؤال
Find a geometric power series for the function 
centered at 0.
A)
B)
C)
D)
E)
centered at 0.A)
B)
C)
D)
E)
سؤال
Find the sum of the convergent series 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use Theorem 9.11 to determine the convergence or divergence of the series. 
A) diverges
B) converges
C) Theorem 9.11 inconclusive
A) diverges
B) converges
C) Theorem 9.11 inconclusive
سؤال
Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of f at 
. What is P1 called? 
A)
; tangent line to 
at 
B)
; secant line to 
at 
C)
; tangent line to 
at 
D)
; differential of 
at 
E)
; tangent line to 
at 
. What is P1 called? A)
; tangent line to at B)
; secant line to at C)
; tangent line to at D)
; differential of at E)
; tangent line to at سؤال
Use the Ratio Test to determine the convergence or divergence of the series. 
A) converges
B) Ratio Test inconclusive
C) diverges
A) converges
B) Ratio Test inconclusive
C) diverges
سؤال
The terms of a series 
are defined recursively. Determine the convergence or divergence of the series. Explain your reasoning. 
, 
A) diverges; Ratio Test
B) converges; Ratio Test
C) converges; Integral Test
D) diverges; Alternating Series Test
E) diverges; Root Test
are defined recursively. Determine the convergence or divergence of the series. Explain your reasoning. , A) diverges; Ratio Test
B) converges; Ratio Test
C) converges; Integral Test
D) diverges; Alternating Series Test
E) diverges; Root Test
سؤال
Identify the interval of convergence of a power series 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Find a power series for the function 
centered at 1.
A)
B)
C)
D)
E)
centered at 1.A)
B)
C)
D)
E)
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ملء الشاشة (f)
Deck 9: Infinite Series
1
Use the Direct Comparison Test (if possible) to determine whether the series
A) diverges
B) converges
A) diverges
B) converges
B
2
Identify the graph of the first 10 terms of the sequence of partial sum of the series for .
A)
B)
C)
D)
E)
for .A)
B)
C)
D)
E)
E
3
Find the fourth degree Maclaurin polynomial for the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
E
4
Identify the most appropriate test to be used to determine whether the series converges or diverges.
A) Ratio Test
B) ρ-Series Test
C) Alternating Series Test
D) Telescoping Series Test
E) Root Test
converges or diverges.A) Ratio Test
B) ρ-Series Test
C) Alternating Series Test
D) Telescoping Series Test
E) Root Test
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5
Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.
A) converges; Integral Test
B) converges; Ratio Test
C) converges; Alternating Series Test
D) diverges; Ratio Test
E) diverges; Integral Test
A) converges; Integral Test
B) converges; Ratio Test
C) converges; Alternating Series Test
D) diverges; Ratio Test
E) diverges; Integral Test
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6
Use the Ratio Test to determine the convergence or divergence of the series .
A) converges
B) diverges
.A) converges
B) diverges
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7
True or false: The series converges.
converges. فتح الحزمة
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8
Find the Maclaurin polynomial of degree 5 for the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.
A) diverges; Ratio Test
B) converges; both p-series and Integral Test
C) converges; p-series
D) converges; Integral Test
E) diverges; p-series
A) diverges; Ratio Test
B) converges; both p-series and Integral Test
C) converges; p-series
D) converges; Integral Test
E) diverges; p-series
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10
Use a graphing utility to graph and P1, a first-degree polynomial function whose value and slope agree with the value and slope of f at .
A)
B)
C)
D)
E)
and P1, a first-degree polynomial function whose value and slope agree with the value and slope of f at . A)
B)
C)
D)
E)
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11
Use the Direct Comparison Test to determine the convergence or divergence of the series .
A) The series diverges.
B) The series converges.
.A) The series
diverges.B) The series
converges. فتح الحزمة
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12
Match the sequence with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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13
Approximate the sum of the series by using the first six terms.
A) 0.723 < S < 0.743
B) 0.683 < S < 0.763
C) 0.733 < S < 0.738
D) 0.693 < S < 0.733
E) 0.73 < S < 0.736
A) 0.723 < S < 0.743
B) 0.683 < S < 0.763
C) 0.733 < S < 0.738
D) 0.693 < S < 0.733
E) 0.73 < S < 0.736
فتح الحزمة
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k this deck
14
Match the sequence with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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k this deck
15
Match the sequence with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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k this deck
16
Use the definition to find the Taylor series centered at for the function .
A)
B)
C)
D)
E)
for the function .A)
B)
C)
D)
E)
فتح الحزمة
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17
Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x.
A)
B)
C)
D)
E) The series diverges for all x.
A)
B)
C)
D)
E) The series diverges for all x.
فتح الحزمة
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18
Use the Root Test to determine the convergence or divergence of the series.
A) Root Test inconclusive
B) diverges
C) converges
A) Root Test inconclusive
B) diverges
C) converges
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19
True or false. The series is convergent.
is convergent. فتح الحزمة
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20
Write the first three terms of the sequence.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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21
Find the Maclaurin polynomial of degree 3 for the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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22
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.
A) The sequence converges to 0.
B) The sequence diverges to -2.
C) The sequence converges to 1.
D) The sequence converges to -1.
E) The sequence diverges.
A) The sequence converges to 0.
B) The sequence diverges to -2.
C) The sequence converges to 1.
D) The sequence converges to -1.
E) The sequence diverges.
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23
Find a power series for the function centered at 0.
A)
B)
C)
D)
E)
centered at 0.A)
B)
C)
D)
E)
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24
Find the Maclaurin polynomial of degree 4 for the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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25
Approximate the sum of the series by using the first six terms.
A) 0.783 < S < 4.630
B) 2.066 < S < 3.348
C) 1.745 < S < 3.669
D) 0.569 < S < 4.844
E) 0.302 < S < 5.111
A) 0.783 < S < 4.630
B) 2.066 < S < 3.348
C) 1.745 < S < 3.669
D) 0.569 < S < 4.844
E) 0.302 < S < 5.111
فتح الحزمة
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26
Write the first five terms of the sequence of partial sums.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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27
Determine the convergence or divergence of the series.
A) cannot be determined from the methods in the chapter
B) Diverges
C) Converges
A) cannot be determined from the methods in the chapter
B) Diverges
C) Converges
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28
Consider the function given by . Find the interval of convergence for .
A)
B)
C)
D)
E)
. Find the interval of convergence for .A)
B)
C)
D)
E)
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29
If the rate of inflation is per year and the average price of a car is currently $35,000, the average price after n years is . Compute the average price after 8 years. Round your answer to two decimal places.
A) $22,259.86
B) $53,714.03
C) $295,400.00
D) $46,685.40
E) $264,600.00
per year and the average price of a car is currently $35,000, the average price after n years is . Compute the average price after 8 years. Round your answer to two decimal places.A) $22,259.86
B) $53,714.03
C) $295,400.00
D) $46,685.40
E) $264,600.00
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30
Use the polynomial test to determine whether the series converges or diverges.
A) The series converges.
B) The series diverges.
converges or diverges.A) The series
converges.B) The series
diverges. فتح الحزمة
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31
A government program that currently costs taxpayers $3.5 billion per year is cut back by 40 percent per year. Compute the budget after the fourth year. Round your answer to the nearest integer.
A) $1,433,600,000
B) $165,995,062
C) $89,600,000
D) $1,012,217,284
E) $453,600,000
A) $1,433,600,000
B) $165,995,062
C) $89,600,000
D) $1,012,217,284
E) $453,600,000
فتح الحزمة
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32
Determine the convergence or divergence of the series.
A) diverges
B) converges
C) cannot be determined
A) diverges
B) converges
C) cannot be determined
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33
Determine whether the series converges conditionally or absolutely, or diverges.
A) The series converges conditionally but does not converge absolutely.
B) The series converges absolutely but does not converge conditionally.
C) The series diverges.
D) The series converges absolutely.
converges conditionally or absolutely, or diverges.A) The series converges conditionally but does not converge absolutely.
B) The series converges absolutely but does not converge conditionally.
C) The series diverges.
D) The series converges absolutely.
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34
Consider the sequence whose nth term is given by where P is the principal, is the account balance in dollars after n months, and r is the interest rate compounded annually. Find the sixth term of the sequence if and . Round your answer to two decimal places.
A) $9,518.26
B) $10,061.16
C) $9,696.45
D) $9,342.82
E) $9,412.67
whose nth term is given by where P is the principal, is the account balance in dollars after n months, and r is the interest rate compounded annually. Find the sixth term of the sequence if and . Round your answer to two decimal places. A) $9,518.26
B) $10,061.16
C) $9,696.45
D) $9,342.82
E) $9,412.67
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35
Determine whether the series converges absolutely, converges conditionally, or diverges.
A) converges conditionally
B) diverges
C) converges absolutely
converges absolutely, converges conditionally, or diverges.A) converges conditionally
B) diverges
C) converges absolutely
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36
Suppose the winner of a $10,000,000 sweepstakes will be paid $200,000 per year for 50 years, starting a year from now. The money earns 6% interest per year. The present value of the winnings is Compute the present value using the formula for the nth partial sum of a geometric series. Round your answer to two decimal places.
A) $10,542,883.62
B) $3,323,509.25
C) $7,028,589.08
D) $2,556,671.23
E) $3,152,372.13
Compute the present value using the formula for the nth partial sum of a geometric series. Round your answer to two decimal places.A) $10,542,883.62
B) $3,323,509.25
C) $7,028,589.08
D) $2,556,671.23
E) $3,152,372.13
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37
Identify the interval of convergence of a power series .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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38
Use the Ratio Test to determine the convergence or divergence of the series .
A) diverges
B) converges
.A) diverges
B) converges
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39
Approximate the sum of the series by using the first six terms.
A) 5.398 < S < 5.404
B) 5.393 < S < 5.405
C) 5.381 < S < 5.416
D) 5.391 < S < 5.391
E) 5.297 < S < 5.501
A) 5.398 < S < 5.404
B) 5.393 < S < 5.405
C) 5.381 < S < 5.416
D) 5.391 < S < 5.391
E) 5.297 < S < 5.501
فتح الحزمة
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40
Use a power series to approximate the value of the integral with an error less than 0.001. Round your answer to four decimal places.
A) 0.1063
B) 0.0900
C) 0.0982
D) 0.1071
E) 0.0985
with an error less than 0.001. Round your answer to four decimal places.A) 0.1063
B) 0.0900
C) 0.0982
D) 0.1071
E) 0.0985
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41
Write the next two apparent terms of the sequence .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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42
Suppose the annual spending by tourists in a resort city is $100 million. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the same city, and so on. Summing all of this spending indefinitely, leads to the geometric series . Find the sum of this series.
A) $800 million
B) $401 million
C) $200 million
D) $801 million
E) $400 million
. Find the sum of this series.A) $800 million
B) $401 million
C) $200 million
D) $801 million
E) $400 million
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43
Write the first five terms of the sequence of partial sums.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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44
True or false: The series converges.
converges. فتح الحزمة
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45
Sketch the graph of the sequence of partial sum of the series .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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46
Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of at .
A)
B)
C)
D)
E)
at .A)
B)
C)
D)
E)
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47
Use the Limit Comparison 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. فتح الحزمة
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48
Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007.
A) 5
B) 4
C) 2
D) 6
E) 3
A) 5
B) 4
C) 2
D) 6
E) 3
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49
Find the sum of the convergent series.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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50
Use the binomial series to find the Maclaurian series for the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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51
Use the Limit Comparison Test (if possible) to determine whether the series converges or diverges.
A) diverges
B) converges
converges or diverges. A) diverges
B) converges
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52
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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53
Find the interval of convergence of the power series . (Be sure to include a check for convergence at the endpoints of the interval.)
A)
B)
C)
D)
E)
. (Be sure to include a check for convergence at the endpoints of the interval.)A)
B)
C)
D)
E)
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54
Find the fourth degree Taylor polynomial centered at for the function.
A)
B)
C)
D)
E)
for the function. A)
B)
C)
D)
E)
فتح الحزمة
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55
Use the polynomial test to determine whether the series converges or diverges.
A) The series diverges.
B) The series converges.
converges or diverges.A) The series
diverges.B) The series
converges. فتح الحزمة
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56
Use a power series to approximate the value of the integral with an error of less than 0.01. Round your answer to two decimal places.
A) 0.74
B) 0.89
C) 0.88
D) 0.84
E) 0.81
with an error of less than 0.01. Round your answer to two decimal places. A) 0.74
B) 0.89
C) 0.88
D) 0.84
E) 0.81
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57
Suppose an electronic games manufacturer producing a new product estimates the annual sales to be 7,000 units. Each year 25% of the units that have been sold will become inoperative. So, 7,000 units will be in use after 1 year, units will be in use after 2 years, and so on. How many units will be in use after n years?
A) units
B) units
C) units
D) units
E) units
units will be in use after 2 years, and so on. How many units will be in use after n years? A)
unitsB)
unitsC)
unitsD)
unitsE)
units فتح الحزمة
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58
Use the Integral Test to determine the convergence or divergence of the series.
A) diverges
B) converges
C) Integral Test inconclusive
A) diverges
B) converges
C) Integral Test inconclusive
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59
Use the power series to determine a power series centered at 0 for the function . .
A)
B)
C)
D)
E)
to determine a power series centered at 0 for the function . .A)
B)
C)
D)
E)
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60
State where the power series is centered.
A) 0
B) -3
C) 9
D) 3
E) -9
is centered.A) 0
B) -3
C) 9
D) 3
E) -9
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61
Suppose you go to work at a company that pays $0.02 for the first day, $0.04 for the second day, $0.08 for the third day, and so on. If the daily wage keeps doubling, what would your total income be for working 29 days? Round your answer to two decimal places.
A) $5,368,709.12
B) $2,684,354.56
C) $10,737,418.22
D) $42,949,672.88
E) $21,474,836.44
A) $5,368,709.12
B) $2,684,354.56
C) $10,737,418.22
D) $42,949,672.88
E) $21,474,836.44
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62
Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges.
A) converges
B) diverges
converges or diverges. A) converges
B) diverges
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63
Use the binomial series to find the Maclaurian series for the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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64
Explain how to use the geometric series to find the series for the function .
A) replace x with
B) replace x with and multiply the series by
C) replace x with and divide the series by
D) replace x with and divide the series by
E) replace x with
to find the series for the function .A) replace x with
B) replace x with
and multiply the series by C) replace x with
and divide the series by D) replace x with
and divide the series by E) replace x with
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65
Find the Maclaurin series for the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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66
Determine whether the series converges conditionally or absolutely, or diverges.
A) The series converges absolutely.
B) The series diverges.
C) The series converges absolutely but does not converge conditionally.
D) The series converges conditionally but does not converge absolutely.
converges conditionally or absolutely, or diverges.A) The series converges absolutely.
B) The series diverges.
C) The series converges absolutely but does not converge conditionally.
D) The series converges conditionally but does not converge absolutely.
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67
Find the Maclaurin polynomial of degree 4 for the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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68
Find the radius of convergence of the power series.
A)
B)
C) 8
D)
E) 64
A)
B)
C) 8
D)
E) 64
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69
Use the definition to find the Taylor series centered at for the function .
A)
B)
C)
D)
E)
for the function .A)
B)
C)
D)
E)
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70
Use the power series to determine a power series for the function .
A)
B)
C)
D)
E)
to determine a power series for the function .A)
B)
C)
D)
E)
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71
Use the Direct Comparison 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. فتح الحزمة
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72
Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.006. Round your answer to four decimal places.
A)
B)
C)
D)
E)
can be replaced by the Taylor polynomial if the error cannot exceed 0.006. Round your answer to four decimal places.A)
B)
C)
D)
E)
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73
Find a geometric power series for the function centered at 0.
A)
B)
C)
D)
E)
centered at 0.A)
B)
C)
D)
E)
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74
Find the sum of the convergent series
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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75
Use Theorem 9.11 to determine the convergence or divergence of the series.
A) diverges
B) converges
C) Theorem 9.11 inconclusive
A) diverges
B) converges
C) Theorem 9.11 inconclusive
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76
Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of f at . What is P1 called?
A) ; tangent line to at
B) ; secant line to at
C) ; tangent line to at
D) ; differential of at
E) ; tangent line to at
. What is P1 called? A)
; tangent line to at B)
; secant line to at C)
; tangent line to at D)
; differential of at E)
; tangent line to at فتح الحزمة
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77
Use the Ratio Test to determine the convergence or divergence of the series.
A) converges
B) Ratio Test inconclusive
C) diverges
A) converges
B) Ratio Test inconclusive
C) diverges
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78
The terms of a series are defined recursively. Determine the convergence or divergence of the series. Explain your reasoning. ,
A) diverges; Ratio Test
B) converges; Ratio Test
C) converges; Integral Test
D) diverges; Alternating Series Test
E) diverges; Root Test
are defined recursively. Determine the convergence or divergence of the series. Explain your reasoning. , A) diverges; Ratio Test
B) converges; Ratio Test
C) converges; Integral Test
D) diverges; Alternating Series Test
E) diverges; Root Test
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79
Identify the interval of convergence of a power series .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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80
Find a power series for the function centered at 1.
A)
B)
C)
D)
E)
centered at 1.A)
B)
C)
D)
E)
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