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Deck 8: Infinite Sequences and Series
Full screen (f)
Question
Write the fourth-degree Taylor polynomial centered about the origin for the function 
.
.
Question
Which of the following is the degree 4 Taylor polynomial centered at 
for 
?
1)
2) 
3) 
a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
Question
Find the second-degree Taylor polynomial of the function 
.
. Question
According to Taylor's Formula, what is the maximum error possible in the use of the sum 
to approximate 
in the interval 
?
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
to approximate in the interval ?A)
e. b. f. c. g. d. h. Question
Estimate the range of values of x for which the approximation ![<strong>Estimate the range of values of x for which the approximation is accurate to within 0.01.</strong> A)[0.68, 1.41] E)[0.95, 1.05] B)[0.61, 1.54] F)[0.80, 1.23] C)[0.995, 1.005] G)[0.980, 1.023] D)[1.51, 2.59] H)[0.89, 1.14] <div style=padding-top: 35px>](https://storage.examlex.com/TB2033/11eaa8e2_0da3_dfec_96ab_33a9a51832cc_TB2033_11.jpg)
is accurate to within 0.01.
A)[0.68, 1.41]
E)[0.95, 1.05]
B)[0.61, 1.54]
F)[0.80, 1.23]
C)[0.995, 1.005]
G)[0.980, 1.023]
D)[1.51, 2.59]
H)[0.89, 1.14]
is accurate to within 0.01.A)[0.68, 1.41]
E)[0.95, 1.05]
B)[0.61, 1.54]
F)[0.80, 1.23]
C)[0.995, 1.005]
G)[0.980, 1.023]
D)[1.51, 2.59]
H)[0.89, 1.14]
Question
Give the 4th-degree Taylor polynomial for 
about the point 
. Using this polynomial, approximate 
. Give the maximum error for this approximation.
about the point . Using this polynomial, approximate . Give the maximum error for this approximation. Question
Find an approximation for 
accurate to 6 decimal places.(Note: sin's argument is measured in radians.)
accurate to 6 decimal places.(Note: sin's argument is measured in radians.) Question
Which of the following is the degree 2 Taylor polynomial centered at 
for 
?
1)
2) 
3) 
a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
Question
Which of the following is the degree 2 Taylor polynomial centered at 
for 
?
1)
2) 
3) 
a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
Question
Which of the following is the degree 2 Taylor polynomial centered at 
for 
?
1)
2) 
3) 
a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
Question
What is the smallest value of n that will guarantee (according to Taylor's Formula) that the Taylor polynomial 
at the number 0 will be within 0.0001 of 
for 
?
A)4
E)7
B)5
F)2
C)8
G)3
D)6
H)9
at the number 0 will be within 0.0001 of for ?A)4
E)7
B)5
F)2
C)8
G)3
D)6
H)9
Question
Estimate the range of values of x for which the approximation 
is accurate to within 0.001.
is accurate to within 0.001. Question
Estimate the range of values of x for which the approximation 
is accurate to within 0.0002.
is accurate to within 0.0002. Question
Estimate the range of values of x for which the approximation ![<strong>Estimate the range of values of x for which the approximation is accurate to within 0.01.</strong> A)[1.08, 3.20] E)[0.45, 1.78] B)[1.80, 2.20] F)[0.71, 1.33] C)[0.89, 3.56] G)[1.90, 2.10] D)[1.43, 2.66] H)[1.99, 2.01] <div style=padding-top: 35px>](https://storage.examlex.com/TB2033/11eaa8e2_0da3_dfed_96ab_830f012e48f0_TB2033_11.jpg)
is accurate to within 0.01.
A)[1.08, 3.20]
E)[0.45, 1.78]
B)[1.80, 2.20]
F)[0.71, 1.33]
C)[0.89, 3.56]
G)[1.90, 2.10]
D)[1.43, 2.66]
H)[1.99, 2.01]
is accurate to within 0.01.A)[1.08, 3.20]
E)[0.45, 1.78]
B)[1.80, 2.20]
F)[0.71, 1.33]
C)[0.89, 3.56]
G)[1.90, 2.10]
D)[1.43, 2.66]
H)[1.99, 2.01]
Question
Consider the function 
.(a) Find the fourth-degree Taylor polynomial of f at 
.(b) What is the remainder?
(c) What is the absolute minimum value of f, and where does it occur?
.(a) Find the fourth-degree Taylor polynomial of f at .(b) What is the remainder?(c) What is the absolute minimum value of f, and where does it occur?
Question
Find the second-degree Taylor polynomial for 
, centered about 
. Also obtain a bound for the error in using this polynomial to approximate 
.
, centered about . Also obtain a bound for the error in using this polynomial to approximate . Question
Find the coefficient of 
in the Taylor polynomial 
for the function 
at the number 2.
A)3
E)2
B)0
F)5
C)1
G)8
D)6
H)4
in the Taylor polynomial for the function at the number 2.A)3
E)2
B)0
F)5
C)1
G)8
D)6
H)4
Question
Find the Taylor polynomial 
for the function 
at the point 
.
for the function at the point . Question
Which of the following is the degree 3 Taylor polynomial centered at 
for 
?
1)
2) 
3) 
a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
Question
Which of the following is the degree 3 Taylor polynomial centered at 
for 
?
1)
2) 
3) 
a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
Question
Find the coefficient of 
in the Maclaurin series for 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
in the Maclaurin series for .A)
e. b. f. c. g. d. h. Question
Find the terms in the Maclaurin series for the function 
, as far as the term in 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
, as far as the term in .A)
e. b. f. c. g. d. h. Question
(a) Find the third-order Taylor polynomial associated with 
.(b) Use the Taylor polynomial from part (a) to find an approximation of 
.(c) Compare the value you calculated in part (b) with your calculator's value for 
.(b) Use the Taylor polynomial from part (a) to find an approximation of .(c) Compare the value you calculated in part (b) with your calculator's value for Question
Find the third-degree Taylor polynomial of the function 
.
. Question
Find the terms in the Maclaurin series for the function 
, as far as the term in 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
, as far as the term in .A)
e. b. f. c. g. d. h. Question
Find the third-degree Taylor polynomial centered at 
for 
. Use this result to approximate 
.
for . Use this result to approximate . Question
Given 
,
(a) calculate
.(b) calculate 
.(c) calculate 
.
,(a) calculate
.(b) calculate .(c) calculate . Question
Find the radius of convergence of the Maclaurin series for 
.
A)1
E)
b. 
f.4
C)
g.8
D)
h.2
.A)1
E)
b. f.4C)
g.8D)
h.2 Question
Find the coefficient of 
in the Maclaurin series for 
.
A)16
E)-16
B)
f. 
c.3
G)-3
D)4
H)0
in the Maclaurin series for .A)16
E)-16
B)
f. c.3G)-3
D)4
H)0
Question
Find the coefficient of 
in the Maclaurin series for 
.
A)16
E)-16
B)
f. 
c.3
G)-3
D)4
H)0
in the Maclaurin series for .A)16
E)-16
B)
f. c.3G)-3
D)4
H)0
Question
Use the 3rd-degree Taylor polynomial of 
about 
to approximate 
. Use the remainder term to give an upper bound for the error in this approximation.
about to approximate . Use the remainder term to give an upper bound for the error in this approximation. Question
Find the coefficient of 
in the Maclaurin series for 
.Note: The series is unique except for the constant of integration.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
in the Maclaurin series for .Note: The series is unique except for the constant of integration.A)
e. b. f. c. g. d. h. Question
Write the Taylor polynomial at 0 of degree 4 for 
.
. Question
Find the second-degree Taylor polynomial of the function 
.
. Question
(a) Use series to compute 
correct to three decimal places.(b) Use integration by parts to compute 
.(c) Compare your answers in parts (a) and (b) above.
correct to three decimal places.(b) Use integration by parts to compute .(c) Compare your answers in parts (a) and (b) above. Question
Use series to compute 
correct to four decimal places.
correct to four decimal places. Question
Find the third Taylor polynomial associated with 
. What is the remainder?
. What is the remainder? Question
Find the first four terms in the Maclaurin series for 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
.A)
e. b. f. c. g. d. h. Question
The first three derivatives of 
are 
, 
and 
.(a) Give the first four terms of the Taylor series associated with f at 
.(b) Give the second-order Taylor polynomial, 
, associated with f at 
.(c) Suppose that 
and that 
from part (b) is used to approximate 
. Prove that the error in this approximation does not exceed 
.
are , and .(a) Give the first four terms of the Taylor series associated with f at .(b) Give the second-order Taylor polynomial, , associated with f at .(c) Suppose that and that from part (b) is used to approximate . Prove that the error in this approximation does not exceed . Question
Find the third-degree Taylor polynomial of the function 
.
. Question
Give the Taylor series expansion of 
about the point 
.
about the point . Question
Find the coefficient of 
in the binomial series for 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
in the binomial series for .A)
e. b. f. c. g. d. h. Question
(a) Express 
as a Maclaurin series.(b) Evaluate 
as a series.
as a Maclaurin series.(b) Evaluate as a series. Question
Express 
as a Maclaurin Series.
as a Maclaurin Series. Question
Find the terms of the Maclaurin series for 
, as far as the term in 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
, as far as the term in .A)
e. b. f. c. g. d. h. Question
(a) Express 
as a Maclaurin series.(b) Evaluate 
as a series.
as a Maclaurin series.(b) Evaluate as a series. Question
Find the coefficient of 
in the binomial series for 
.
A)6
E)-20
B)20
F)-12
C)-6
G)10
D)-10
H)12
in the binomial series for .A)6
E)-20
B)20
F)-12
C)-6
G)10
D)-10
H)12
Question
Find the terms of the Maclaurin series for 
, as far as the term in 
.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
, as far as the term in .A)
e. b. f. c. g. d. h. Question
Find the Taylor series for 
at 2.
at 2. Question
Express 
as a Maclaurin Series.
as a Maclaurin Series. Question
Find the Maclaurin series expansion with 
for 
. Use this expansion to approximate 
.
for . Use this expansion to approximate . Question
Find the Maclaurin series expansion for 
and determine the interval of convergence.
and determine the interval of convergence. Question
Find the Taylor polynomial of degree 4 at 0 for the function defined by 
. Then compute the value of 
accurate to as many decimal places as the polynomial of degree 4 allows.
. Then compute the value of accurate to as many decimal places as the polynomial of degree 4 allows. Question
Express 
as a Maclaurin Series.
as a Maclaurin Series. Question
If the Maclaurin series for 
is 
, find 
.
is , find . Question
Find the coefficient of 
in the binomial series for 
.
A)2
E)
b.-1
F)
c.1
G)-2
D)
h. 
in the binomial series for .A)2
E)
b.-1F)
c.1G)-2
D)
h. Question
How many coefficients in the binomial series expansion of 
are divisible by 7?
A)0
E)2
B)5
F)6
C)7
G)1
D)3
H)4
are divisible by 7?A)0
E)2
B)5
F)6
C)7
G)1
D)3
H)4
Question
Find the coefficient of 
in the binomial series for 
.
A)3
E)10
B)6
F)5
C)15
G)16
D)20
H)12
in the binomial series for .A)3
E)10
B)6
F)5
C)15
G)16
D)20
H)12
Question
Use the binomial series to expand the function 
as a power series. Give the coefficient of 
in that series.
A)
e. 
b. 
f. 
c. 
g. 
d. 
h. 
as a power series. Give the coefficient of in that series.A)
e. b. f. c. g. d. h. Question
Find the Taylor series for 
about the origin.
about the origin. Question
Find the coefficient of 
in the Maclaurin series for 
.
in the Maclaurin series for . Question
Use the binomial series to expand 
as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Question
Find the terms in the power series expansion for the function 
, as far as the term in 
.
, as far as the term in . Question
Find the sum of the series 
.
. Question
Find the sum of the series 
.
. Question
Use the binomial series to expand 
as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Question
Which of the following is the power series centered at 
for 
?
1)
2) 
3) 
a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
Question
Which of the following is the power series centered at 
for 
?
1)
2) 
3) 
a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
Question
Use the binomial series formula to obtain the Maclaurin series for 
.
. Question
Which of the following is the power series centered at 
for 
?
1)
2) 
3) 
a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
Question
If 
, compute 
.
, compute . Question
Use the binomial series to expand 
as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Question
Find the sum of the series 
.
. Question
Let 
, compute 
.
, compute . Question
Find the terms of the Maclaurin series for 
, as far as the term in 
.
, as far as the term in . Question
Find the sum of the series 
.
. Question
If 
, compute 
.
, compute . Question
Use the binomial series to expand 
as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Question
Use the binomial series to expand 
as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Question
Use the binomial series to expand 
as a power series. State the radius of convergence.
as a power series. State the radius of convergence.
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Full screen (f)
Deck 8: Infinite Sequences and Series
1
Write the fourth-degree Taylor polynomial centered about the origin for the function .
.
2
Which of the following is the degree 4 Taylor polynomial centered at for ?
1) 2) 3) a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
G
3
Find the second-degree Taylor polynomial of the function .
.
4
According to Taylor's Formula, what is the maximum error possible in the use of the sum to approximate in the interval ?
A) e. b. f. c. g. d. h.
to approximate in the interval ?A)
e. b. f. c. g. d. h. Unlock Deck
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5
Estimate the range of values of x for which the approximation is accurate to within 0.01.
A)[0.68, 1.41]
E)[0.95, 1.05]
B)[0.61, 1.54]
F)[0.80, 1.23]
C)[0.995, 1.005]
G)[0.980, 1.023]
D)[1.51, 2.59]
H)[0.89, 1.14]
is accurate to within 0.01.A)[0.68, 1.41]
E)[0.95, 1.05]
B)[0.61, 1.54]
F)[0.80, 1.23]
C)[0.995, 1.005]
G)[0.980, 1.023]
D)[1.51, 2.59]
H)[0.89, 1.14]
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6
Give the 4th-degree Taylor polynomial for about the point . Using this polynomial, approximate . Give the maximum error for this approximation.
about the point . Using this polynomial, approximate . Give the maximum error for this approximation. Unlock Deck
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7
Find an approximation for accurate to 6 decimal places.(Note: sin's argument is measured in radians.)
accurate to 6 decimal places.(Note: sin's argument is measured in radians.) Unlock Deck
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8
Which of the following is the degree 2 Taylor polynomial centered at for ?
1) 2) 3) a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
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9
Which of the following is the degree 2 Taylor polynomial centered at for ?
1) 2) 3) a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
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10
Which of the following is the degree 2 Taylor polynomial centered at for ?
1) 2) 3) a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
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11
What is the smallest value of n that will guarantee (according to Taylor's Formula) that the Taylor polynomial at the number 0 will be within 0.0001 of for ?
A)4
E)7
B)5
F)2
C)8
G)3
D)6
H)9
at the number 0 will be within 0.0001 of for ?A)4
E)7
B)5
F)2
C)8
G)3
D)6
H)9
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12
Estimate the range of values of x for which the approximation is accurate to within 0.001.
is accurate to within 0.001. Unlock Deck
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13
Estimate the range of values of x for which the approximation is accurate to within 0.0002.
is accurate to within 0.0002. Unlock Deck
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14
Estimate the range of values of x for which the approximation is accurate to within 0.01.
A)[1.08, 3.20]
E)[0.45, 1.78]
B)[1.80, 2.20]
F)[0.71, 1.33]
C)[0.89, 3.56]
G)[1.90, 2.10]
D)[1.43, 2.66]
H)[1.99, 2.01]
is accurate to within 0.01.A)[1.08, 3.20]
E)[0.45, 1.78]
B)[1.80, 2.20]
F)[0.71, 1.33]
C)[0.89, 3.56]
G)[1.90, 2.10]
D)[1.43, 2.66]
H)[1.99, 2.01]
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15
Consider the function .(a) Find the fourth-degree Taylor polynomial of f at .(b) What is the remainder?
(c) What is the absolute minimum value of f, and where does it occur?
.(a) Find the fourth-degree Taylor polynomial of f at .(b) What is the remainder?(c) What is the absolute minimum value of f, and where does it occur?
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16
Find the second-degree Taylor polynomial for , centered about . Also obtain a bound for the error in using this polynomial to approximate .
, centered about . Also obtain a bound for the error in using this polynomial to approximate . Unlock Deck
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17
Find the coefficient of in the Taylor polynomial for the function at the number 2.
A)3
E)2
B)0
F)5
C)1
G)8
D)6
H)4
in the Taylor polynomial for the function at the number 2.A)3
E)2
B)0
F)5
C)1
G)8
D)6
H)4
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18
Find the Taylor polynomial for the function at the point .
for the function at the point . Unlock Deck
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19
Which of the following is the degree 3 Taylor polynomial centered at for ?
1) 2) 3) a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
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20
Which of the following is the degree 3 Taylor polynomial centered at for ?
1) 2) 3) a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
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21
Find the coefficient of in the Maclaurin series for .
A) e. b. f. c. g. d. h.
in the Maclaurin series for .A)
e. b. f. c. g. d. h. Unlock Deck
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22
Find the terms in the Maclaurin series for the function , as far as the term in .
A) e. b. f. c. g. d. h.
, as far as the term in .A)
e. b. f. c. g. d. h. Unlock Deck
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23
(a) Find the third-order Taylor polynomial associated with .(b) Use the Taylor polynomial from part (a) to find an approximation of .(c) Compare the value you calculated in part (b) with your calculator's value for
.(b) Use the Taylor polynomial from part (a) to find an approximation of .(c) Compare the value you calculated in part (b) with your calculator's value for Unlock Deck
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24
Find the third-degree Taylor polynomial of the function .
. Unlock Deck
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25
Find the terms in the Maclaurin series for the function , as far as the term in .
A) e. b. f. c. g. d. h.
, as far as the term in .A)
e. b. f. c. g. d. h. Unlock Deck
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26
Find the third-degree Taylor polynomial centered at for . Use this result to approximate .
for . Use this result to approximate . Unlock Deck
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27
Given ,
(a) calculate .(b) calculate .(c) calculate .
,(a) calculate
.(b) calculate .(c) calculate . Unlock Deck
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28
Find the radius of convergence of the Maclaurin series for .
A)1
E) b. f.4
C) g.8
D) h.2
.A)1
E)
b. f.4C)
g.8D)
h.2 Unlock Deck
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29
Find the coefficient of in the Maclaurin series for .
A)16
E)-16
B) f. c.3
G)-3
D)4
H)0
in the Maclaurin series for .A)16
E)-16
B)
f. c.3G)-3
D)4
H)0
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30
Find the coefficient of in the Maclaurin series for .
A)16
E)-16
B) f. c.3
G)-3
D)4
H)0
in the Maclaurin series for .A)16
E)-16
B)
f. c.3G)-3
D)4
H)0
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31
Use the 3rd-degree Taylor polynomial of about to approximate . Use the remainder term to give an upper bound for the error in this approximation.
about to approximate . Use the remainder term to give an upper bound for the error in this approximation. Unlock Deck
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32
Find the coefficient of in the Maclaurin series for .Note: The series is unique except for the constant of integration.
A) e. b. f. c. g. d. h.
in the Maclaurin series for .Note: The series is unique except for the constant of integration.A)
e. b. f. c. g. d. h. Unlock Deck
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33
Write the Taylor polynomial at 0 of degree 4 for .
. Unlock Deck
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34
Find the second-degree Taylor polynomial of the function .
. Unlock Deck
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35
(a) Use series to compute correct to three decimal places.(b) Use integration by parts to compute .(c) Compare your answers in parts (a) and (b) above.
correct to three decimal places.(b) Use integration by parts to compute .(c) Compare your answers in parts (a) and (b) above. Unlock Deck
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36
Use series to compute correct to four decimal places.
correct to four decimal places. Unlock Deck
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37
Find the third Taylor polynomial associated with . What is the remainder?
. What is the remainder? Unlock Deck
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38
Find the first four terms in the Maclaurin series for .
A) e. b. f. c. g. d. h.
.A)
e. b. f. c. g. d. h. Unlock Deck
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39
The first three derivatives of are , and .(a) Give the first four terms of the Taylor series associated with f at .(b) Give the second-order Taylor polynomial, , associated with f at .(c) Suppose that and that from part (b) is used to approximate . Prove that the error in this approximation does not exceed .
are , and .(a) Give the first four terms of the Taylor series associated with f at .(b) Give the second-order Taylor polynomial, , associated with f at .(c) Suppose that and that from part (b) is used to approximate . Prove that the error in this approximation does not exceed . Unlock Deck
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40
Find the third-degree Taylor polynomial of the function .
. Unlock Deck
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41
Give the Taylor series expansion of about the point .
about the point . Unlock Deck
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42
Find the coefficient of in the binomial series for .
A) e. b. f. c. g. d. h.
in the binomial series for .A)
e. b. f. c. g. d. h. Unlock Deck
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43
(a) Express as a Maclaurin series.(b) Evaluate as a series.
as a Maclaurin series.(b) Evaluate as a series. Unlock Deck
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44
Express as a Maclaurin Series.
as a Maclaurin Series. Unlock Deck
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45
Find the terms of the Maclaurin series for , as far as the term in .
A) e. b. f. c. g. d. h.
, as far as the term in .A)
e. b. f. c. g. d. h. Unlock Deck
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46
(a) Express as a Maclaurin series.(b) Evaluate as a series.
as a Maclaurin series.(b) Evaluate as a series. Unlock Deck
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47
Find the coefficient of in the binomial series for .
A)6
E)-20
B)20
F)-12
C)-6
G)10
D)-10
H)12
in the binomial series for .A)6
E)-20
B)20
F)-12
C)-6
G)10
D)-10
H)12
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48
Find the terms of the Maclaurin series for , as far as the term in .
A) e. b. f. c. g. d. h.
, as far as the term in .A)
e. b. f. c. g. d. h. Unlock Deck
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49
Find the Taylor series for at 2.
at 2. Unlock Deck
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50
Express as a Maclaurin Series.
as a Maclaurin Series. Unlock Deck
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51
Find the Maclaurin series expansion with for . Use this expansion to approximate .
for . Use this expansion to approximate . Unlock Deck
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52
Find the Maclaurin series expansion for and determine the interval of convergence.
and determine the interval of convergence. Unlock Deck
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53
Find the Taylor polynomial of degree 4 at 0 for the function defined by . Then compute the value of accurate to as many decimal places as the polynomial of degree 4 allows.
. Then compute the value of accurate to as many decimal places as the polynomial of degree 4 allows. Unlock Deck
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54
Express as a Maclaurin Series.
as a Maclaurin Series. Unlock Deck
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55
If the Maclaurin series for is , find .
is , find . Unlock Deck
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56
Find the coefficient of in the binomial series for .
A)2
E) b.-1
F) c.1
G)-2
D) h.
in the binomial series for .A)2
E)
b.-1F)
c.1G)-2
D)
h. Unlock Deck
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57
How many coefficients in the binomial series expansion of are divisible by 7?
A)0
E)2
B)5
F)6
C)7
G)1
D)3
H)4
are divisible by 7?A)0
E)2
B)5
F)6
C)7
G)1
D)3
H)4
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58
Find the coefficient of in the binomial series for .
A)3
E)10
B)6
F)5
C)15
G)16
D)20
H)12
in the binomial series for .A)3
E)10
B)6
F)5
C)15
G)16
D)20
H)12
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59
Use the binomial series to expand the function as a power series. Give the coefficient of in that series.
A) e. b. f. c. g. d. h.
as a power series. Give the coefficient of in that series.A)
e. b. f. c. g. d. h. Unlock Deck
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60
Find the Taylor series for about the origin.
about the origin. Unlock Deck
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61
Find the coefficient of in the Maclaurin series for .
in the Maclaurin series for . Unlock Deck
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62
Use the binomial series to expand as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Unlock Deck
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63
Find the terms in the power series expansion for the function , as far as the term in .
, as far as the term in . Unlock Deck
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64
Find the sum of the series .
. Unlock Deck
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65
Find the sum of the series .
. Unlock Deck
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66
Use the binomial series to expand as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Unlock Deck
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67
Which of the following is the power series centered at for ?
1) 2) 3) a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
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68
Which of the following is the power series centered at for ?
1) 2) 3) a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
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69
Use the binomial series formula to obtain the Maclaurin series for .
. Unlock Deck
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70
Which of the following is the power series centered at for ?
1) 2) 3) a.None
E)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
for ?1)
2) 3) a.NoneE)1, 2
B)1
F)1, 3
C)2
G)2, 3
D)3
H)1, 2, 3
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71
If , compute .
, compute . Unlock Deck
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72
Use the binomial series to expand as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Unlock Deck
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73
Find the sum of the series .
. Unlock Deck
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74
Let , compute .
, compute . Unlock Deck
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75
Find the terms of the Maclaurin series for , as far as the term in .
, as far as the term in . Unlock Deck
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76
Find the sum of the series .
. Unlock Deck
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77
If , compute .
, compute . Unlock Deck
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78
Use the binomial series to expand as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Unlock Deck
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79
Use the binomial series to expand as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Unlock Deck
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80
Use the binomial series to expand as a power series. State the radius of convergence.
as a power series. State the radius of convergence. Unlock Deck
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Unlock Deck
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