Deck 9: Infinte Series

Question 1

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

Answer 1

1.03448

Question 2

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

Answer 2

1.00104

Question 3

Use a suitable Maclaurin Series to estimate to five decimal-place accuracy.

A) 0.15888
B) 0.15788
C) 0.15848
D) 0.15838
E) 0.15828

Answer 3

0.15838

Question 4

Find the radius of convergence for the series:

A)
B) 1
C)
D)
E) 8

Question 5

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

A) 0.99032
B) 0.99022
C) 0.99037
D) 0.99027
E) 0.99017

Question 6

Use a suitable Maclaurin Series to estimate to five decimal-place accuracy.

Question 7

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

Question 8

Find the radius of convergence for the series:

A) 2
B) 1
C)
D)
E) 4

Question 9

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

Question 10

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

Question 11

Use a suitable Maclaurin Series to estimate to four decimal place accuracy.

Question 12

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

A) 0.99993
B) 0.99983
C) 0.99998
D) 0.99988
E) 0.99978

Question 13

Use a suitable Maclaurin Series to estimate to five decimal-place accuracy.

A) 0.09528
B) 0.09428
C) 0.09488
D) 0.09478
E) 0.09468

Question 14

Find the radius of convergence for the series:

A) 4
B) 1
C)
D)
E) 2

Question 15

Use the Remainder Estimation Theorem to find an interval containing 0 over which can be approximated by within an accuracy of .

Question 16

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

A) 0.07482
B) 0.07472
C) 0.07487
D) 0.07477
E) 0.07467

Question 17

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

A) 1.00129
B) 1.00119
C) 1.00134
D) 1.00124
E) 1.00114

Question 18

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

A) 0.00915
B) 0.00905
C) 0.00920
D) 0.00910
E) 0.00900

Question 19

Use a suitable Maclaurin Series to estimate to five decimal place accuracy.

A) 0.30907
B) 0.30897
C) 0.30912
D) 0.30902
E) 0.30892

Question 20

Use the Remainder Estimation Theorem to find an interval containing 0 over which can be approximated by within an accuracy of .

Question 21

Find the radius of convergence for the series:

A) 6
B) 1
C)
D)
E) 2

Question 22

Find the interval of convergence for the series:

A)
B)
C)
D)
E)

Question 23

Find the interval of convergence for the series:

A)
B)
C)
D)
E)

Question 24

Find the interval of convergence for the series:

Question 25

Find the interval of convergence for the series:

Question 26

Find the interval of convergence for the series:

A)
B)
C)
D)
E)

Question 27

Find the interval of convergence for the series:

Question 28

Find the radius of convergence for the series:

A) 2
B)
C)
D)
E) 5

Question 29

Find the interval of convergence for the series:

A)
B) ( ]
C) [ )
D)
E)

Question 30

Find the interval of convergence for the series:

A) [ )
B)
C) ( ]
D)
E)

Question 31

Find the interval of convergence for the series:

Question 32

Find the interval of convergence for the series:

Question 33

Find the radius of convergence for the series:

A) 2
B) 1
C)
D)
E) 3

Question 34

Find the interval of convergence for the series:

Question 35

Find the interval of convergence for the series:

Question 36

Find the interval of convergence for the series:

A)
B)
C)
D)
E)

Question 37

Find the interval of convergence for the series:

A)
B)
C)
D)
E)

Question 38

Find the interval of convergence for the series:

Question 39

Find the interval of convergence for the series:

A)
B)
C)
D)
E)

Question 40

Find the interval of convergence for the series:

Question 41

Find the Maclaurin polynomial of order 2 for

Question 42

Find the interval of convergence for the series:

Question 43

Find the Maclaurin polynomial of order 2 for

A)
B)
C)
D)
E)

Question 44

Find the interval of convergence for the series:

Question 45

Find the Taylor polynomial of order 2 for , centered about .

A)
B)
C)
D)
E)

Question 46

Find the interval of convergence for the series:

Question 47

Find the Maclaurin polynomial of order 2 for

Question 48

Find the Maclaurin polynomial of order 2 for .

A)
B)
C)
D)
E)

Question 49

Find the Maclaurin polynomial of order 2 for .

A)
B)
C)
D)
E)

Question 50

Find the Taylor polynomial of order 2 for , centered about .

A)
B)
C)
D)
E)

Question 51

Find the interval of convergence for the series:

Question 52

Find the Maclaurin polynomial of order 2 for

Question 53

Find the Taylor polynomial of order 2 for , centered about .

A)
B)
C)
D)
E)

Question 54

Find the Taylor polynomial of order 2 for

A)
B)
C)
D)
E)

Question 55

Find the interval of convergence for the series:

Question 56

Find the Maclaurin polynomial of order 2 for .

A)
B)
C)
D)
E)

Question 57

Find the Maclaurin polynomial of order 2 for .

A)
B)
C)
D)
E)

Question 58

Find the Taylor polynomial of order 2 for , centered about .

A)
B)
C)
D)
E)

Question 59

Find the interval of convergence for the series:

Question 60

Find the interval of convergence for the series:

Question 61

Find the Maclaurin polynomial of order 3 for .

Question 62

Find the Taylor polynomial of order 4 for the function centered at .

Question 63

Classify the following series as absolutely convergent, conditionally convergent, or divergent.

A) Absolutely convergent
B) Conditionally convergent
C) Divergent

Question 64

Find the Taylor polynomial of order 4 for the function centered at .

Question 65

Classify the following series as absolutely convergent, conditionally convergent, or divergent.

A) Absolutely convergent
B) Conditionally convergent
C) Divergent

Question 66

Find the Taylor polynomial of order 3 for the function centered at .

Question 67

Find the Maclaurin polynomial of order 2 for by multiplying known Maclaurin series for the two functions.

Question 68

Find the third order Taylor polynomial for , centered at .

Question 69

Find the second order Taylor polynomial for the function , centered at .

Question 70

Find the third order Taylor polynomial for , centered at .

Question 71

Use the Remainder Estimation Theorem to find an interval containing 0 over which can be approximated by within an accuracy of . Give answers to six decimal places.

Question 72

Find the Taylor polynomial of order 3 for the function centered at .

Question 73

Classify the following series as absolutely convergent, conditionally convergent, or divergent.

A) Absolutely convergent
B) Conditionally convergent
C) Divergent

Question 74

Find the third order Taylor polynomial for , centered at .

Question 75

Classify the following series as absolutely convergent, conditionally convergent, or divergent.

A) Absolutely convergent
B) Conditionally convergent
C) Divergent

Question 76

Use the Remainder Estimation Theorem to find an interval containing 0 over which can be approximated by within an accuracy of . Give answers to six decimal places.

Question 77

Find the Taylor polynomial of order 3 for the function centered at .

Question 78

Find the third order Taylor polynomial for , centered at .

Question 79

Classify the following series as absolutely convergent, conditionally convergent, or divergent.

A) Absolutely convergent
B) Conditionally convergent
C) Divergent

Question 80

Find the Taylor polynomial of order 3 for the function centered at .