# Quiz 8: Series

Mathematics

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E

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D

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C

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Q 5Q 5

Find the Maclaurin series for f (x) using the definition of the Maclaurin series.
A)
B)
C)
D)
E)

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Q 6Q 6

Use series to approximate the definite integral to within the indicated accuracy.
A)0.1447
B)0.0354
C)0.0625
D)0.0125
E)0.2774

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Q 7Q 7

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function.
A)
B)
C)
D)
E)

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Q 9Q 9

Find the Taylor series for centered at the given value of
a. Assume that f has a power series expansion. Also find the associated radius of convergence.

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Q 10Q 10

Use the binomial series to expand the function as a power series. Find the radius of convergence.

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Q 13Q 13

Find a power series representation for the function and determine the interval of convergence.
A)
B)
C)
D)
E)

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Q 14Q 14

Find a power series representation for the function and determine the interval of convergence.
A)
B)
C)
D)
E)

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Q 15Q 15

Find a power series representation for the function and determine the interval of convergence.
A)
B)
C)
D)
E)

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Q 16Q 16Find a power series representation for the function and determine the interval of convergence.
A)
B)
C)
D)
E)

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Q 17Q 17

Find a power series representation for the function and determine the radius of convergence.
A)
B)
C)
D)
E)

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Q 18Q 18

Find the radius of convergence and the interval of convergence of the power series.
A)
B)
C)
D)

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Q 19Q 19

Find the radius of convergence and the interval of convergence of the power series.
A)
B)
C)
D)

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Q 21Q 21

Find the radius of convergence and the interval of convergence of the power series.
A)
B)
C)
D)

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Q 25Q 25

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
A)divergent
B)absolutely convergent
C)conditionally convergent

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Q 26Q 26

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
A)divergent
B)conditionally convergent
C)absolutely convergent

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Q 28Q 28

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

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Q 36Q 36

Determine whether the given series converges or diverges. If it converges, find its sum.
A)
B)Diverges
C)
D)

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Q 37Q 37

Determine whether the given series converges or diverges. If it converges, find its sum.
A)
B)Diverges
C)1
D)

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Q 38Q 38

Determine whether the geometric series converges or diverges. If it converges, find its sum.
A)
B)
C)
D)Diverges

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Q 39Q 39

Determine whether the series is convergent or divergent by expressing as a telescoping sum. If it is convergent, find its sum. .
A)
B)diverges
C)
D)
E)

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Q 40Q 40

Determine whether the series is convergent or divergent by expressing as a telescoping sum. If it is convergent, find its sum. .
A)diverges
B)
C)
D)
E)

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Q 41Q 41

When money is spent on goods and services, those that receive the money also spend some of it. The people receiving some of the twice-spent money will spend some of that, and so on. Economists call this chain reaction the multiplier effect. In a hypothetical isolated community, the local government begins the process by spending D dollars. Suppose that each recipient of spent money spends and saves of the money that he or she receives. The values c and s are called the marginal propensity to consume and the marginal propensity to save and, of course, .The number k = 1/s is called the multiplier. What is the multiplier if the marginal propensity to consume is ?
A)4
B)6
C)3
D)7
E)2.5

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Q 43Q 43

A right triangle ABC is given with and . CD is drawn perpendicular to AB, DE is drawn perpendicular to BC, EF AB and this process is continued indefinitely as shown in the figure. Find the total length of all the perpendiculars Write your answer to two decimal places.

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Q 44Q 44

A sequenceis defined recursively by the equation for where . Use your calculator to guess the limit of the sequence.

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Q 47Q 47

Determine whether the sequence defined by converges or diverges. If it converges, find its limit.
A)-5
B)Diverges
C)
D)

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Q 48Q 48

Determine whether the sequence defined by converges or diverges. If it converges, find its limit.
A)1
B)Diverges
C)
D)0

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Q 49Q 49

Determine whether the sequence defined by converges or diverges. If it converges, find its limit.
A)1
B)Diverges
C)0
D)

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Q 50Q 50

If $600 is invested at interest, compounded annually, then after n years the investment is worth dollars. Find the size of investment after 7 years.
A)$430.21
B)$789.56
C)$1,860.81
D)$1,230.81
E)$1,321.06

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Q 51Q 51

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?
A)increasing
B)not monotonic
C)decreasing
D)bounded

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