Quiz 8: Series

Find the Taylor polynomial for the function centered at the number . A) B) C) D) E)

Approximate by a Taylor polynomial with degree at the number . A) B) C) D) E)

Approximate by a Taylor polynomial with degree at the number . A) B) C) D) E)

Approximate by a Taylor polynomial with degree at the number . A) B) C) D) E)

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

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

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)

Find the Maclaurin series for using the definition of a Maclaurin serires.

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.

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

Evaluate the indefinite integral as an infinite series.

Find the sum of the series.

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

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

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

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

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

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

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

Find the interval of convergence of the series. A)diverges everywhere B) C) D) E)

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

Find the radius of convergence of the series. A) B) C) D) E)

Find the radius of convergence and the interval of convergence of the power series.

Which of the given series are absolutely convergent? A) B)

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

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

For which positive integers k is the series convergent? A) B) C) D) E)

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

Find all positive values of u for which the series converges. A) B) C) D) E)

Determine whether the series is convergent or divergent.

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

Use the Integral Test to determine whether the series is convergent or divergent.

Determine whether the given series is convergent or divergent.

Determine whether the series is convergent or divergent.

Use the Comparison Test to determine whether the series is convergent or divergent.

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

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

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

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)

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)

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

Express the number as a ratio of integers.

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.

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

Determine whether the given series converges or diverges. If it converges, find its sum.

Express the number as a rational number.

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

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

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

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

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