Essential Calculus: Early Transcendentals
2nd Edition
ISBN: 9781133112280
Author: James Stewart
Publisher: Cengage Learning
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Textbook Question
Chapter 8.2, Problem 59E
Consider the series
(a) Find the partial sums s1, s2, s3, and s4. Do you recognize the denominators? Use the pattern to guess a formula for sn.
(b) Use mathematical induction to prove your guess.
(c) Show that the given infinite series is convergent, and find its sum.
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Chapter 8 Solutions
Essential Calculus: Early Transcendentals
Ch. 8.1 - (a) What is a sequence? (b) What does it mean to...Ch. 8.1 - Prob. 2ECh. 8.1 - List the first six terms of the sequence defined...Ch. 8.1 - List the first nine terms of the sequence...Ch. 8.1 - Find a formula for the general term an of the...Ch. 8.1 - Find a formula for the general term an of the...Ch. 8.1 - Find a formula for the general term an of the...Ch. 8.1 - Find a formula for the general term an of the...Ch. 8.1 - Determine whether sequence converges or diverges....Ch. 8.1 - Determine whether the sequence converges or...
Ch. 8.1 - Determine whether the sequence converges or...Ch. 8.1 - Determine whether the sequence converges or...Ch. 8.1 - Find a formula for the general term an of the...Ch. 8.1 - Determine whether the sequence converges or...Ch. 8.1 - Determine whether the sequence converges or...Ch. 8.1 - Determine whether the sequence converges or...Ch. 8.1 - Determine whether the sequence converges or...Ch. 8.1 - Determine whether sequence converges or diverges....Ch. 8.1 - Prob. 19ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 21ECh. 8.1 - Determine whether sequence converges or diverges....Ch. 8.1 - Prob. 23ECh. 8.1 - Determine whether sequence converges or diverges....Ch. 8.1 - Determine whether sequence converges or diverges....Ch. 8.1 - Prob. 26ECh. 8.1 - Determine whether sequence converges or diverges....Ch. 8.1 - Prob. 31ECh. 8.1 - Prob. 30ECh. 8.1 - Determine whether sequence converges or diverges....Ch. 8.1 - Determine whether sequence converges or diverges....Ch. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 37ECh. 8.1 - Determine whether the sequence is increasing,...Ch. 8.1 - Determine whether the sequence is increasing,...Ch. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - A sequence {an} is given by a1=2,an+1=2+an. (a) By...Ch. 8.1 - Use induction to show that the sequence defined by...Ch. 8.1 - Show that the sequence defined by a1=2an+1=13an...Ch. 8.1 - (a) Fibonacci posed the following problem: Suppose...Ch. 8.1 - (a) Let a1 = a, a2 = f(a), a3 = f(a2) = f(f(a)), ....Ch. 8.1 - We know that limn(0.8)n=0 [from 8 with r = 0.8]....Ch. 8.1 - Use Definition 2 directly to prove that limn rn =...Ch. 8.1 - Prove Theorem 6. [Hint: Use either Definition 2 or...Ch. 8.1 - Prove the Continuity and Convergence Theorem.Ch. 8.1 - Prove that if limn an = 0 and {bn} is bounded,...Ch. 8.1 - (a) Show that if limna2n = L and limna2n+1 = L,...Ch. 8.1 - The size of an undisturbed fish population has...Ch. 8.2 - (a) What is the difference between a sequence and...Ch. 8.2 - Explain what it means to say that n=1an=5.Ch. 8.2 - Calculate the first eight terms of the sequence of...Ch. 8.2 - Determine whether the geometric series is...Ch. 8.2 - Determine whether the geometric series is...Ch. 8.2 - Calculate the first eight terms of the sequence of...Ch. 8.2 - Determine whether the geometric series is...Ch. 8.2 - Determine whether the geometric series is...Ch. 8.2 - Prob. 9ECh. 8.2 - Determine whether the geometric series is...Ch. 8.2 - Determine whether the geometric series is...Ch. 8.2 - Determine whether the geometric series is...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Determine whether the series is convergent or...Ch. 8.2 - Let X = 0.99999 .... (a) Do you think that x 1 or...Ch. 8.2 - A sequence of terms is defined by a1, = 1 an,= (5 ...Ch. 8.2 - Prob. 31ECh. 8.2 - Express the number as a ratio of integers. 52....Ch. 8.2 - Express the number as a ratio of integers. 53....Ch. 8.2 - Prob. 34ECh. 8.2 - Find the values of x for which the series...Ch. 8.2 - Find the values of x for which the series...Ch. 8.2 - Find the values of x for which the series...Ch. 8.2 - We have seen that the harmonic series is a...Ch. 8.2 - If the nth partial sum of a series n=1an is...Ch. 8.2 - If the nth partial sum of a series n=1an is sn = 3...Ch. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - When money is spent on goods and services, those...Ch. 8.2 - A certain ball has the property that each time it...Ch. 8.2 - Find the value of c if n=2(1+c)n=2Ch. 8.2 - Graph the curves y = xn, 0x1, for n = 0, 1, 2, 3,...Ch. 8.2 - The figure shows two circles C and D of radius 1...Ch. 8.2 - A right triangle ABC is given with A = and...Ch. 8.2 - What is wrong with the following calculation?...Ch. 8.2 - Suppose thatn=1an(an0) is known to be a convergent...Ch. 8.2 - Prove part (i) of Theorem 8.Ch. 8.2 - If an is divergent and c 0, show thatan, is...Ch. 8.2 - If an is convergent and bn is divergent, show that...Ch. 8.2 - If an and bn are both divergent, is (an + bn)...Ch. 8.2 - Suppose that a series an bas positive terms and...Ch. 8.2 - The Fibonacci sequence was defined in Section 8.1...Ch. 8.2 - The Cantor set, named after the German...Ch. 8.2 - (a) A sequence {an} is defined recursively by the...Ch. 8.2 - Consider the series n=1n/(n+1)!. (a) Find the...Ch. 8.2 - In the figure at the right there are infinitely...Ch. 8.3 - Draw a picture to show that n=21n1.311x1.3dx What...Ch. 8.3 - Suppose f is a continuous positive decreasing...Ch. 8.3 - Use the Integral Test to determine whether the...Ch. 8.3 - Use the Integral Test to determine whether the...Ch. 8.3 - Use the Integral Test to determine whether the...Ch. 8.3 - Prob. 11ECh. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - 11-30 Determine whether the series is convergent...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Find the values of p for which the series is...Ch. 8.3 - Find the values of p for which the series is...Ch. 8.3 - (a) Find the partial sum s10 of the series...Ch. 8.3 - (a) Use the sum of the first 10 terms and Exercise...Ch. 8.3 - Find the sum of the series n11/n5 correct to three...Ch. 8.3 - Show that if we want to approximate the sum of the...Ch. 8.3 - (a) Use a graph of y = 1/x to show that if sn is...Ch. 8.3 - Find all values of c for which the following...Ch. 8.3 - Prob. 3ECh. 8.3 - Suppose an and bn are series with positive terms...Ch. 8.3 - The meaning of the decimal representation of a...Ch. 8.3 - Find all positive values of b for which the series...Ch. 8.3 - Prove that if an 0 and an converges. Then an2...Ch. 8.3 - (a) Suppose that an and bn are series with...Ch. 8.3 - (a) Suppose that an and bn are series with...Ch. 8.3 - Give an example of a pair of series an and bn...Ch. 8.3 - Show that if an 0 and limnnan0 then an is...Ch. 8.3 - Show that if an 0 and an is convergent, then...Ch. 8.3 - Prob. 41ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 9ECh. 8.3 - Use the Comparison Test to determine whether the...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Determine whether the series is convergent or...Ch. 8.3 - Let s be the sum of a series an that has been...Ch. 8.4 - (a) What is an alternating series? (b) Under what...Ch. 8.4 - Test the series for convergence or divergence....Ch. 8.4 - Test the series for convergence or divergence....Ch. 8.4 - Test the series for convergence or divergence....Ch. 8.4 - Test the series for convergence or divergence....Ch. 8.4 - Test the series for convergence or divergence. 7....Ch. 8.4 - Test the series for convergence or divergence. 18....Ch. 8.4 - Show that the series is convergent. How many terms...Ch. 8.4 - Show that the series is convergent. How many terms...Ch. 8.4 - Show that the series is convergent. How many terms...Ch. 8.4 - Show that the series is convergent. How many terms...Ch. 8.4 - Approximate the sum of the series correct to four...Ch. 8.4 - Approximate the sum of the series correct to four...Ch. 8.4 - Approximate the sum of the series correct to four...Ch. 8.4 - Approximate the sum of the series correct to four...Ch. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - What can you say about the series an in each of...Ch. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Prob. 21ECh. 8.4 - Prob. 25ECh. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Prob. 22ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 27ECh. 8.4 - Prob. 26ECh. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Use the Ratio Test to determine whether the series...Ch. 8.4 - Use the Ratio Test to determine whether the series...Ch. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Determine whether the series is absolutely...Ch. 8.4 - Use any test to determine whether the series is...Ch. 8.4 - Use any test to determine whether the series is...Ch. 8.4 - Let {bn} be a sequence of positive numbers that...Ch. 8.4 - Let {bn} be a sequence of positive numbers that...Ch. 8.4 - For which of the following series is the Ratio...Ch. 8.4 - For which positive integers k is the following...Ch. 8.4 - (a) Show that n=0xn/n! converges for all x. (b)...Ch. 8.4 - Prove the Root Test. [Hint for part (i): Take any...Ch. 8.4 - Around 1910, the Indian mathematician Srinivasa...Ch. 8.5 - What is a power series?Ch. 8.5 - (a) What is the radius of convergence of a power...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - Find the radius of convergence and interval of...Ch. 8.5 - If n=0cn4n is convergent, can we conclude that...Ch. 8.5 - Suppose that n=0cnxn converges when x = 4 and...Ch. 8.5 - If k is a positive integer, find the radius of...Ch. 8.5 - Let p and q be real numbers with p q. Find a...Ch. 8.5 - Is it possible to find a power series whose...Ch. 8.5 - Graph the first several partial sums sn(x) of the...Ch. 8.5 - A function f is defined by f(x)=1+2x+x2+2x3+x4+...Ch. 8.5 - If f(x)=n=0cnxn, where cn+4 = cn for all n 0,...Ch. 8.5 - Show that if limn|cn|n=c, where c 0, then the...Ch. 8.5 - Suppose that the power series cn(xa)n satisfies...Ch. 8.5 - Suppose the series cnxn has radius of convergence...Ch. 8.5 - Suppose that the radius of convergence of the...Ch. 8.6 - If the radius of convergence of the power series...Ch. 8.6 - Suppose you know that the series n=0bnxn converges...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Express the function as the sum of a power series...Ch. 8.6 - Express the function as the sum of a power series...Ch. 8.6 - (a) Use differentiation to find a power series...Ch. 8.6 - (a) Use Equation I to find a power series...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for the...Ch. 8.6 - Find a power series representation for f, and...Ch. 8.6 - Find a power series representation for f, and...Ch. 8.6 - Find a power series representation for f , and...Ch. 8.6 - Find a power series representation for f , and...Ch. 8.6 - Evaluate the indefinite integral as a power...Ch. 8.6 - Evaluate the indefinite integral as a power...Ch. 8.6 - Evaluate the indefinite integral as a power...Ch. 8.6 - Evaluate the indefinite integral as a power...Ch. 8.6 - Use a power series to approximate the definite...Ch. 8.6 - Use a power series to approximate the definite...Ch. 8.6 - Use a power series to approximate the defnite...Ch. 8.6 - Use a power series to approximate the definite...Ch. 8.6 - Use the result of Example 7 to compute arctan 0.2...Ch. 8.6 - Show that the function f(x)=n=0(1)nx2n(2n)! is a...Ch. 8.6 - (a) Show that J0 (the Bessel function of order 0...Ch. 8.6 - The Bessel function of order l is defined by...Ch. 8.6 - (a) Show that the function f(x)=n=0xnn! is a...Ch. 8.6 - Let fn(x)=(sinnx)/n2.Show that the series fn(x)...Ch. 8.6 - Let f(x)=n=1xnn2 Find the intervals of convergence...Ch. 8.6 - (a) Starting with lhe geometric series n=0xn, find...Ch. 8.6 - Use the power series for tan-1x to prove the...Ch. 8.6 - Find the sum of the series n=14nn5nCh. 8.7 - If f(x)=n=0bn(x5)n for all x, write a formula for...Ch. 8.7 - The graph of f is shown. (a) Explain why the...Ch. 8.7 - If f(n)(0) = (n + 1)! for n = 0, 1, 2, , find the...Ch. 8.7 - Find the Taylor series for f centered at 4 if...Ch. 8.7 - Find the Maclaurin series for f(x) using the...Ch. 8.7 - Find the Maclaurin series for f(x) using the...Ch. 8.7 - Find the Maclaurin series for f(x) using the...Ch. 8.7 - Find the Maclaurin series for f(x) using the...Ch. 8.7 - Find the Maclaurin series for f(x) using the...Ch. 8.7 - Find the Maclaurin series for f(x) using the...Ch. 8.7 - Find the Taylor series for f(x) centered at the...Ch. 8.7 - Find the Taylor series for f(x) centered at the...Ch. 8.7 - Find the Taylor series for .f(x) centered at the...Ch. 8.7 - Find the Taylor series for .f(x) centered at the...Ch. 8.7 - Find the Taylor series for f(x) centered at the...Ch. 8.7 - Find the Taylor series for f(x) centered at the...Ch. 8.7 - Find the Taylor series for f(x) centered at the...Ch. 8.7 - Find the Taylor series for f(x) centered at the...Ch. 8.7 - Prove that the series obtained in Exercise 7...Ch. 8.7 - Prove that the series obtained in Exercise 16...Ch. 8.7 - Prove that the series obtained in Exercise 9...Ch. 8.7 - Prove that the series obtained in Exercise 10...Ch. 8.7 - Prob. 23ECh. 8.7 - Prob. 24ECh. 8.7 - Use the binomial series to expand the function as...Ch. 8.7 - Use the binomial series to expand the function as...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Use a Maclaurin series in Table 1 to obtain the...Ch. 8.7 - Find the Maclaurin series of f (by any method) and...Ch. 8.7 - Find the Maclaurin series of f (by any method) and...Ch. 8.7 - Use the Maclaurin series for cos x to compute cos...Ch. 8.7 - Use the Maclaurin series for ex to calculate 1/e10...Ch. 8.7 - (a) Use the binomial series to expand 1/1x2. (b)...Ch. 8.7 - (a) Expand 1/1+x4 as a power series. (b) Use part...Ch. 8.7 - Evaluate the indefinite integral as an infinite...Ch. 8.7 - Evaluate the indefinite integral as an infinite...Ch. 8.7 - Evaluate the indefinite integral as an infinite...Ch. 8.7 - Evaluate the indefinite integral as an infinite...Ch. 8.7 - Use series to approximate the definite integral to...Ch. 8.7 - Use series to approximate the definite integral to...Ch. 8.7 - Use series to approximate the definite integral to...Ch. 8.7 - Use series to approximate the definite integral to...Ch. 8.7 - Use series to evaluate the limit. 61....Ch. 8.7 - Use series to evaluate the limit. 62....Ch. 8.7 - Use series to evaluate the limit. 63....Ch. 8.7 - Use the series in Example 11(b) to evaluate...Ch. 8.7 - Use multiplication or division of power series to...Ch. 8.7 - Use multiplication or division of power series to...Ch. 8.7 - Use multiplication or division of power series to...Ch. 8.7 - Use multiplication or division of power series to...Ch. 8.7 - Find the sum of the series. 73. n=0(1)nx4nn!Ch. 8.7 - Find the sum of the series. 74. n=0(1)n2n62n(2n)!Ch. 8.7 - Find the sum of the series. 76. n=03n5nn!Ch. 8.7 - Find the sum of the series. 77....Ch. 8.7 - Find the sum of the series. 78....Ch. 8.7 - Find the sum of the series. 79. 3+92!+273!+814!+Ch. 8.7 - (a) Expand f(x) = x/(1 x)2 as a power series. (b)...Ch. 8.7 - (a) Expand f(x) = (x + x2)/(1 x)3 as a power...Ch. 8.7 - Show that if p is an nth-degree polynomial, then...Ch. 8.7 - If f(x) = ( 1 + x3)30, what is f(58)(0)?Ch. 8.7 - (a) Show that the function defined by...Ch. 8.7 - Use the following steps to prove 18. (a) Let...Ch. 8.8 - (a) Find the Taylor polynomials up to degree 6 for...Ch. 8.8 - (a) Find the Taylor polynomials up to degree 3 for...Ch. 8.8 - Find the Taylor polynomial T3(x) for the function...Ch. 8.8 - Find the Taylor polynomial T3(x) for the function...Ch. 8.8 - Find the Taylor polynomial T3(x) for the function...Ch. 8.8 - Find the Taylor polynomial T3(x) for the function...Ch. 8.8 - Find the Taylor polynomial T3(x) for the function...Ch. 8.8 - Find the Taylor polynomial T3(x) for the function...Ch. 8.8 - (a) Approxinate f by a Taylor polynomial with...Ch. 8.8 - (a) Approxinate f by a Taylor polynomial with...Ch. 8.8 - (a) Approximate f by a Taylor polynomial with...Ch. 8.8 - (a) Approximate f by a Taylor polynomial with...Ch. 8.8 - (a) Approximate f by a Taylor polynomial with...Ch. 8.8 - (a) Approximate f by a Taylor polynomial with...Ch. 8.8 - Prob. 16ECh. 8.8 - Prob. 15ECh. 8.8 - Use the information from Exercise 5 to estimate...Ch. 8.8 - Prob. 18ECh. 8.8 - Prob. 19ECh. 8.8 - Use the Alternating Series Estimation Theorem or...Ch. 8.8 - Use the Alternating Series Estimation Theorem or...Ch. 8.8 - Prob. 20ECh. 8.8 - A car is moving with speed 20 m/s and acceleration...Ch. 8.8 - Prob. 24ECh. 8.8 - Prob. 25ECh. 8.8 - Prob. 26ECh. 8.8 - If a surveyor measures differences in elevation...Ch. 8.8 - Prob. 28ECh. 8.8 - Prob. 29ECh. 8.8 - Prob. 30ECh. 8 - Prob. 1RCCCh. 8 - Prob. 2RCCCh. 8 - Prob. 3RCCCh. 8 - Prob. 4RCCCh. 8 - Prob. 5RCCCh. 8 - Prob. 6RCCCh. 8 - Prob. 7RCCCh. 8 - (a) Write the general form of a power series. (b)...Ch. 8 - Suppose f(x) is the sum of a power series with...Ch. 8 - Prob. 10RCCCh. 8 - Prob. 11RCCCh. 8 - Prob. 12RCCCh. 8 - Prob. 1RQCh. 8 - Prob. 2RQCh. 8 - Prob. 3RQCh. 8 - Determine whether the statement is true or false....Ch. 8 - Prob. 5RQCh. 8 - Prob. 6RQCh. 8 - Prob. 7RQCh. 8 - Prob. 8RQCh. 8 - Prob. 9RQCh. 8 - Prob. 10RQCh. 8 - Prob. 11RQCh. 8 - Prob. 12RQCh. 8 - Prob. 13RQCh. 8 - Prob. 14RQCh. 8 - Prob. 15RQCh. 8 - Prob. 16RQCh. 8 - Prob. 17RQCh. 8 - Prob. 18RQCh. 8 - Prob. 19RQCh. 8 - Prob. 20RQCh. 8 - Prob. 21RQCh. 8 - Prob. 22RQCh. 8 - Determine whether the sequence is convergent or...Ch. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Determine whether the sequence is convergent or...Ch. 8 - Determine whether the sequence is convergent or...Ch. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Determine whether the sequence is convergent or...Ch. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is convergent or...Ch. 8 - Determine whether the series is conditionally...Ch. 8 - Determine whether the series is conditionally...Ch. 8 - Determine whether the series is conditionally...Ch. 8 - Determine whether the series is conditionally...Ch. 8 - Find the sum of the series. 25. n122n+15nCh. 8 - Find the sum of the series. 28. n=11n(n+3)Ch. 8 - Find the sum of the series. 29....Ch. 8 - Find the sum of the series. 30. n=0(1)nn32n(2n)!Ch. 8 - Find the sum of the series. 31. 1e+e22!e33!+e44!Ch. 8 - Express the repeating decimal 4.17326326326 . . ....Ch. 8 - Show that cosh x1+12x2 for all x.Ch. 8 - For what values of x does the series n=1(Inx)n...Ch. 8 - Find the sum of the series n=1(1)n+1n5 correct to...Ch. 8 - (a) Show that the series n=1nn(2n)! is convergent....Ch. 8 - Prove that if the seriesn=1an is absolutely...Ch. 8 - Find the radius of convergence and interval of...Ch. 8 - Find the radius of convergence and interval of...Ch. 8 - Find the radius of convergence and interval of...Ch. 8 - Find the radius of convergence and interval of...Ch. 8 - Find the radius of convergence of the series...Ch. 8 - Find the Taylor series of f(x) = sin x at a = /6.Ch. 8 - Find the Taylor series of f(x) = cos x at a = /3.Ch. 8 - Find the Maclaurin series for f and its radius of...Ch. 8 - Find the Maclaurin series for f and its radius of...Ch. 8 - Find the Maclaurin series for f and its radius of...Ch. 8 - Find the Maclaurin series for f and its radius of...Ch. 8 - Find the Maclaurin series for f and its radius of...Ch. 8 - Find the Maclaurin series for f and its radius of...Ch. 8 - Find the Maclaurin series for f and its radius of...Ch. 8 - Find the Maclaurin series for f and its radius of...Ch. 8 - Evaluate exxdx as an infinite series.Ch. 8 - Use series to approximate 011+x4dx correct to two...Ch. 8 - (a) Approximate f by a Taylor polynomial with...Ch. 8 - (a) Approximate f by a Taylor polynomial with...Ch. 8 - Use series to evaluate the following limit....Ch. 8 - The force due to gravity on an object with mass m...Ch. 8 - Suppose that f(x)=n=0cnxn for all x. (a) If f is...Ch. 8 - If f(x)=ex2, show that f(2n)(0)=(2n)!n!.
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- Question 8 Use the graph of f to evaluate the following: 6 f(x) 5 4 3 2 1 -1 1 2 3 4 5 -1 t The average rate of change of f from 4 to 5 = Question 9 10 ☑ 4parrow_forwardQuestion 15 ✓ 6 pts 1 Details The function shown below is f(x). We are interested in the transformed function g(x) = 3f(2x) - 1 a) Describe all the transformations g(x) has made to f(x) (shifts, stretches, etc). b) NEATLY sketch the transformed function g(x) and upload your graph as a PDF document below. You may use graph paper if you want. Be sure to label your vertical and horizontal scales so that I can tell how big your function is. 1- 0 2 3 4 -1- Choose File No file chosen Question 16 0 pts 1 Detailsarrow_forwardhelparrow_forward
- Question 2 Let F be a solenoidal vector field, suppose V × F = (-8xy + 12z², −9x² + 4y² + 9z², 6y²), and let (P,Q,R) = V²F(.725, —.283, 1.73). Then the value of sin(2P) + sin(3Q) + sin(4R) is -2.024 1.391 0.186 -0.994 -2.053 -0.647 -0.588 -1.851 1 ptsarrow_forward1 pts Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is Question 1 -0.246 0.072 -0.934 0.478 -0.914 -0.855 0.710 0.262 .arrow_forwardanswerarrow_forward
- 1. Given the vector field F(x, y, z) = -zi, verify the relation 1 VF(0,0,0) lim +0+ volume inside S ff F• Nds S. where S, is the surface enclosing a cube centred at the origin and having edges of length 2€. Then, determine if the origin is sink or source.arrow_forwardLet a = (-4, 5, 4) and 6 = (1,0, -1). Find the angle between the vector 1) The exact angle is cos 2) The approximation in radians isarrow_forwardFind the (exact) direction cosines and (rounded to 1 decimal place) direction angles of = (3,7,6)arrow_forward
- Let a = (-1, -2, -3) and 6 = (-4, 0, 1). Find the component of b onto a.arrow_forwardForces of 9 pounds and 15 pounds act on each other with an angle of 72°. The magnitude of the resultant force The resultant force has an angle of pounds. * with the 9 pound force. The resultant force has an angle of with the 15 pound force. It is best to calculate each angle separately and check by seeing if they add to 72°.arrow_forward= Let (6,2,-5) and = (5,4, -6). Compute the following: บี.บี. บี. นี = 2 −4(u. v) = (-4). v= ū. (-40) (ū. v) v =arrow_forward
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