EBK WEBASSIGN FOR STEWART'S ESSENTIAL C
2nd Edition
ISBN: 9781337772020
Author: Stewart
Publisher: VST
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Chapter 8.3, Problem 1E
Draw a picture to show that
What can you conclude about the series?
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0
Chapter 8 Solutions
EBK WEBASSIGN FOR STEWART'S ESSENTIAL C
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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- (10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward
- (8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward(4) (10 points) Evaluate √(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z. Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸arrow_forward
- (2) (12 points) Let f(x,y) = x²e¯. (a) (4 points) Calculate Vf. (b) (4 points) Given x directional derivative 0, find the line of vectors u = D₁f(x, y) = 0. (u1, 2) such that the - (c) (4 points) Let u= (1+3√3). Show that Duƒ(1, 0) = ¦|▼ƒ(1,0)| . What is the angle between Vf(1,0) and the vector u? Explain.arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a b 29 39 66.50 C 17.40 d 0 54.0 126° a Ꮎ b darrow_forward(5) (10 points) Let D be the parallelogram in the xy-plane with vertices (0, 0), (1, 1), (1, 1), (0, -2). Let f(x,y) = xy/2. Use the linear change of variables T(u, v)=(u,u2v) = (x, y) 1 to calculate the integral f(x,y) dA= 0 ↓ The domain of T is a rectangle R. What is R? |ǝ(x, y) du dv. |ð(u, v)|arrow_forward
- 2 Anot ined sove in peaper PV+96252 Q3// Find the volume of the region between the cylinder z = y2 and the xy- plane that is bounded by the planes x=1, x=2,y=-2,andy=2. vertical rect a Q4// Draw and Evaluate Soxy-2sin (ny2)dydx D Lake tarrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. B 13 cm 97° Law of Sines Law of Cosines A 43° Then solve the triangle. (Round your answers to two decimal places.) b = x C = A = 40.00arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a 29 b 39 d Ꮎ 126° a Ꮎ b darrow_forward
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