Single Variable Calculus
Single Variable Calculus
8th Edition
ISBN: 9781305266636
Author: James Stewart
Publisher: Cengage Learning
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Sequence and Series
A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.
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Chapter 11.1, Problem 63E

Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the margin note on page 739 for advice on graphing sequences.)

63. a n = 1 ⋅ 3 ⋅ 5 ⋅ ⋯ ( 2 n − 1 ( 2 n ) n

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Chapter 11 Solutions

Single Variable Calculus

Ch. 11.1 - (a) What is a sequence? (b) What does it mean to...Ch. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Calculate, to four decimal places, the first ten...Ch. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Prob. 47ECh. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Prob. 53ECh. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Determine whether the sequence converges or...Ch. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Prob. 59ECh. 11.1 - Use a graph of the sequence to decide whether the...Ch. 11.1 - Prob. 61ECh. 11.1 - Prob. 62ECh. 11.1 - Use a graph of the sequence to decide whether the...Ch. 11.1 - (a) Determine whether the sequence defined as...Ch. 11.1 - Prob. 65ECh. 11.1 - Prob. 66ECh. 11.1 - Prob. 67ECh. 11.1 - Find the first 40 terms of the sequence defined...Ch. 11.1 - For what values of r is the sequence {nrn}...Ch. 11.1 - Prob. 70ECh. 11.1 - Prob. 71ECh. 11.1 - Determine whether the sequence is increasing,...Ch. 11.1 - Prob. 73ECh. 11.1 - Prob. 74ECh. 11.1 - Determine whether the sequence is increasing,...Ch. 11.1 - Determine whether the sequence is increasing,...Ch. 11.1 - Prob. 77ECh. 11.1 - Determine whether the sequence is increasing,...Ch. 11.1 - Prob. 79ECh. 11.1 - Prob. 80ECh. 11.1 - Show that the sequence defined by a1=1an+1=31an is...Ch. 11.1 - Prob. 82ECh. 11.1 - (a) Fibonacci posed the following problem: Suppose...Ch. 11.1 - (a) Let a1 = a, a2 =f(a), a3 = f(a2) = f(f(a)),,...Ch. 11.1 - Prob. 85ECh. 11.1 - Prob. 86ECh. 11.1 - Prob. 87ECh. 11.1 - Prob. 88ECh. 11.1 - Prove that if limn an = 0 and {bn} is bounded,...Ch. 11.1 - Let an(1+1n)n (a) Show that if 0 a b, then...Ch. 11.1 - Let a and b be positive numbers with a b. Let a1...Ch. 11.1 - Prob. 92ECh. 11.1 - Prob. 93ECh. 11.2 - (a) What is the difference between a sequence and...Ch. 11.2 - Explain what it means to say that n=1an=5.Ch. 11.2 - Calculate the sum of the series n=1an whose...Ch. 11.2 - Calculate the sum of the series n=1an whose...Ch. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Let an=2n3n+1. (a) Determine whether {an} is...Ch. 11.2 - (a) Explain the difference between i=1naiandj=1naj...Ch. 11.2 - Determine whether the geometric series is...Ch. 11.2 - Determine whether the geometric series is...Ch. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Determine whether the geometric series is...Ch. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Determine whether the geometric series is...Ch. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Prob. 28ECh. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Prob. 45ECh. 11.2 - Determine whether the series is convergent or...Ch. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - A sequence of terms is defined by a1=1an=(5n)an1...Ch. 11.2 - Prob. 51ECh. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Prob. 54ECh. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.2 - Prob. 57ECh. 11.2 - Find the values of x for which the series...Ch. 11.2 - Prob. 59ECh. 11.2 - Find the values of x for which the series...Ch. 11.2 - Find the values of x for which the series...Ch. 11.2 - Find the values of x for which the series...Ch. 11.2 - Prob. 63ECh. 11.2 - Prob. 64ECh. 11.2 - Prob. 67ECh. 11.2 - If the nth partial sum of a series n=1an is sn = 3...Ch. 11.2 - Prob. 69ECh. 11.2 - Prob. 70ECh. 11.2 - Prob. 71ECh. 11.2 - Prob. 72ECh. 11.2 - Prob. 73ECh. 11.2 - Prob. 74ECh. 11.2 - Prob. 75ECh. 11.2 - Prob. 76ECh. 11.2 - Prob. 77ECh. 11.2 - Prob. 78ECh. 11.2 - Prob. 79ECh. 11.2 - Prob. 80ECh. 11.2 - Prob. 81ECh. 11.2 - Prob. 82ECh. 11.2 - Prob. 83ECh. 11.2 - Prob. 84ECh. 11.2 - If an is convergent and bn is divergent, show...Ch. 11.2 - Prob. 86ECh. 11.2 - Prob. 87ECh. 11.2 - Prob. 88ECh. 11.2 - The Cantor set, named after the German...Ch. 11.2 - Prob. 90ECh. 11.2 - Prob. 91ECh. 11.2 - Prob. 92ECh. 11.3 - Draw a picture to show that n=21n1,311x1,3dx What...Ch. 11.3 - Suppose f is a continuous positive decreasing...Ch. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Prob. 15ECh. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Prob. 19ECh. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Prob. 21ECh. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Prob. 23ECh. 11.3 - Determine whether the series is convergent or...Ch. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Explain why the Integral Test cant be used to...Ch. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Find the values of p for which the series is...Ch. 11.3 - Prob. 33ECh. 11.3 - Leonhard Euler was able to calculate the exact sum...Ch. 11.3 - Prob. 35ECh. 11.3 - (a) Find the partial sum s10 of the series...Ch. 11.3 - Prob. 37ECh. 11.3 - Find the sum of the series n=1ne2n correct to four...Ch. 11.3 - Estimate n=1(2n+1)6 correct to five decimal...Ch. 11.3 - How many terms of the series n=21/[n(lnn)2] would...Ch. 11.3 - Prob. 41ECh. 11.3 - Prob. 43ECh. 11.3 - Prob. 44ECh. 11.3 - Prob. 45ECh. 11.3 - Prob. 46ECh. 11.4 - Suppose an and bn are series with positive terms...Ch. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Prob. 45ECh. 11.4 - Prob. 46ECh. 11.5 - (a) What is an alternating series? (b) Under what...Ch. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Test the series for convergence or divergence. 4....Ch. 11.5 - Prob. 5ECh. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - Prob. 19ECh. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Prob. 23ECh. 11.5 - Show that the series is convergent. How many terms...Ch. 11.5 - Show that the series is convergent. How many terms...Ch. 11.5 - Prob. 26ECh. 11.5 - Prob. 27ECh. 11.5 - Prob. 28ECh. 11.5 - Approximate the sum of the series correct to four...Ch. 11.5 - Prob. 30ECh. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - For what values of p is each series convergent?...Ch. 11.5 - Prob. 35ECh. 11.5 - Prob. 36ECh. 11.6 - What can you say about the series an in each of...Ch. 11.6 - Prob. 2ECh. 11.6 - Determine whether the series is absolutely...Ch. 11.6 - Prob. 4ECh. 11.6 - Prob. 5ECh. 11.6 - Prob. 6ECh. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Prob. 9ECh. 11.6 - Use the Ratio Test to determine whether the series...Ch. 11.6 - Prob. 11ECh. 11.6 - Prob. 12ECh. 11.6 - Prob. 13ECh. 11.6 - Prob. 14ECh. 11.6 - Prob. 15ECh. 11.6 - Prob. 16ECh. 11.6 - Prob. 17ECh. 11.6 - Prob. 18ECh. 11.6 - Prob. 19ECh. 11.6 - Prob. 20ECh. 11.6 - Prob. 21ECh. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - Prob. 25ECh. 11.6 - Prob. 26ECh. 11.6 - Prob. 27ECh. 11.6 - Prob. 28ECh. 11.6 - Prob. 29ECh. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Prob. 33ECh. 11.6 - Prob. 34ECh. 11.6 - Prob. 35ECh. 11.6 - Prob. 36ECh. 11.6 - Prob. 37ECh. 11.6 - Use any test to determine whether the series is...Ch. 11.6 - Prob. 39ECh. 11.6 - Prob. 40ECh. 11.6 - Prob. 41ECh. 11.6 - Prob. 42ECh. 11.6 - Prob. 43ECh. 11.6 - Prob. 44ECh. 11.6 - (a) Show that n0xn/n! converges for all x. (b)...Ch. 11.6 - Prob. 46ECh. 11.6 - Prob. 47ECh. 11.6 - Use the sum of the first 10 terms to approximate...Ch. 11.6 - Prob. 49ECh. 11.6 - Prob. 50ECh. 11.6 - Given any series an we define a series an+ whose...Ch. 11.6 - Prob. 52ECh. 11.6 - Suppose the series an is conditionally...Ch. 11.7 - Test the series for convergence or divergence. 1....Ch. 11.7 - Test the series for convergence or divergence. 2....Ch. 11.7 - Prob. 3ECh. 11.7 - Test the series for convergence or divergence. 4....Ch. 11.7 - Prob. 5ECh. 11.7 - Prob. 6ECh. 11.7 - Prob. 7ECh. 11.7 - Test the series for convergence or divergence. 8....Ch. 11.7 - Test the series for convergence or divergence. 9....Ch. 11.7 - Test the series for convergence or divergence. 10....Ch. 11.7 - Prob. 11ECh. 11.7 - Prob. 12ECh. 11.7 - Prob. 13ECh. 11.7 - Test the series for convergence or divergence....Ch. 11.7 - Prob. 15ECh. 11.7 - Test the series for convergence or divergence. 16....Ch. 11.7 - Prob. 17ECh. 11.7 - Prob. 18ECh. 11.7 - Prob. 19ECh. 11.7 - Test the series for convergence or divergence. 20....Ch. 11.7 - Prob. 21ECh. 11.7 - Test the series for convergence or divergence. 22....Ch. 11.7 - Prob. 23ECh. 11.7 - Prob. 24ECh. 11.7 - Prob. 25ECh. 11.7 - Test the series for convergence or divergence. 26....Ch. 11.7 - Prob. 27ECh. 11.7 - Test the series for convergence or divergence. 28....Ch. 11.7 - Prob. 29ECh. 11.7 - Prob. 30ECh. 11.7 - Prob. 31ECh. 11.7 - Test the series for convergence or divergence. 32....Ch. 11.7 - Prob. 33ECh. 11.7 - Test the series for convergence or divergence. 34....Ch. 11.7 - Test the series for convergence or divergence. 35....Ch. 11.7 - Prob. 36ECh. 11.7 - Prob. 37ECh. 11.7 - Prob. 38ECh. 11.8 - What is a power series?Ch. 11.8 - (a) What is the radius of convergence of a power...Ch. 11.8 - Prob. 3ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Prob. 7ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Prob. 9ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Prob. 11ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Prob. 13ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Prob. 15ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Prob. 17ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Prob. 19ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Prob. 21ECh. 11.8 - Prob. 22ECh. 11.8 - Prob. 23ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - Prob. 25ECh. 11.8 - Prob. 26ECh. 11.8 - Prob. 27ECh. 11.8 - Find the radius of convergence and interval of...Ch. 11.8 - If n=0cn4n is convergent, can we conclude that...Ch. 11.8 - Suppose that n=0cnxn converges when x = 4 and...Ch. 11.8 - Prob. 31ECh. 11.8 - Prob. 32ECh. 11.8 - Prob. 33ECh. 11.8 - Prob. 34ECh. 11.8 - Prob. 37ECh. 11.8 - Prob. 38ECh. 11.8 - Prob. 39ECh. 11.8 - Prob. 40ECh. 11.8 - Prob. 41ECh. 11.8 - Prob. 42ECh. 11.9 - If the radius of convergence of the power series...Ch. 11.9 - Suppose you know that the series n=0bnxn converges...Ch. 11.9 - Prob. 3ECh. 11.9 - Find a power series representation for the...Ch. 11.9 - Prob. 5ECh. 11.9 - Find a power series representation for the...Ch. 11.9 - Prob. 7ECh. 11.9 - Find a power series representation for the...Ch. 11.9 - Prob. 9ECh. 11.9 - Prob. 10ECh. 11.9 - Prob. 11ECh. 11.9 - Express the function as the sum of a power series...Ch. 11.9 - Prob. 13ECh. 11.9 - (a) Use Equation 1 to find a power series...Ch. 11.9 - Find a power series representation for the...Ch. 11.9 - Find a power series representation for the...Ch. 11.9 - Prob. 17ECh. 11.9 - Find a power series representation for the...Ch. 11.9 - Prob. 19ECh. 11.9 - Find a power series representation for the...Ch. 11.9 - Find a power series representation for f, and...Ch. 11.9 - Prob. 22ECh. 11.9 - Prob. 23ECh. 11.9 - Prob. 24ECh. 11.9 - Prob. 25ECh. 11.9 - Evaluate the indefinite integral as a power...Ch. 11.9 - Prob. 27ECh. 11.9 - Evaluate the indefinite integral as a power...Ch. 11.9 - Prob. 29ECh. 11.9 - Use a power series to approximate the definite...Ch. 11.9 - Prob. 31ECh. 11.9 - Use a power series to approximate the definite...Ch. 11.9 - Prob. 33ECh. 11.9 - Prob. 34ECh. 11.9 - Prob. 35ECh. 11.9 - Prob. 36ECh. 11.9 - (a) Show that the function f(x)=n=0xnn! is a...Ch. 11.9 - Prob. 38ECh. 11.9 - Prob. 39ECh. 11.9 - Prob. 40ECh. 11.9 - Prob. 41ECh. 11.9 - Prob. 42ECh. 11.10 - Prob. 1ECh. 11.10 - The graph of f is shown. (a) Explain why the...Ch. 11.10 - Prob. 3ECh. 11.10 - Find the Taylor series for f centered at 4 if...Ch. 11.10 - Use the definition of a Taylor series to find the...Ch. 11.10 - Use the definition of a Taylor series to find the...Ch. 11.10 - Prob. 7ECh. 11.10 - Use the definition of a Taylor series to find the...Ch. 11.10 - Prob. 9ECh. 11.10 - Prob. 10ECh. 11.10 - Prob. 11ECh. 11.10 - Find the Maclaurin series for f(x) using the...Ch. 11.10 - Prob. 13ECh. 11.10 - Find the Maclaurin series for f(x) using the...Ch. 11.10 - Prob. 15ECh. 11.10 - Prob. 16ECh. 11.10 - Prob. 17ECh. 11.10 - Prob. 18ECh. 11.10 - Prob. 19ECh. 11.10 - Find the Taylor series for f(x) centered at the...Ch. 11.10 - Find the Taylor series for f(x) centered at the...Ch. 11.10 - Prob. 22ECh. 11.10 - Prob. 23ECh. 11.10 - Find the Taylor series for f(x) centered at the...Ch. 11.10 - Find the Taylor series for f(x) centered at the...Ch. 11.10 - Prob. 26ECh. 11.10 - Prove that the series obtained in Exercise 13...Ch. 11.10 - Prove that the series obtained in Exercise 25...Ch. 11.10 - Prob. 29ECh. 11.10 - Prob. 30ECh. 11.10 - Prob. 31ECh. 11.10 - Prob. 32ECh. 11.10 - Prob. 33ECh. 11.10 - Prob. 34ECh. 11.10 - Prob. 35ECh. 11.10 - Use a Maclaurin series in Table 1 to obtain the...Ch. 11.10 - Prob. 37ECh. 11.10 - Use a Maclaurin series in Table 1 to obtain the...Ch. 11.10 - Prob. 39ECh. 11.10 - Prob. 40ECh. 11.10 - Prob. 41ECh. 11.10 - Prob. 42ECh. 11.10 - Prob. 43ECh. 11.10 - Prob. 44ECh. 11.10 - Prob. 45ECh. 11.10 - Find the Maclaurin series of f (by any method) and...Ch. 11.10 - Prob. 47ECh. 11.10 - Find the Maclaurin series of f (by any method) and...Ch. 11.10 - Use the Maclaurin series for cos x to compute cos...Ch. 11.10 - Use the Maclaurin series for ex to calculate 1/e10...Ch. 11.10 - Prob. 51ECh. 11.10 - (a) Expand 1/1+x4 as a power series. (b) Use part...Ch. 11.10 - Prob. 53ECh. 11.10 - Prob. 54ECh. 11.10 - Prob. 55ECh. 11.10 - Evaluate the indefinite integral as an infinite...Ch. 11.10 - Prob. 57ECh. 11.10 - Use series to approximate the definite integral to...Ch. 11.10 - Prob. 59ECh. 11.10 - Use series to approximate the definite integral to...Ch. 11.10 - Prob. 61ECh. 11.10 - Use series to evaluate the limit. 62....Ch. 11.10 - Prob. 63ECh. 11.10 - Use series to evaluate the limit. 64....Ch. 11.10 - Prob. 65ECh. 11.10 - Use the series in Example 13(b) to evaluate...Ch. 11.10 - Prob. 67ECh. 11.10 - Prob. 68ECh. 11.10 - Prob. 69ECh. 11.10 - Use multiplication or division of power series to...Ch. 11.10 - Prob. 71ECh. 11.10 - Prob. 72ECh. 11.10 - Prob. 73ECh. 11.10 - Prob. 74ECh. 11.10 - Find the sum of the series. 75. n=1(1)n13nn5nCh. 11.10 - Find the sum of the series. 76. n=03n5nn!Ch. 11.10 - Prob. 77ECh. 11.10 - Find the sum of the series. 78....Ch. 11.10 - Prob. 79ECh. 11.10 - Find the sum of the series. 80. 1121323+15251727+Ch. 11.10 - Prob. 81ECh. 11.10 - If f(x) = (1 + x3)30, what is f(58)(0)?Ch. 11.10 - Prob. 83ECh. 11.10 - Prob. 84ECh. 11.10 - Prob. 85ECh. 11.10 - Prob. 86ECh. 11.11 - Prob. 1ECh. 11.11 - Prob. 2ECh. 11.11 - Prob. 3ECh. 11.11 - Prob. 4ECh. 11.11 - Find the Taylor polynomial T3(x) for the function...Ch. 11.11 - Prob. 6ECh. 11.11 - Prob. 7ECh. 11.11 - Prob. 8ECh. 11.11 - Prob. 9ECh. 11.11 - Prob. 10ECh. 11.11 - Prob. 13ECh. 11.11 - Prob. 14ECh. 11.11 - Prob. 15ECh. 11.11 - Prob. 16ECh. 11.11 - (a) Approximate f by a Taylor polynomial with...Ch. 11.11 - Prob. 18ECh. 11.11 - Prob. 19ECh. 11.11 - (a) Approximate f by a Taylor polynomial with...Ch. 11.11 - Prob. 21ECh. 11.11 - Prob. 22ECh. 11.11 - Use the information from Exercise 5 to estimate...Ch. 11.11 - Prob. 24ECh. 11.11 - Use Taylors Inequality to determine the number of...Ch. 11.11 - Prob. 26ECh. 11.11 - Prob. 27ECh. 11.11 - Prob. 28ECh. 11.11 - Prob. 29ECh. 11.11 - Suppose you know that f(n)(4)=(1)nn!3n(n+1) and...Ch. 11.11 - Prob. 31ECh. 11.11 - Prob. 32ECh. 11.11 - Prob. 33ECh. 11.11 - Prob. 34ECh. 11.11 - Prob. 35ECh. 11.11 - A uniformly charged disk has radius R and surface...Ch. 11.11 - Prob. 37ECh. 11.11 - Prob. 38ECh. 11.11 - Prob. 39ECh. 11 - (a) What is a convergent sequence? (b) What is a...Ch. 11 - (a) What is a bounded sequence? (b) What is a...Ch. 11 - Prob. 3RCCCh. 11 - Suppose an=3 and sn is the nth partial sum of the...Ch. 11 - State the following. (a) The Test for Divergence...Ch. 11 - (a) What is an absolutely convergent series? (b)...Ch. 11 - Prob. 7RCCCh. 11 - (a) Write the general form of a power series. (b)...Ch. 11 - Prob. 9RCCCh. 11 - Prob. 10RCCCh. 11 - Prob. 11RCCCh. 11 - Write the binomial series expansion of (1 + x)k....Ch. 11 - Prob. 1RQCh. 11 - Prob. 2RQCh. 11 - Prob. 3RQCh. 11 - Prob. 4RQCh. 11 - Prob. 5RQCh. 11 - Prob. 6RQCh. 11 - Prob. 7RQCh. 11 - Prob. 8RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Prob. 10RQCh. 11 - Prob. 11RQCh. 11 - Prob. 12RQCh. 11 - Prob. 13RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Prob. 15RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Prob. 17RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Prob. 19RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Prob. 21RQCh. 11 - Determine whether the statement is true or false....Ch. 11 - Determine whether the sequence is convergent or...Ch. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Determine whether the series is conditionally...Ch. 11 - Prob. 25RECh. 11 - Determine whether the series is conditionally...Ch. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Prob. 47RECh. 11 - Prob. 48RECh. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Prob. 55RECh. 11 - Prob. 56RECh. 11 - Prob. 57RECh. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - The force due to gravity on an object with mass m...Ch. 11 - Prob. 61RECh. 11 - Prob. 62RECh. 11 - Prob. 1PCh. 11 - Prob. 2PCh. 11 - Prob. 3PCh. 11 - Let {Pn} be a sequence of points determined as in...Ch. 11 - Prob. 5PCh. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - Prob. 8PCh. 11 - Prob. 9PCh. 11 - Prob. 10PCh. 11 - Prob. 11PCh. 11 - Suppose you have a large supply of books, all the...Ch. 11 - Prob. 13PCh. 11 - If p 1. evaluate the expression...Ch. 11 - Prob. 15PCh. 11 - Prob. 16PCh. 11 - Prob. 17PCh. 11 - Prob. 18PCh. 11 - Prob. 19PCh. 11 - Prob. 20PCh. 11 - Prob. 21PCh. 11 - Right-angled triangles are constructed as in the...Ch. 11 - Prob. 23PCh. 11 - (a) Show that the Maclaurin series of the function...Ch. 11 - Let...Ch. 11 - Prob. 26P
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