EBK THOMAS' CALCULUS
14th Edition
ISBN: 9780134654874
Author: WEIR
Publisher: VST
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Question
Chapter 10.7, Problem 33E
(a)
To determine
Calculate the radius of convergence and the interval of convergence for the series.
(b)
To determine
Calculate the value of x at which the series converge absolutely.
(c)
To determine
Calculate the value of x at which the series converge conditionally.
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Chapter 10 Solutions
EBK THOMAS' CALCULUS
Ch. 10.1 - Each of Exercises 1–6 gives a formula for the nth...Ch. 10.1 - Each of Exercises 1–6 gives a formula for the nth...Ch. 10.1 - Each of Exercises 1–6 gives a formula for the nth...Ch. 10.1 - Each of Exercises 1–6 gives a formula for the nth...Ch. 10.1 - Each of Exercises 1–6 gives a formula for the nth...Ch. 10.1 - Each of Exercises 1–6 gives a formula for the nth...Ch. 10.1 - Each of Exercises 7–12 gives the first term or two...Ch. 10.1 - Each of Exercises 7–12 gives the first term or two...Ch. 10.1 - Each of Exercises 7–12 gives the first term or two...Ch. 10.1 - Each of Exercises 7–12 gives the first term or two...
Ch. 10.1 - Each of Exercises 7–12 gives the first term or two...Ch. 10.1 - Each of Exercises 7–12 gives the first term or two...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - Prob. 18ECh. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - Prob. 20ECh. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - Prob. 22ECh. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - Prob. 24ECh. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - In Exercises 13–30, find a formula for the nth...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31−100...Ch. 10.1 - Prob. 38ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 47ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 56ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 64ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 72ECh. 10.1 - Prob. 73ECh. 10.1 - Prob. 74ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31−100...Ch. 10.1 - Prob. 77ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 79ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 83ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 86ECh. 10.1 - Prob. 87ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 89ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 93ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 95ECh. 10.1 - Prob. 96ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Prob. 98ECh. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - Which of the sequences {an} in Exercises 31–100...Ch. 10.1 - In Exercises 101–108, assume that each sequence...Ch. 10.1 - In Exercises 101–108, assume that each sequence...Ch. 10.1 - In Exercises 101–108, assume that each sequence...Ch. 10.1 - In Exercises 101–108, assume that each sequence...Ch. 10.1 - Prob. 105ECh. 10.1 - Prob. 106ECh. 10.1 - In Exercises 101–108, assume that each sequence...Ch. 10.1 - In Exercises 101–108, assume that each sequence...Ch. 10.1 - The first term of a sequence is x1 = 1. Each...Ch. 10.1 - A sequence of rational numbers is described as...Ch. 10.1 - Prob. 111ECh. 10.1 - Prob. 112ECh. 10.1 - Prob. 113ECh. 10.1 - Prob. 114ECh. 10.1 - Assuming that limn→∞ (1/nc) = 0 if c is any...Ch. 10.1 - Prob. 116ECh. 10.1 - Prob. 117ECh. 10.1 - Prove that
Ch. 10.1 - Prob. 119ECh. 10.1 - Prob. 120ECh. 10.1 - Prob. 121ECh. 10.1 - Prob. 122ECh. 10.1 - In Exercises 121–124, determine whether the...Ch. 10.1 - Prob. 124ECh. 10.1 - Prob. 125ECh. 10.1 - Prob. 126ECh. 10.1 - Prob. 127ECh. 10.1 - Prob. 128ECh. 10.1 - Prob. 129ECh. 10.1 - Which of the sequences in Exercises 125−134...Ch. 10.1 - Which of the sequences in Exercises 125−134...Ch. 10.1 - Prob. 132ECh. 10.1 - Prob. 133ECh. 10.1 - Prob. 134ECh. 10.1 - In Exercises 135–136, use the definition of...Ch. 10.1 - Prob. 136ECh. 10.1 - The sequence {n/{n + 1)} has a least upper bound...Ch. 10.1 - Prob. 138ECh. 10.1 - Prob. 139ECh. 10.1 - Prob. 140ECh. 10.1 - Prob. 141ECh. 10.1 - Limits and subsequences If the terms of one...Ch. 10.1 - For a sequence {an} the terms of even index are...Ch. 10.1 - Prob. 144ECh. 10.1 - Prob. 145ECh. 10.1 - A recursive definition of π/2 If you start with x1...Ch. 10.2 - In Exercises 1–6, find a formula for the nth...Ch. 10.2 - In Exercises 1–6, find a formula for the nth...Ch. 10.2 - In Exercises 1–6, find a formula for the nth...Ch. 10.2 - In Exercises 1–6, find a formula for the nth...Ch. 10.2 - In Exercises 1–6, find a formula for the nth...Ch. 10.2 - In Exercises 1–6, find a formula for the nth...Ch. 10.2 - In Exercises 7–14, write out the first eight terms...Ch. 10.2 - In Exercises 7–14, write out the first eight terms...Ch. 10.2 - In Exercises 7–14, write out the first eight terms...Ch. 10.2 - In Exercises 7–14, write out the first eight terms...Ch. 10.2 - In Exercises 7–14, write out the first eight terms...Ch. 10.2 - In Exercises 7–14, write out the first eight terms...Ch. 10.2 - In Exercises 7–14, write out the first eight terms...Ch. 10.2 - In Exercises 7–14, write out the first eight terms...Ch. 10.2 - In Exercises 15–22, determine whether the...Ch. 10.2 - Prob. 16ECh. 10.2 - In Exercises 15–22, determine whether the...Ch. 10.2 - Prob. 18ECh. 10.2 - In Exercises 15–22, determine whether the...Ch. 10.2 - Prob. 20ECh. 10.2 - In Exercises 15–22, determine whether the...Ch. 10.2 - In Exercises 15–22, determine whether the...Ch. 10.2 - Express each of the numbers in Exercises 23–30 as...Ch. 10.2 - Prob. 24ECh. 10.2 - Express each of the numbers in Exercises 23–30 as...Ch. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Express each of the numbers in Exercises 23–30 as...Ch. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - In Exercises 31–38, use the nth-Term Test for...Ch. 10.2 - In Exercises 31–38, use the nth-Term Test for...Ch. 10.2 - In Exercises 31–38, use the nth-Term Test for...Ch. 10.2 - In Exercises 31–38, use the nth-Term Test for...Ch. 10.2 - In Exercises 31–38, use the nth-Term Test for...Ch. 10.2 - In Exercises 31–38, use the nth-Term Test for...Ch. 10.2 - In Exercises 31–38, use the nth-Term Test for...Ch. 10.2 - In Exercises 31–38, use the nth-Term Test for...Ch. 10.2 - In Exercises 39–44, find a formula for the nth...Ch. 10.2 - In Exercises 39–44, find a formula for the nth...Ch. 10.2 - In Exercises 39–44, find a formula for the nth...Ch. 10.2 - In Exercises 39–44, find a formula for the nth...Ch. 10.2 - In Exercises 39–44, find a formula for the nth...Ch. 10.2 - In Exercises 39–44, find a formula for the nth...Ch. 10.2 - Find the sum of each series in Exercises...Ch. 10.2 - Prob. 46ECh. 10.2 - Find the sum of each series in Exercises...Ch. 10.2 - Prob. 48ECh. 10.2 - Find the sum of each series in Exercises...Ch. 10.2 - Find the sum of each series in Exercises...Ch. 10.2 - Find the sum of each series in Exercises...Ch. 10.2 - Prob. 52ECh. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Prob. 60ECh. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Prob. 62ECh. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Prob. 64ECh. 10.2 - Convergence or Divergence
Which series in...Ch. 10.2 - Prob. 66ECh. 10.2 - Convergence or Divergence
Which series in...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Prob. 72ECh. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Prob. 74ECh. 10.2 - Which series in Exercises 53–76 converge, and...Ch. 10.2 - Prob. 76ECh. 10.2 - Prob. 77ECh. 10.2 - Prob. 78ECh. 10.2 - Prob. 79ECh. 10.2 - Prob. 80ECh. 10.2 - Prob. 81ECh. 10.2 - Prob. 82ECh. 10.2 - Prob. 83ECh. 10.2 - Prob. 84ECh. 10.2 - Prob. 85ECh. 10.2 - Prob. 86ECh. 10.2 - The series in Exercise 5 can also be written...Ch. 10.2 - Prob. 88ECh. 10.2 - Prob. 89ECh. 10.2 - Prob. 90ECh. 10.2 - Prob. 91ECh. 10.2 - Prob. 92ECh. 10.2 - Prob. 93ECh. 10.2 - Prob. 94ECh. 10.2 - Prob. 95ECh. 10.2 - Prob. 96ECh. 10.2 - Prob. 97ECh. 10.2 - Prob. 98ECh. 10.2 - For what values of r does the infinite series ...Ch. 10.2 - The accompanying figure shows the first five of a...Ch. 10.2 - Prob. 101ECh. 10.2 - Prob. 102ECh. 10.2 - Prob. 103ECh. 10.2 - Prob. 104ECh. 10.2 - Prob. 105ECh. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Use the Integral Test to determine whether the...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Prob. 18ECh. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Prob. 20ECh. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Prob. 22ECh. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Prob. 26ECh. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Prob. 38ECh. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Prob. 40ECh. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Which of the series in Exercises 13–46 converge,...Ch. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - For what values of a, if any, do the series in...Ch. 10.3 - Prob. 48ECh. 10.3 - Prob. 49ECh. 10.3 - Are there any values of x for which converges?...Ch. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Estimate the value of to within 0.01 of its exact...Ch. 10.3 - Prob. 56ECh. 10.3 - Prob. 57ECh. 10.3 - Prob. 58ECh. 10.3 - Prob. 59ECh. 10.3 - Use the Cauchy condensation test from Exercise 59...Ch. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.3 - Prob. 67ECh. 10.3 - Prob. 68ECh. 10.4 - In Exercises 1–8, use the Direct Comparison Test...Ch. 10.4 - In Exercises 1–8, use the Direct Comparison Test...Ch. 10.4 - In Exercises 1–8, use the Direct Comparison Test...Ch. 10.4 - In Exercises 1–8, use the Direct Comparison Test...Ch. 10.4 - In Exercises 1–8, use the Direct Comparison Test...Ch. 10.4 - In Exercises 1–8, use the Direct Comparison Test...Ch. 10.4 - In Exercises 1–8, use the Direct Comparison Test...Ch. 10.4 - In Exercises 1–8, use the Direct Comparison Test...Ch. 10.4 - In Exercises 9–16, use the Limit Comparison Test...Ch. 10.4 - In Exercises 9–16, use the Limit Comparison Test...Ch. 10.4 - In Exercises 9–16, use the Limit Comparison Test...Ch. 10.4 - In Exercises 9–16, use the Limit Comparison Test...Ch. 10.4 - In Exercises 9–16, use the Limit Comparison Test...Ch. 10.4 - In Exercises 9–16, use the Limit Comparison Test...Ch. 10.4 - In Exercises 9–16, use the Limit Comparison Test...Ch. 10.4 - In Exercises 9–16, use the Limit Comparison Test...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Prob. 24ECh. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Which of the series in Exercises 17–56 converge,...Ch. 10.4 - Prove (a) Part 2 and (b) Part 3 of the Limit...Ch. 10.4 - If is a convergent series of nonnegative numbers,...Ch. 10.4 - Suppose that an > 0 and bn > 0 for n ≥ N (N an...Ch. 10.4 - Prove that if ∑an is a convergent series of...Ch. 10.4 - Prob. 61ECh. 10.4 - Prob. 62ECh. 10.4 - Show that converges for −∞ < q < ∞ and p >...Ch. 10.4 - (Continuation of Exercise 63.) Show that diverges...Ch. 10.4 - Decimal numbers Any real number in the interval...Ch. 10.4 - Prob. 66ECh. 10.4 - In Exercises 67–72, use the results of Exercises...Ch. 10.4 - Prob. 68ECh. 10.4 - Prob. 69ECh. 10.4 - In Exercises 67–72, use the results of Exercises...Ch. 10.4 - Prob. 71ECh. 10.4 - In Exercises 67–72, use the results of Exercises...Ch. 10.5 - In Exercises 1–8, use the Ratio Test to determine...Ch. 10.5 - In Exercises 1–8, use the Ratio Test to determine...Ch. 10.5 - In Exercises 1–8, use the Ratio Test to determine...Ch. 10.5 - In Exercises 1–8, use the Ratio Test to determine...Ch. 10.5 - In Exercises 1–8, use the Ratio Test to determine...Ch. 10.5 - Prob. 6ECh. 10.5 - In Exercises 1–8, use the Ratio Test to determine...Ch. 10.5 - In Exercises 1–8, use the Ratio Test to determine...Ch. 10.5 - In Exercises 9–16, use the Root Test to determine...Ch. 10.5 - In Exercises 9–16, use the Root Test to determine...Ch. 10.5 - In Exercises 9–16, use the Root Test to determine...Ch. 10.5 - In Exercises 9–16, use the Root Test to determine...Ch. 10.5 - In Exercises 9–16, use the Root Test to determine...Ch. 10.5 - In Exercises 9–16, use the Root Test to determine...Ch. 10.5 - In Exercises 9–16, use the Root Test to determine...Ch. 10.5 - Prob. 16ECh. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - Prob. 26ECh. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - Prob. 30ECh. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - Prob. 32ECh. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - Prob. 34ECh. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - Prob. 36ECh. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - Prob. 40ECh. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - Prob. 45ECh. 10.5 - In Exercises 17–46, use any method to determine...Ch. 10.5 - Recursively Defined Terms Which of the series ...Ch. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Recursively Defined Terms Which of the series ...Ch. 10.5 - Prob. 51ECh. 10.5 - Prob. 52ECh. 10.5 - Prob. 53ECh. 10.5 - Prob. 54ECh. 10.5 - Recursively Defined Terms Which of the series ...Ch. 10.5 - Prob. 56ECh. 10.5 - Prob. 57ECh. 10.5 - Prob. 58ECh. 10.5 - Which of the series in Exercises 57–64 converge,...Ch. 10.5 - Prob. 60ECh. 10.5 - Prob. 61ECh. 10.5 - Prob. 62ECh. 10.5 - Which of the series in Exercises 57–64 converge,...Ch. 10.5 - Prob. 64ECh. 10.5 - Assume that bn is a sequence of positive numbers...Ch. 10.5 - Prob. 66ECh. 10.5 - Neither the Ratio Test nor the Root Test helps...Ch. 10.5 - Prob. 68ECh. 10.5 - Prob. 69ECh. 10.5 - Show that diverges. Recall from the Laws of...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - In Exercises 1–14, determine whether the...Ch. 10.6 - Prob. 14ECh. 10.6 - Which of the series in Exercises 15-48 converge...Ch. 10.6 - Which of the series in Exercises 15-48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Prob. 24ECh. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Prob. 28ECh. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15-48 converge...Ch. 10.6 - Prob. 32ECh. 10.6 - Which of the series in Exercises 15-48 converge...Ch. 10.6 - Prob. 34ECh. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Prob. 38ECh. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Prob. 42ECh. 10.6 - Which of the series in Exercises 15–48 converge...Ch. 10.6 - Prob. 44ECh. 10.6 - Prob. 45ECh. 10.6 - Prob. 46ECh. 10.6 - Prob. 47ECh. 10.6 - Prob. 48ECh. 10.6 - In Exercises 49–52, estimate the magnitude of the...Ch. 10.6 - Prob. 50ECh. 10.6 - In Exercises 49–52, estimate the magnitude of the...Ch. 10.6 - Prob. 52ECh. 10.6 - In Exercises 53–56, determine how many terms...Ch. 10.6 - Prob. 54ECh. 10.6 - Prob. 55ECh. 10.6 - Prob. 56ECh. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - Prob. 58ECh. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - Prob. 64ECh. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - Prob. 66ECh. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - Prob. 68ECh. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - Prob. 70ECh. 10.6 - Prob. 71ECh. 10.6 - Prob. 72ECh. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - Prob. 74ECh. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - Prob. 76ECh. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - Prob. 78ECh. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - In Exercises 57–82, use any method to determine...Ch. 10.6 - Prob. 81ECh. 10.6 - Prob. 82ECh. 10.6 - Prob. 83ECh. 10.6 - Prob. 84ECh. 10.6 - Prob. 85ECh. 10.6 - Prob. 86ECh. 10.6 - Prob. 87ECh. 10.6 - Show that the sum of the first 2n terms of the...Ch. 10.6 - Show that if diverges, then diverges.
Ch. 10.6 - Prob. 90ECh. 10.6 - Prob. 91ECh. 10.6 - Show by example that may diverge even if and ...Ch. 10.6 - Prob. 93ECh. 10.6 - Prob. 94ECh. 10.6 - Prob. 95ECh. 10.6 - Prob. 96ECh. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - Prob. 14ECh. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - Prob. 18ECh. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - Prob. 22ECh. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - Prob. 24ECh. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - Prob. 28ECh. 10.7 - Prob. 29ECh. 10.7 - Prob. 30ECh. 10.7 - Prob. 31ECh. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 1–36,
find the series’ radius and...Ch. 10.7 - In Exercises 1–36, (a) find the series’ radius and...Ch. 10.7 - In Exercises 37–40, find the series’ radius of...Ch. 10.7 - In Exercises 37–40, find the series’ radius of...Ch. 10.7 - In Exercises 37–40, find the series’ radius of...Ch. 10.7 - Prob. 40ECh. 10.7 - In Exercises 41–48, use Theorem 20 to find the...Ch. 10.7 - In Exercises 41–48, use Theorem 20 to find the...Ch. 10.7 - Prob. 43ECh. 10.7 - Prob. 44ECh. 10.7 - In Exercises 41–48, use Theorem 20 to find the...Ch. 10.7 - Prob. 46ECh. 10.7 - In Exercises 41–48, use Theorem 20 to find the...Ch. 10.7 - Prob. 48ECh. 10.7 - Prob. 49ECh. 10.7 - Prob. 50ECh. 10.7 - Prob. 51ECh. 10.7 - Prob. 52ECh. 10.7 - For what values of x does the series
converge?...Ch. 10.7 - If you integrate the series in Exercise 53 term by...Ch. 10.7 - Prob. 55ECh. 10.7 - The series
converges to for all x.
Find a series...Ch. 10.7 - Prob. 57ECh. 10.7 - Prob. 58ECh. 10.7 - Uniqueness of convergent power series
Show that if...Ch. 10.7 - Prob. 60ECh. 10.7 - The sum of the alternating harmonic series This...Ch. 10.7 - Assume that the series ∑anxn converges for x = 4...Ch. 10.7 - Assume that the series ∑an(x − 2)n converges for x...Ch. 10.7 - Proof of Theorem 21 Assume that a = 0 in Theorem...Ch. 10.7 - Proof of Theorem 22 Assume that a = 0 in Theorem...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - In Exercises 1–10, find the Taylor polynomials of...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Find the Maclaurin series for the functions in...Ch. 10.8 - Prob. 24ECh. 10.8 - In Exercises 25–34, find the Taylor series...Ch. 10.8 - Prob. 26ECh. 10.8 - In Exercises 25–34, find the Taylor series...Ch. 10.8 - Prob. 28ECh. 10.8 - Prob. 29ECh. 10.8 - Prob. 30ECh. 10.8 - In Exercises 25–34, find the Taylor series...Ch. 10.8 - Prob. 32ECh. 10.8 - In Exercises 25–34, find the Taylor series...Ch. 10.8 - Prob. 34ECh. 10.8 - In Exercises 35–40, find the first three nonzero...Ch. 10.8 - Prob. 36ECh. 10.8 - In Exercises 35-40, find the first three nonzero...Ch. 10.8 - In Exercises 35-40, find the first three nonzero...Ch. 10.8 - In Exercises 35-40, find the first three nonzero...Ch. 10.8 - Prob. 40ECh. 10.8 - Prob. 41ECh. 10.8 - Prob. 42ECh. 10.8 - Prob. 43ECh. 10.8 - Prob. 44ECh. 10.8 - Prob. 45ECh. 10.8 - Prob. 46ECh. 10.8 - Prob. 47ECh. 10.8 - Prob. 48ECh. 10.8 - Prob. 49ECh. 10.8 - Prob. 50ECh. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to find the...Ch. 10.9 - Use substitution (as in Formula (7)) to Find the...Ch. 10.9 - Use substitution (as in Formula (7)) to Find the...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Prob. 17ECh. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Prob. 27ECh. 10.9 - Prob. 28ECh. 10.9 - Use power series operations to find the Taylor...Ch. 10.9 - Prob. 30ECh. 10.9 - Prob. 31ECh. 10.9 - Prob. 32ECh. 10.9 - Prob. 33ECh. 10.9 - Prob. 34ECh. 10.9 - Prob. 35ECh. 10.9 - Prob. 36ECh. 10.9 - Find the first four nonzero terms in the Maclaurin...Ch. 10.9 - Prob. 38ECh. 10.9 - Estimate the error if P3(x) = x − (x3/6) is used...Ch. 10.9 - Prob. 40ECh. 10.9 - For approximately what values of x can you replace...Ch. 10.9 - Prob. 42ECh. 10.9 - Prob. 43ECh. 10.9 - The estimate is used when x is small. Estimate...Ch. 10.9 - Prob. 45ECh. 10.9 - (Continuation of Exercise 45.) When x < 0, the...Ch. 10.9 - Use the identity to obtain the Maclaurin series...Ch. 10.9 - Prob. 48ECh. 10.9 - Prob. 49ECh. 10.9 - Linearizations at inflection points Show that if...Ch. 10.9 - Prob. 51ECh. 10.9 - A cubic approximation Use Taylor’s formula with a...Ch. 10.9 - Prob. 53ECh. 10.9 - Improving approximations of π
Let P be an...Ch. 10.9 - Prob. 55ECh. 10.9 - Taylor series for even functions and odd functions...Ch. 10.10 - Find the first four nonzero terms of the Taylor...Ch. 10.10 - Prob. 2ECh. 10.10 - Prob. 3ECh. 10.10 - Prob. 4ECh. 10.10 - Prob. 5ECh. 10.10 - Prob. 6ECh. 10.10 - Prob. 7ECh. 10.10 - Prob. 8ECh. 10.10 - Find the first four terms of the binomial series...Ch. 10.10 - Prob. 10ECh. 10.10 - Prob. 11ECh. 10.10 - Prob. 12ECh. 10.10 - Prob. 13ECh. 10.10 - Prob. 14ECh. 10.10 - Prob. 15ECh. 10.10 - Prob. 16ECh. 10.10 - In Exercises 15–18, use series to estimate the...Ch. 10.10 - In Exercises 15–18, use series to estimate the...Ch. 10.10 - Prob. 19ECh. 10.10 - Prob. 20ECh. 10.10 - Prob. 21ECh. 10.10 - Prob. 22ECh. 10.10 - Estimate the error if cos t2 is approximated by ...Ch. 10.10 - Estimate the error if is approximated by in the...Ch. 10.10 - In Exercises 25–28, find a polynomial that will...Ch. 10.10 - Prob. 26ECh. 10.10 - Prob. 27ECh. 10.10 - In Exercises 25–28, find a polynomial that will...Ch. 10.10 - Use series to evaluate the limits in Exercises...Ch. 10.10 - Prob. 30ECh. 10.10 - Prob. 31ECh. 10.10 - Use series to evaluate the limits in Exercises...Ch. 10.10 - Prob. 33ECh. 10.10 - Use series to evaluate the limits in Exercises...Ch. 10.10 - Use series to evaluate the limits in Exercises...Ch. 10.10 - Prob. 36ECh. 10.10 - Prob. 37ECh. 10.10 - Use series to evaluate the limits in Exercises...Ch. 10.10 - Use series to evaluate the limits in Exercises...Ch. 10.10 - Prob. 40ECh. 10.10 - Prob. 41ECh. 10.10 - In Exercises 41–52, use Table 10.1 to find the sum...Ch. 10.10 - In Exercises 41–52, use Table 10.1 to find the sum...Ch. 10.10 - Prob. 44ECh. 10.10 - In Exercises 41–52, use Table 10.1 to find the sum...Ch. 10.10 - Prob. 46ECh. 10.10 - Prob. 47ECh. 10.10 - Prob. 48ECh. 10.10 - In Exercises 41–52, use Table 10.1 to find the sum...Ch. 10.10 - In Exercises 41–52, use Table 10.1 to find the sum...Ch. 10.10 - Prob. 51ECh. 10.10 - Prob. 52ECh. 10.10 - Replace x by − x in the Taylor series for ln (1 +...Ch. 10.10 - How many terms of the Taylor series for ln (1 + x)...Ch. 10.10 - Prob. 55ECh. 10.10 - Prob. 56ECh. 10.10 - Prob. 57ECh. 10.10 - Prob. 58ECh. 10.10 - Prob. 59ECh. 10.10 - Series for sinh−1x Find the first four nonzero...Ch. 10.10 - Prob. 61ECh. 10.10 - Prob. 62ECh. 10.10 - Prob. 63ECh. 10.10 - Prob. 64ECh. 10.10 - Prob. 65ECh. 10.10 - Prob. 66ECh. 10.10 - Prob. 67ECh. 10.10 - Use Equation (4) to show that
DEFINITION For any...Ch. 10.10 - Prob. 69ECh. 10.10 - Prob. 70ECh. 10.10 - Prob. 71ECh. 10.10 - Prob. 72ECh. 10.10 - Prob. 73ECh. 10.10 - Prob. 74ECh. 10 - Prob. 1GYRCh. 10 - What is a monotonic sequence? Under what...Ch. 10 - What theorems are available for calculating limits...Ch. 10 - Prob. 4GYRCh. 10 - Prob. 5GYRCh. 10 - What is an infinite series? What does it mean for...Ch. 10 - Prob. 7GYRCh. 10 - Besides geometric series, what other convergent...Ch. 10 - Prob. 9GYRCh. 10 - Prob. 10GYRCh. 10 - Prob. 11GYRCh. 10 - How do you reindex a series? Why might you want to...Ch. 10 - Prob. 13GYRCh. 10 - Prob. 14GYRCh. 10 - When do p-series converge? Diverge? How do you...Ch. 10 - Prob. 16GYRCh. 10 - Prob. 17GYRCh. 10 - Prob. 18GYRCh. 10 - Prob. 19GYRCh. 10 - Prob. 20GYRCh. 10 - Prob. 21GYRCh. 10 - Prob. 22GYRCh. 10 - Prob. 23GYRCh. 10 - What is the Taylor series generated by a function...Ch. 10 - Prob. 25GYRCh. 10 - Prob. 26GYRCh. 10 - Prob. 27GYRCh. 10 - Prob. 28GYRCh. 10 - What is the binomial series? On what interval does...Ch. 10 - How can you sometimes use power series to estimate...Ch. 10 - What are the Taylor series for 1/(1 – x), 1/(1 +...Ch. 10 - Which of the sequences whose nth terms appear in...Ch. 10 - Which of the sequences whose nth terms appear in...Ch. 10 - Which of the sequences whose nth terms appear in...Ch. 10 - Prob. 4PECh. 10 - Which of the sequences whose nth terms appear in...Ch. 10 - Prob. 6PECh. 10 - Which of the sequences whose nth terms appear in...Ch. 10 - Prob. 8PECh. 10 - Which of the sequences whose nth terms appear in...Ch. 10 - Prob. 10PECh. 10 - Prob. 11PECh. 10 - Prob. 12PECh. 10 - Which of the sequences whose nth terms appear in...Ch. 10 - Prob. 14PECh. 10 - Prob. 15PECh. 10 - Which of the sequences whose nth terms appear in...Ch. 10 - Which of the sequences whose nth terms appear in...Ch. 10 - Prob. 18PECh. 10 - Prob. 19PECh. 10 - Prob. 20PECh. 10 - Prob. 21PECh. 10 - Prob. 22PECh. 10 - Find the sums of the series in Exercises...Ch. 10 - Prob. 24PECh. 10 - Which of the series in Exercises 25–44 converge...Ch. 10 - Prob. 26PECh. 10 - Prob. 27PECh. 10 - Prob. 28PECh. 10 - Prob. 29PECh. 10 - Which of the series in Exercises 25–44 converge...Ch. 10 - Which of the series in Exercises 25–44 converge...Ch. 10 - Prob. 32PECh. 10 - Prob. 33PECh. 10 - Prob. 34PECh. 10 - Prob. 35PECh. 10 - Prob. 36PECh. 10 - Prob. 37PECh. 10 - Prob. 38PECh. 10 - Prob. 39PECh. 10 - Prob. 40PECh. 10 - Prob. 41PECh. 10 - Prob. 42PECh. 10 - Prob. 43PECh. 10 - Prob. 44PECh. 10 - Prob. 45PECh. 10 - In Exercises 45–54, (a) find the series’ radius...Ch. 10 - Prob. 47PECh. 10 - Prob. 48PECh. 10 - In Exercises 45–54, (a) find the series’ radius...Ch. 10 - Prob. 50PECh. 10 - Prob. 51PECh. 10 - Prob. 52PECh. 10 - Prob. 53PECh. 10 - Prob. 54PECh. 10 - Prob. 55PECh. 10 - Prob. 56PECh. 10 - Prob. 57PECh. 10 - Prob. 58PECh. 10 - Prob. 59PECh. 10 - Each of the series in Exercises 55–60 is the value...Ch. 10 - Prob. 61PECh. 10 - Prob. 62PECh. 10 - Prob. 63PECh. 10 - Prob. 64PECh. 10 - Prob. 65PECh. 10 - Prob. 66PECh. 10 - Prob. 67PECh. 10 - Prob. 68PECh. 10 - Prob. 69PECh. 10 - Prob. 70PECh. 10 - Prob. 71PECh. 10 - Prob. 72PECh. 10 - Prob. 73PECh. 10 - Prob. 74PECh. 10 - Prob. 75PECh. 10 - Prob. 76PECh. 10 - Prob. 77PECh. 10 - Prob. 78PECh. 10 - Prob. 79PECh. 10 - Prob. 80PECh. 10 - Prob. 81PECh. 10 - Prob. 82PECh. 10 - Use a series representation of sin 3x to find...Ch. 10 - Prob. 84PECh. 10 - Prob. 85PECh. 10 - Prob. 86PECh. 10 - Prob. 87PECh. 10 - Prob. 88PECh. 10 - a. Find the interval of convergence of the...Ch. 10 - Prob. 90PECh. 10 - Prob. 91PECh. 10 - Prob. 92PECh. 10 - Prove that the sequence {xn} and the series both...Ch. 10 - Prob. 94PECh. 10 - Prob. 95PECh. 10 - Prob. 96PECh. 10 - Prob. 97PECh. 10 - Determine whether converges or diverges.
a.
b.
Ch. 10 - Prob. 99PECh. 10 - Prob. 100PECh. 10 - Prob. 101PECh. 10 - Prob. 102PECh. 10 - Which of the series defined by the formulas in...Ch. 10 - Prob. 2AAECh. 10 - Prob. 3AAECh. 10 - Prob. 4AAECh. 10 - Prob. 5AAECh. 10 - Prob. 6AAECh. 10 - Prob. 7AAECh. 10 - Prob. 8AAECh. 10 - Prob. 9AAECh. 10 - Prob. 10AAECh. 10 - Prob. 11AAECh. 10 - Prob. 12AAECh. 10 - Prob. 13AAECh. 10 - In Exercises 9–14, what Taylor series would you...Ch. 10 - Prob. 15AAECh. 10 - Prob. 16AAECh. 10 - Prob. 17AAECh. 10 - Prob. 18AAECh. 10 - Prob. 20AAECh. 10 - Prob. 21AAECh. 10 - Prob. 22AAECh. 10 - Prob. 23AAECh. 10 - Prob. 24AAECh. 10 - Prob. 25AAECh. 10 - Prob. 26AAECh. 10 - Prob. 27AAECh. 10 - Prob. 28AAECh. 10 - Nicole Oresme’s Theorem Prove Nicole Oresme’s...Ch. 10 - Prob. 30AAECh. 10 - Prob. 31AAECh. 10 - Prob. 32AAECh. 10 - Prob. 33AAECh. 10 - Prob. 34AAE
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- 4.2 Product and Quotient Rules 1. Use the product and/or quotient rule to find the derivative of each function. 2.5 a. g(x)=+1 y14+2 √x-1) b. y=(2x-3)(x-:arrow_forward3. The total profit (in dollars) from selling x watches is P(x)=0.52x²-0.0002x². Find and interpret the following. a) P(100) b) P'(100)arrow_forward3. Find the slope and the equation of the tangent line to the graph of the given function at the given value of x. -4 f(x)=x-x³;x=2arrow_forward
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- 2. Find each derivative. Write answers with positive exponents. a) Dx 9x -3 [97] b) f'(3) if f(x) = x²-5x² 8arrow_forwardA ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt= feet/sec. (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt= feet/sec.arrow_forwardTwo cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z² = x²+ +12 x Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. 2z dz dt dx 2x. +2y dt dx dy dz x +y dt dt dt 2z dy dt × dx (x+y dt dy dtarrow_forward
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