It can be shown using material from a later section that [ete de is given by (-1)"a²n+1 n!2¹ (2n + 1) n=0 for any positive value of a. When a is positive, this series is an alternating series. (a) Approximate Leva dx to four decimal places accuracy by using the Alternating Series Test and its remainder theorem. (Be careful to not round intermediate steps.) (b) Using the same number of terms as you used in your sum in part (a), compute the midpoint approximation M₁, for the integral fet de е (c) Which approximation is more accurate? This should be determined using just parts (a) and (b).
It can be shown using material from a later section that [ete de is given by (-1)"a²n+1 n!2¹ (2n + 1) n=0 for any positive value of a. When a is positive, this series is an alternating series. (a) Approximate Leva dx to four decimal places accuracy by using the Alternating Series Test and its remainder theorem. (Be careful to not round intermediate steps.) (b) Using the same number of terms as you used in your sum in part (a), compute the midpoint approximation M₁, for the integral fet de е (c) Which approximation is more accurate? This should be determined using just parts (a) and (b).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. It can be shown using material from a later section that
Set ² d
da
is given by
(−1)na²n+1
n!2n (2n + 1)
n=0
for any positive value of a. When a is positive, this series is an alternating series.
(a) Approximate
dx
to four decimal places accuracy by using the Alternating Series Test and its remainder
theorem. (Be careful to not round intermediate steps.)
(b) Using the same number of terms as you used in your sum in part (a), compute the
midpoint approximation Mn for the integral
fe-t³² da
(c) Which approximation is more accurate? This should be determined using just parts (a)
and (b).
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