(b) Now, letS evaluate the same integral using power series. First, find th- 40 f(x) = . Then, integrate it from 0 to 2, and call it S. S should be an 12+4 What are the first few terms of S? ao %3D a1 a2 %3D az =

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Chapter2: Second-order Linear Odes
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ents/604fb34cf005b90037f4013d
8.6 Power Series
OPEN
Turned in automatically when
(b) Now, lets evaluate the same integral using power series. First, find the power series for the function
f(x) = 14
40
Then, integrate it from 0 to 2, and call it S. S should be an infinite series an .
What are the first few terms of S?
ao
ai =
a2 =
az =
a4 =
(c) The answer in part (a) equals the sum of the infinite series in part (b) (why?). Hence, if you divide
your
infinite series from (b) by k (the answer to (a)), you have found an estimate for the value of r in terms of an
infinite series. Approximate the value of r by the first 5 terms.
(d) What is an upper bound for your error of your estimate if you use the first 12 terms? (Use the alternating
series estimation.)
11:03 PM
ENG
4/8/2021
Transcribed Image Text:ents/604fb34cf005b90037f4013d 8.6 Power Series OPEN Turned in automatically when (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x) = 14 40 Then, integrate it from 0 to 2, and call it S. S should be an infinite series an . What are the first few terms of S? ao ai = a2 = az = a4 = (c) The answer in part (a) equals the sum of the infinite series in part (b) (why?). Hence, if you divide your infinite series from (b) by k (the answer to (a)), you have found an estimate for the value of r in terms of an infinite series. Approximate the value of r by the first 5 terms. (d) What is an upper bound for your error of your estimate if you use the first 12 terms? (Use the alternating series estimation.) 11:03 PM ENG 4/8/2021
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