. Use the power series representation: 1 1+x ==0(-1)"x"=1-x+x²-x³+.... - a. Find a power series representation for functionf (x) = 1 1+x5' b. Use the above power series representation to approximate the integral accurate within five decimal places. 0.4 1 c. Use the Simpson's Rule with N = 4 to approximate the integralf work. 1+x5 0.4 1 dx 1+x5 dx. Show your
. Use the power series representation: 1 1+x ==0(-1)"x"=1-x+x²-x³+.... - a. Find a power series representation for functionf (x) = 1 1+x5' b. Use the above power series representation to approximate the integral accurate within five decimal places. 0.4 1 c. Use the Simpson's Rule with N = 4 to approximate the integralf work. 1+x5 0.4 1 dx 1+x5 dx. Show your
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:Use the power series representation:
1
= Σno(-1)" x = 1-x+x²-x³+....
1+x
a. Find a power series representation for functionf (x) =
1
1+x5'
0.4
1
b. Use the above power series representation to approximate the integral fo 1+x5 dx
accurate within five decimal places.
c. Use the Simpson's Rule with N=4 to approximate the integralf
work.
0.4 1
1+x5
dx. Show your
d. Use the Trapezoid Rule with N = 4 to approximate the integral f 0.4 1
dx.
0
1+x5
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can you also use the trapezoid rule with N=4 to approximate the
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