4. Compute the exact value of (-1)"(n+2) xn+1 Ln=0 2n+1 (nt1) 100

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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PLEASE ANSWER NUMBER 4

Given: In(1 + x) = En=0
(-1)" n+1 ¡f |x| < 1.
100
n+1
1. Find the Maclaurin series for f(x) = xln(1+;).
2. Evaluate f(2022)(0).
3. Use the third degree Maclaurin polynomial of f
to approximate the value of 0.2 In(1.1), give
your answer in decimals.
4. Compute the exact value of
(-1)"(n+2) yn+1
Ln=0 2n+1(n+1)
Transcribed Image Text:Given: In(1 + x) = En=0 (-1)" n+1 ¡f |x| < 1. 100 n+1 1. Find the Maclaurin series for f(x) = xln(1+;). 2. Evaluate f(2022)(0). 3. Use the third degree Maclaurin polynomial of f to approximate the value of 0.2 In(1.1), give your answer in decimals. 4. Compute the exact value of (-1)"(n+2) yn+1 Ln=0 2n+1(n+1)
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