Given: In(1+x) = (-1)" -2n+1 _if ]æ| < 1. n + 1 n=0 1. Find the Maclaurin series for f(x) = x ln (1+).
Given: In(1+x) = (-1)" -2n+1 _if ]æ| < 1. n + 1 n=0 1. Find the Maclaurin series for f(x) = x ln (1+).
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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Answer the LAST NUMBER ONLY (#4). I prefer HANDWRITTEN SOLUTION :)
Transcribed Image Text:Given: In(1+x) = >)
Σ
n +1
(-1)"
xn+1
if |x| < 1.
n=0
1. Find the Maclaurin series for f(x) = x ln (1+ * ).
2
2. Evaluate f(2022)
(0).
3. Use the third degree Maclaurin polynomial of f to approximate the
value of 0.2 ln(1.1), give your answer in decimals.
(-1)" (n + 2)
2n+1(n + 1)
4. Compute the exact value of
n=0
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