Given that equation 1 attached below is true for all x ∈ R, do the following: a) Find the Maclaurin series for xsin(x2) b) Approximate the value of 0.1sin(0.01) using the 7th degree Maclaurin polynomial for xsin(x^2) c) Differentiate the series found in subpart a to determine the exact value of the series attached below.
Given that equation 1 attached below is true for all x ∈ R, do the following: a) Find the Maclaurin series for xsin(x2) b) Approximate the value of 0.1sin(0.01) using the 7th degree Maclaurin polynomial for xsin(x^2) c) Differentiate the series found in subpart a to determine the exact value of the series attached below.
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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Given that equation 1 attached below is true for all x ∈ R, do the following:
a) Find the Maclaurin series for xsin(x2)
b) Approximate the value of 0.1sin(0.01) using the 7th degree Maclaurin polynomial for xsin(x^2)
c) Differentiate the series found in subpart a to determine the exact value of the series attached below.
Transcribed Image Text:+∞
Σ
n=0
(−1)″(4n+3)π²n+1
(2n + 1)!
Transcribed Image Text:Equation 1: sing
=
+∞
Σ
n=0
(−1)n 2n+1
X
(2n + 1)!
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