Σn=0 (2n +∞0 (-1)" x²n+1 , XER a. Find the Maclaurin series for x sin (x²) b. Approximate the value of 0.1 sin(0.01) using the 7th degree Maclaurin polynomial for x sin(x²) C. Differentiate the Maclaurin series for x sin (x²) to solve for the exact value of +1)! Σ 2n+1 ¹+∞ (−1)n(4n + 3)π²n+¹ (2n + 1)! n=0

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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(-1)" 2n+1
X
no (2n + 1)!^
+∞
, XER
a.
Find the Maclaurin series for x sin (x²)
b. Approximate the value of 0.1 sin(0.01) using the 7th degree Maclaurin polynomial for x sin(x²)
Differentiate the Maclaurin series for x sin (x²) to solve for the exact value of
C.
++
n=0
(−1)”(4n+3) 2n+1
(2n + 1)!
Transcribed Image Text:(-1)" 2n+1 X no (2n + 1)!^ +∞ , XER a. Find the Maclaurin series for x sin (x²) b. Approximate the value of 0.1 sin(0.01) using the 7th degree Maclaurin polynomial for x sin(x²) Differentiate the Maclaurin series for x sin (x²) to solve for the exact value of C. ++ n=0 (−1)”(4n+3) 2n+1 (2n + 1)!
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