Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R₁(x) → 0.] f(x) = sin(x), a = π f(x) = 00 n = 0 R = ∞ (-1)^²n+1 (2n + 1)! - (x − x)²n+1 Find the associated radius of convergence R. X

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]
f(x) = sin(x), a = π
f(x)
=
∞
Σ
n = 0
(−1)n ²n+1
(2n + 1)!
R = ∞
(x − π) ²n+1
Find the associated radius of convergence R.
)
Transcribed Image Text:Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = sin(x), a = π f(x) = ∞ Σ n = 0 (−1)n ²n+1 (2n + 1)! R = ∞ (x − π) ²n+1 Find the associated radius of convergence R. )
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