Find the Taylor series of f(x) = = cosa at a = π/3

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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Q 19. 

Find the Taylor series of f(x) = cost
O cost = Σ% (-1)".
(20) (a - Στ
} Σ% (-1)" by (2 - €)2n _ * Σ% (-1)+1 20 -
1
2
(2n)!
Cosa =
Cosa =
at a = π/3
cosa =
1
(2n+1)!
Σ% (-1)*+1, (x - 3)²n+1
2
- Σ% (-1)" 2h) (ar - #12n + Σ% (-1)n+1.
(2n)!
(* - *)2n+1
1
(2n+1)!
¡(x - ²)²n+1
Transcribed Image Text:Find the Taylor series of f(x) = cost O cost = Σ% (-1)". (20) (a - Στ } Σ% (-1)" by (2 - €)2n _ * Σ% (-1)+1 20 - 1 2 (2n)! Cosa = Cosa = at a = π/3 cosa = 1 (2n+1)! Σ% (-1)*+1, (x - 3)²n+1 2 - Σ% (-1)" 2h) (ar - #12n + Σ% (-1)n+1. (2n)! (* - *)2n+1 1 (2n+1)! ¡(x - ²)²n+1
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