2 (a) Derive a formula for the Taylor series expansion of f(x) = using a = 0. 2-x Use f(x) = E f") (x - a)" =f(a) +f'(a)(x – a) + f"(a) (x- a)² + 2! (a) (x - a)³ 3! n! n = 0 " (a) 2 (x – a)* 4! " (a) (x – a)" +... п! Write f(x) = 2-x 2(2 – x) to facilitate differentiation. (b) Find the approximate value of f(x) 2 using the Taylor series obtained above when x = 1.10. 2- Employ zero- to fourth-order versions and determine the absolute true relative percent error e, in each case. Round-off each approximation to 5 significant figures.
2 (a) Derive a formula for the Taylor series expansion of f(x) = using a = 0. 2-x Use f(x) = E f") (x - a)" =f(a) +f'(a)(x – a) + f"(a) (x- a)² + 2! (a) (x - a)³ 3! n! n = 0 " (a) 2 (x – a)* 4! " (a) (x – a)" +... п! Write f(x) = 2-x 2(2 – x) to facilitate differentiation. (b) Find the approximate value of f(x) 2 using the Taylor series obtained above when x = 1.10. 2- Employ zero- to fourth-order versions and determine the absolute true relative percent error e, in each case. Round-off each approximation to 5 significant figures.
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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Transcribed Image Text:2
(a) Derive a formula for the Taylor series expansion of f(x) =
using a = 0.
2-x
Use f(x) = E f")
(x - a)"
=f(a) +f'(a)(x – a) +
f"(a)
(x- a)² +
2!
(a)
(x - a)³
3!
n!
n = 0
" (a)
2 (x – a)*
4!
" (a)
(x – a)" +...
п!
Write f(x) = 2-x
2(2 – x) to facilitate differentiation.
(b) Find the approximate value of f(x)
2
using the Taylor series obtained above when x = 1.10.
2-
Employ zero- to fourth-order versions and determine the absolute true relative percent error ɛ, in each
case. Round-off each approximation to 5 significant figures.
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