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 R,(x) → 0.]f(x) = xª – 3x²+3, a = 1P(x- 1)^ = 1 – 2(x – 1) + 3(x – 1)2 + 4(x – 1)3 + (x – 1)ªn!n = 0fn(1) (x- 1) = -1 – 2(x – 1) + 3(x – 1)² – 4(x – 1)3 + (x – 1)ªn!n = 0Os "(1)(x – 1)^ = 1 – 2(x – 1) + 4(x – 1)2 + 3(x – 1)³ + (x –- 1)4.n!n = 0Os "(1)(x – 1)^ = -1 + 2(x – 1) + 3(x = 1)² + 4(x - 1)³ + (x – 1)4n!n = 0"(1)(x - 1)° = 1– 2(x – 1) – 4(X = 1)² + 3(x = 1)³ – (x - 1)ªn!n = 0Find the associated radius of convergence R.R =

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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 R,(x) → 0.] f(x) = xª – 3x²+3, a = 1 ) "(x - 1)^ = 1 – 2(x – 1) + 3(x – 1)2 + 4(x – 1)³ + (x – 1)ª n! n = 0 PA(x – 1)^ = -1 – 2(x – 1) + 3(x = 1)² - 4(x – 1)3 + (x – 1)ª n! n = 0 Os ")(x – 1)^ = 1 – 2(x – 1) + 4(x – 1)2 + 3(x - 1)³ + (x - 1)ª. n! n= 0 "(1)(x - 1)^ = -1 + 2(x – 1) + 3(x – 1)2 + 4(x = 1)³ + (x – 1)4 n! Os ")(x - 1)^ = 1 – 2(x – 1) = 4(x = 1)² + 3(x – 1)3 = (x – 1)ª n!

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 R,(x) → 0.] f(x) = xª – 3x²+3, a = 1 ) "(x - 1)^ = 1 – 2(x – 1) + 3(x – 1)2 + 4(x – 1)³ + (x – 1)ª n! n = 0 PA(x – 1)^ = -1 – 2(x – 1) + 3(x = 1)² - 4(x – 1)3 + (x – 1)ª n! n = 0 Os ")(x – 1)^ = 1 – 2(x – 1) + 4(x – 1)2 + 3(x - 1)³ + (x - 1)ª. n! n= 0 "(1)(x - 1)^ = -1 + 2(x – 1) + 3(x – 1)2 + 4(x = 1)³ + (x – 1)4 n! Os ")(x - 1)^ = 1 – 2(x – 1) = 4(x = 1)² + 3(x – 1)3 = (x – 1)ª n!

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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Question

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 R,(x) → 0.]
f(x) = xª – 3x²+3, a = 1
P(x- 1)^ = 1 – 2(x – 1) + 3(x – 1)2 + 4(x – 1)3 + (x – 1)ª
n!
n = 0
fn(1) (x
- 1) = -1 – 2(x – 1) + 3(x – 1)² – 4(x – 1)3 + (x – 1)ª
n!
n = 0
Os "(1)(x – 1)^ = 1 – 2(x – 1) + 4(x – 1)2 + 3(x – 1)³ + (x –- 1)4.
n!
n = 0
Os "(1)(x – 1)^ = -1 + 2(x – 1) + 3(x = 1)² + 4(x - 1)³ + (x – 1)4
n!
n = 0
"(1)(x - 1)° = 1– 2(x – 1) – 4(X = 1)² + 3(x = 1)³ – (x - 1)ª
n!
n = 0
Find the associated radius of convergence R.
R =

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