(a) Find the power series representation centered at x = 0 for the function and determine the radius of convergence. f(x) = ln (x² + 1) (b) Find the Taylor series for f(x) centered at the given value of a. ƒ(x) = x² + 4x³ + 6x² + 4x+1, a=1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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(a) Find the power series representation centered at x = 0 for the function
and determine the radius of convergence.
f(x) = ln (x² + 1)
(b) Find the Taylor series for f(x) centered at the given value of a.
f(x) = x² + 4x³ + 6x² + 4x + 1, a = 1
Transcribed Image Text:(a) Find the power series representation centered at x = 0 for the function and determine the radius of convergence. f(x) = ln (x² + 1) (b) Find the Taylor series for f(x) centered at the given value of a. f(x) = x² + 4x³ + 6x² + 4x + 1, a = 1
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