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(a) Use differentiation to find a power series representation for 1 f(x) (6 + x) ' Ax) = £ ( %3D n = 0 What is the radius of convergence, R? R

(a) Use differentiation to find a power series representation for 1 f(x) (6 + x) ' Ax) = £ ( %3D n = 0 What is the radius of convergence, R? R

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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Representations of Functions as power series

(a) Use differentiation to find a power series representation for 1 f(x) (6 + x)² ' Č ( f(x) %| n = 0 What is the radius of convergence, R? R (b) Use part (a) to find a power series for 1 f(x) (6 + x)3 00 f(x) = ( Σ n = 0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for x2 f(x) (6 + x)3 f(x) = n = 2 What is the radius of convergence, R? R =
Transcribed Image Text:(a) Use differentiation to find a power series representation for 1 f(x) (6 + x)² ' Č ( f(x) %| n = 0 What is the radius of convergence, R? R (b) Use part (a) to find a power series for 1 f(x) (6 + x)3 00 f(x) = ( Σ n = 0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for x2 f(x) (6 + x)3 f(x) = n = 2 What is the radius of convergence, R? R =
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