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a) Show how to find an expression for C₁ = f(n) (x) if f(x) = ln z. b) Use this expression to write the Taylor Series representation centered at a = 1 of the function f(x) = ln x (Write your answer as both a polynomial with ". c) What is the radius of convergence for this series? " and using summation notation). 15 pts

a) Show how to find an expression for C₁ = f(n) (x) if f(x) = ln z. b) Use this expression to write the Taylor Series representation centered at a = 1 of the function f(x) = ln x (Write your answer as both a polynomial with ". c) What is the radius of convergence for this series? " and using summation notation). 15 pts

Advanced Engineering Mathematics
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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a) Show how to find an expression for C₁ = f(n) (x) if f(x) = Inc. b) Use this expression to write the Taylor Series representation centered at a = 1 of the function f (x) 1 In x (Write your answer as both a polynomial with "..." and using summation notation). c) What is the radius of convergence for this series? d) Show how to use the Taylor Series to find a power series representation for Edit View Insert Format Tools Table 12pt ✓ Paragraph v 뉴 Ai B IU A ev T²V Ililearn.laccd.edu is sharing your screen. H Stop sharing In r 12 da P₂ Hide -dz centered at a = 1 ✓ 15 pts ⠀
Transcribed Image Text:a) Show how to find an expression for C₁ = f(n) (x) if f(x) = Inc. b) Use this expression to write the Taylor Series representation centered at a = 1 of the function f (x) 1 In x (Write your answer as both a polynomial with "..." and using summation notation). c) What is the radius of convergence for this series? d) Show how to use the Taylor Series to find a power series representation for Edit View Insert Format Tools Table 12pt ✓ Paragraph v 뉴 Ai B IU A ev T²V Ililearn.laccd.edu is sharing your screen. H Stop sharing In r 12 da P₂ Hide -dz centered at a = 1 ✓ 15 pts ⠀
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