1. (a)Find the Taylor series of In(x) about a for a > 0. Your answer should be insigma notation. You may use the following fact:dk(In 2) = (-1)*-1 (k > 1)(k – 1)!xkdæk(b)Your work should clearly justify your answer.Find the interval of convergence of the Taylor series of In(x) about x = a.

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Answered: (a) sigma notation. You may use the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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Suppose the Taylor Series for a function, f(x), is given below. f (æ) = Eo (()" -) (æ – 2)" (x – 2)" 3 n! a) Find the interval of convergence. b) Find the Taylor Series of the derivative of f(x). c) Find the Taylor Series of the integral of f(x).
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1. (a) Find the Taylor series of In(x) about a for a > 0. Your answer should be in sigma notation. You may use the following fact: (In x) = (-1)k-1 (k – 1)! (k > 1) drk xk (b) Your work should clearly justify your answer. Find the interval of convergence of the Taylor series of In(x) about x = a.
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(a) sigma notation. You may use the following fact: Find the Taylor series of In(x) about a for a > 0. Your answer should be in dk (In x) = (-1)k-1(k – 1)! (k > 1) dak xk (b) Your work should clearly justify your answer. Find the interval of convergence of the Taylor series of In(x) about x = a.