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(a) From first principles, find To(x), the Taylor series expansion of (1-x)-¹ about x = 0. Include the general term. (b) Use (a) to write down the Taylor series expansion about x = 0 of 1 and 2. (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in x4. (d) The intorral of Quorgongo for the coring in (a) ia lal 1 What are the intervals of onvergo for

(a) From first principles, find To(x), the Taylor series expansion of (1-x)-¹ about x = 0. Include the general term. (b) Use (a) to write down the Taylor series expansion about x = 0 of 1 and 2. (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in x4. (d) The intorral of Quorgongo for the coring in (a) ia lal 1 What are the intervals of onvergo for

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 22RE
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(a) From first principles, find To(x), the Taylor series expansion of (1-x)-¹ about x = 0. Include the general term. (b) Use (a) to write down the Taylor series expansion about x = 0 of 1 and 2 (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in x4. (d) The interval of convergence for the series in (a) is |x| < 1. What are the intervals of convergence for 1 and 1+? 1-x 2-x
Transcribed Image Text:(a) From first principles, find To(x), the Taylor series expansion of (1-x)-¹ about x = 0. Include the general term. (b) Use (a) to write down the Taylor series expansion about x = 0 of 1 and 2 (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in x4. (d) The interval of convergence for the series in (a) is |x| < 1. What are the intervals of convergence for 1 and 1+? 1-x 2-x
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