a) Give the Taylor expansion of the function f(x) = "*-r up to third order for the expansion point xo = 0. b) After the third order the Taylor expansion goes on like this: 16 - 25 +.. T(x) ... + 4! What is the formula for the n-th Taylor coefficient? c) Use the formula you found in b) for calculating the radius of convergence of the Taylor expansion.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 49E
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a) Give the Taylor expansion of the function f (x) = *-x
up to third order for the expansion point xo = 0.
b) After the third order the Taylor expansion goes on like this:
1
16 x4
4!
1
25 x° + · ..
5!
T(x)
.. +
What is the formula for the n-th Taylor coefficient?
c) Use the formula you found in b) for calculating the radius of convergence of the Taylor
expansion.
Transcribed Image Text:a) Give the Taylor expansion of the function f (x) = *-x up to third order for the expansion point xo = 0. b) After the third order the Taylor expansion goes on like this: 1 16 x4 4! 1 25 x° + · .. 5! T(x) .. + What is the formula for the n-th Taylor coefficient? c) Use the formula you found in b) for calculating the radius of convergence of the Taylor expansion.
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