Find the Taylor Series of f(x) = c os() centered at a = Find the interval of convergence. Show all necessary steps. %3D %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I need the interval of convergence.

Find the Taylor Series of f(x)
cos() centered at a
= S. Find the interval of convergence. Show all necessary steps.
= COS
%3D
Maximum file size: 250MB, maximu
Transcribed Image Text:Find the Taylor Series of f(x) cos() centered at a = S. Find the interval of convergence. Show all necessary steps. = COS %3D Maximum file size: 250MB, maximu
Expert Solution
Step 1

Given fx=cosx3 about a=3π2.

The Taylor series of a function, fx about x=a is given by,

fx=fa+x-af'a+x-a22!f"a+

Differentiating fx=cosx3, with respect to x,

fx=cosx3f'x=-13sinx3f"x=-132cosx3f3x=133sinx3

Substitute, x=3π2 in the above equation,

f3π2=0f'3π2=-13f"3π2=0f33π2=133

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