1. a) Use commonly known Taylor series to find the Taylor series of f(x) = cos(x²) %3D centered at a = 0. Show how you obtained the Taylor series and express your answer in summation notation
1. a) Use commonly known Taylor series to find the Taylor series of f(x) = cos(x²) %3D centered at a = 0. Show how you obtained the Taylor series and express your answer in summation notation
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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Step 1
part (a)
given
to find
taylor series of centered at
solution
as we know
taylor series of function centered at is defined as
according to question
series becomes
Step 2
now as
put
differentiate with respect to
differentiate again with respect to
we will use product rule
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