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Asked Dec 1, 2019
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I followed all the steps for Maclauren series but got the wrong answer. Did I miss something?

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R(x) 0.
f(x) sin(x),
a T
(1)"(x-n)2n+1
(2n + 1)!
f(x) =
n 0
X
Find the associated radius of convergence R.
R =
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Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R(x) 0. f(x) sin(x), a T (1)"(x-n)2n+1 (2n + 1)! f(x) = n 0 X Find the associated radius of convergence R. R =

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Step 1

Compute the derivative of the function and its value at a =π.

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f(x) sinx f() 0 f'(x)=coSx; f() f(x)sinx f"(x)=-cos.x f(x)sin x f(n)0 f(T)0 -1 ifn = 4k +1 f(T)1 if n 4k3 otherwise 0

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Step 2

Apply the values in Taylor series expa...

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(x-a) f(a) 1! (a)+ (x-a) -f"(a) 3! f(x)=f(a)+(-a) 2! (x-)() (x-n (x-nfn)+ (x-T) =f()+ 1! f"(7)+ 2! f"(77)+ 3! f"'"(7)+ 4! (x-z (x-7) 7 (x-7 |(x-T -(-1)+0+ (1)+0 7! -1)+0+ 1! (1)+0+ 5! 0+ 3! 5 (*-т), (х-т) (х-т)' (х-т) 1! 3! 5! 7! -(1)- 1) -Σ (2n+1) n-0

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