Question
Asked Nov 22, 2019
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Derive the Taylor series for cos x centered at a=0.

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Expert Answer

Step 1

The Taylor series for the function f(x) centered at a is given by,

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+ f"(a)(x-a) f(x)=f(a)+f(a)(x-a)+f"(a)-a)" .. 2! 3!

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Step 2

Let f(x) = cos x. Then compute the derivatives as follows.

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f'(x)-sinx f'(x)cos.x f"(x) sinx f (x) cosx f(x)-sin x

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Step 3

Substitute x = 0 in the derivatives and ...

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f'(0)sin (0) =0 f(0)cos(0) =-1 f"(0) sin 0 0 f (0) cos 0 -1 f(0)sin0 0

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