What is the Taylor series for? : $f(x)=cospi$ about $a=1/2$

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Answer 1 · 2017-08-21T21:23:23

The required Taylor Series is:

$f(x) = -1$

The Taylor Series of $f(x)$ about the pivot $x=a$ is given by:

$f(x) = f(a) + f'(a)(x-a)/(1!) + f''(a)(x-a)^2/(2!) + ...$

So, for the function $f(x)=cospi$ , we have

$\ \f(1/2) = cospi = -1$

$f'(1/2) = 0$ , along with all higher derivatives.

Hence, the required Taylor Series is:

$f(x) = -1$

What is the Taylor series for? : f(x)=cospif(x)=cospi about a=1/2a=1/2