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

Aug 21, 2017

The required Taylor Series is:

$f \left(x\right) = - 1$

#### Explanation:

The Taylor Series of $f \left(x\right)$ 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 $f \left(x\right) = \cos \pi$, we have

$\setminus \setminus f \left(\frac{1}{2}\right) = \cos \pi = - 1$

$f ' \left(\frac{1}{2}\right) = 0$, along with all higher derivatives.

Hence, the required Taylor Series is:

$f \left(x\right) = - 1$