Question

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

Answer 1

The required Taylor Series is:

`f(x) = -1`

Explanation:

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`