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

##### 1 Answer

Aug 21, 2017

The required Taylor Series is:

# f(x) = -1 #

#### Explanation:

The Taylor Series of

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

So, for the function

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

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

Hence, the required Taylor Series is:

# f(x) = -1 #