How do you find the Taylor polynomial of degree n=4 for x near the point a=pi for the function cosx?

1 Answer
May 15, 2017

-1+(x-pi)^2/2-(x-pi)^4/241+(xπ)22(xπ)424

Explanation:

cos(pi) = -1cos(π)=1
1st Derivative: -sin(x) " then " f'(pi)=0
2nd Derivative: -cos(x) " then "f''(pi)=-1
3rd Derivative: sin(x) " then " "f'''(pi)=0
4th Derivative: cos(x) " then " f''''(pi)=-1

Odd terms except the first is zero then use only the even terms.
Putting it all together:

-1+(x-pi)^2/(2!)-(x-pi)^4/(4!)...