The taylor series about 0 for the function f(x)=cos (x) ?
1 Answer
Mar 12, 2018
The coefficient is
Explanation:
We seek the coefficient of
#f(x)=cos(x)*1/(1-x)#
Using
#cos(x)=(1-x^2/2+x^4/24+...)# #1/(1-x)=(1+x+x^2+x^3+...)#
We can write this as
#f(x)=(1-x^2/2+x^4/24+...)(1+x+x^2+x^3+...)#
Notice the only terms involving
is obtained by
#x^3+(-x^2/2)*x=x^3-x^3/2=color(blue)(1/2)x^3#