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