Please use python3 and include all the analysis and discussion, thank you.

Calculate the Taylor polynomials centered at 0, k=0 T (x= k! for f = cos(x) for the following 4 values of x, 1 2 3 2 3 4 which is equivalent to 10'10'10'10 XE 2 x , for j = 1,2,3,4 10 For each value ofj, find the smallest integer n such that cos