$1\mathrm{.}23$ Use the first seven terms in cos$($x$)=1-$ x$^2/2!+$x$^4/4!-$ x$^6/6!+$ x$^8/8!-$ x$^10/10!+.....$ to calculate an estimated value of $e.$ Determine the true relative error. For the exact

value of $e,$ use exp$(1)$ in Python.

Hint:

# Python sript

import numpy as np

np$.$set$\_$printoptions$($precision$=15)$

$e=np*exp(1)$

print$($e$)$