$1\mathrm{.}23$ 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 $e.$ Do the calculation with

MATLAB $($use format long to display the numbers$).$ Determine the true relative error. For the exact

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

Hint:

Do the following calculation with Python instead of MATLAB:

a$.$ Set the precision with Python $($similar to format long in MATLAB$)$;

b$.$ Calculate value of e$.$

# Python sript

import numpy as np

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

$e=np*exp(1)$

print$($e$)$