Basic Numerical Analysis Code

Compute the value of the base of natural logarithm e up to 7 significant digits. Calculate exact value using exp(1) command. Prepare a table which shows iteration number, numerical solution, approximate percent relative error and true percent relative error on 4 different columns. Obtain the Taylor series for cos(x) about a = 0. How many terms would be necessary in order to compute cos(π/6) up to 6 significant figures. Using the example script given compute e2, e3 and e4 up to 7 significant figure. How many iterations are required for each?? Example math script % Script for iterative calculations val = 1; % Initial guess es = 0.05; % Error tolerance maxit = 200; % Maximum number of iterations iter = 1; % Initialize iterations sol = val; % Assign the initial guess to solution ea = 100; % Initial approximate relative error while 1 solold = sol; % Assign the solution as old solution sol = sol + 0.5^iter / factorial(iter); iter = iter + 1; % Increase iteration by one if sol ~= 0 ea = abs((sol - solold)/sol)*100; end if ea <= es || iter > maxit break; % Exit the loop end end