Instructions:

$1.$ Create using MATLAB

$2.$ Use the following program:

$ClC$

clear

$$Approximate the value of $e^{{?}^{?}}x$ using the Taylor Series

$x=$ input$($ 'Enter the value of $x$ for $e^{{?}^{{?}^{?}}}x.,x=\text{'})$ ;

$t=$ input $($ Enter the amount of desired terms. $,t=1)$;

$i=1$;

e$\_$taylor $=0$; $\%$ initializing the variable for the accumulator

while $it$

e$\_$taylor $=$ e$\_$taylor $+x^{{?}^{{?}^{?}}}\frac{i-1}{?}$ factorial $(i-1)$;

$i=i+1$;$,\frac{2}{0}$ change the value of variable $i$

end

real$\_$value $=$exp$(x)$;

disp$(\text{'}$Real Value' $)$

disp$($real$\_$value$)$

disp$(\text{'}$Approximated value with Taylor series'$)$

disp $($e$\_$taylor$)$

disp$(\text{'}$amount of iterations'$)$

disp$(i)$

disp$(\text{'}$real error'$)$

$E=$ abs $($e$\_$taylor $-$ real$\_$value$)$;

disp$(E)$

$3.$ Modify the program to do:

a$.$ The program calculates the actual value with the Matlab exp$($x$)$ command.

b$.$ Change the while cycle for a for$-$loop command from $1$ to imax iteration.

c$.$ Declare an imax variable equal to $100$ to assign the maximum iteration.

d$.$ Add before the for loop a line with: real $=$ exp $($x$)$;

e$.$ Assign the value of $0\mathrm{.}0001$ to a tolerance variable. If you want to challenge yourself, create a menu to select the tolerance value with different values.

f$.$ Add within the loop algorithm and if abs $($e$\_$taylor $-$ real tolerance, then break.

$4.$ Create the flowchart of the program.