Question

Solve the following problem in MATLAB. Use format compact for all work to suppress extra lines. Show all work and add comments as needed to explain your logic/steps. 1. The function f(x) = e* can be approximated by the following Taylor series: n=0 The first few terms of the Taylor series are: e 1 + x + + + + ...... 2! 3! 4! Keep in mind that the "!" symbol denotes factorial. For example, the factorial of 4 = 4! = 1*2*3*4. MATLAB has a built-in factorial command that can be used. In a script file, prompt the user for the value of the exponent x as an integer (in terms of the function ex). Then with a "while” loop, calculate the approximate value of e' using the above Taylor series. The output message should display "The approximate value of e^x is XX.XXXXXX” where XX.XXXXXX is the numeric value displayed to 6 decimal places. The output value should be correct (or exactly match your calculator's output of e*) up to 6 decimal places.

Answer 1

%Matlab script to input the value of x and calculate the value of exp(x)
% to a precision of 6 decimal places
format compact;
% input of x
x = input('Enter the value of x for calculation of exp(x) : ');
n = 0; % set n=0
% set initial approx value to 0
approx = 0;
% set actual value to exp(x) % actual e^x value
actual = exp(x);
% calculate the absolute difference between the calculateed and approximate
% value
eps = abs(approx-actual);
% loop that continues till the approx value matched the actual value upto 6
% decimal places
while eps > 10^-7
% calculate approx for (n+1)th term
approx = approx + (x^n/factorial(n));
n = n+1; % increment n
% calculate the difference
eps = abs(approx-actual);
end
% display the approximate value upto 6 decimal places
fprintf('The approximate value of e^x is %.6f \n',approx);
%end of script

Output:

Enter the value of x for calculation of exp (x) : 23 The approximate value of enx is 9744803446.248903