Question

OUTO OP Use a numerical method of your choice to solve for x in the following equation. Stop when εa < 0.1%. Choose your initial guess(es). 4 cos(x) = ex

Answer 1

MATLAB Script:

close all
clear
clc

syms x
f = 4*cos(x) - exp(x);
tol = 0.1e-2; % 0.1%
x0 = 1; % Initial guess
x = newton(f, x0, tol);
fprintf('Solution, x = %.4f\n', x)

function x = newton(f, x0, tol)
x = x0;
df = diff(f); % f'(x)
while true
x_ = x; % Save previous iteration's result
x = double(x - subs(f, x)/subs(df, x)); % Newton Update Rule
if abs(x_ - x) <= tol % Stopping criteria
break;
end
end
end

Output:

Solution, x = 0.9048