For this question we must use MATLAB and please show all cod

For this question we must use MATLAB and please show all code, thank you

Refer to lab experiment 6.4 part (a) and find the roots of the equation below f_1 (x) = cos (x) - x = 0, for 0

Solution

Matlab function bisect.m to find root of the function using bisection method

function [Root,Iter] = bisect(f,a,b,tol) % The function definition bisect.m
if nargin ~= 4 %Checking number of arguments to the function bisect
% if number of arguments not equal to 4 print error message
error(\'Number of arguments must be four\');
end
if tol < 0 % is the input tol value is negative
% print error message
error(\'Error tolerence must be a positive quantity\');
end
Max_Iter = 100; % maximum number of iterations allowded
fa = f(a); % functional at a
fb = f(b);% functional at b
if(fa>0 && fb <0) % checking fafb <0 or not
xplus = a;
xminus = b;
elseif(fa<0&&fb>0)
xplus = b;
xminus = a;
else
error(\'Not a valid bracketing interval\');
end
Iter = 0; % iteration counter
xnew=(xplus+xminus)*0.5; % new point in the intervel
err=abs((xplus-xminus)/(xplus+xminus))*100; % estimated error at new x value
while err>tol && Iter<Max_Iter % iterate loop unitil error < tol or Iter > Max_iter
fnew=f(xnew); % function evaluating at newly computed x value
if(fnew>0) % determin the sign of f at new x value
xplus=xnew; % if f is positive replave x+ with new x
else
xminus=xnew; % if f is negative replace x- with new x
end
Iter = Iter +1; % Increment Iteration counter
xnew=(xplus+xminus)*0.5; % new x value
err=abs((xplus-xminus)/(xplus+xminus))*100; % estimated error at new x value
end
if(Iter>=Max_Iter) % faild to converge
error(\'Faild to converge\');
else
Root = xnew; % after the iterations the approximated root will be in xnew
end
end
  

Calling the function get root of the given function

>> f = @(x) cos(x)-x; % The given function
>> a = 0; b = pi/2; % two boundaries
>> tol = 0.1; % percentage of tolerence
>> [Root,Iter] = bisect(f,a,b,tol) % Calling the function to get the root

Root =

0.7390

Iter =

11

>> f(Root)% Validating the result by finding f(root)

ans =

1.5044e-04

>>