I am working on the following Matlab Homework Problem and wanted to compare my answers. I have supplied the problem, Code used and the partial answer. Please show all work in matlab format.

Thanks

$9.$Modify the user$-$defined function Bisection, so that the table is not generated and the outputs are the approximate root and the number of iterations needed for convergence. All other parameters, including default values, are to remain unchanged. Save this function as Bisection$\_2.$ Execute Bisection$\_2$ to find the root of in the interval $.$

Partial Solution:

$>>$ f $=$ @$($x$)($sin$($x$)+2*$cos$($x$)-1)$;

$>>[$c$,$k$]=$ Bisection$\_1($f$,5,6)$

c $=5\mathrm{.}6397$

k $=14$

MatLab Code used:

function c $=$ Bisection$2($f$,$ a$,$ b$,$ kmax, tol$)$

$\%$

$\%$ Bisection$2$ uses the bisection method to approximate a root of f$($x$)=0$

$\%$ in the interval $[$a$,$b$].$

$\%$

$\%$ c $=$ Bisection$2($f$,$ a$,$ b$,$ kmax, tol$),$ where

$\%$

$\%$ f is an anonymous function representing f$($x$),$

$\%$ a and b are the endpoints of interval $[$a$,$b$],$

$\%$ kmax is the maximum number of iterations $($default $20),$

$\%$ tol is the scalar tolerance for convergence $($default $1$e$-4),$

$\%$

$\%$ c is the approximate root of f$($x$)=0.$

$\%$

if nargin $<5||$ isempty$($tol$),$ tol $=1$e$-4$; end

if nargin $<4||$ isempty$($kmax$),$ kmax $=20$; end

if f$($a$)*$f$($b$)>0$

c $=$ 'failure';

return

end

disp$(\text{'}$ k a b c $($b$-$a$)/2\text{'})$

for k $=1$:kmax

c $=($a$+$b$)/2$; $\%$ Find the first midpoint

if f$($c$)==0\%$ Stop if a root has been found

return

end

fprintf$(\text{'}\%3$i $\%11\mathrm{.}6$f$\%11\mathrm{.}6$f$\%11\mathrm{.}6$f$\%11\mathrm{.}6$f

$\text{'},$k$,$a$,$b$,$c$,($b$-$a$)/2)$

if $($b$-$a$)/2<$ tol $\%$ Stop if length of interval is within tolerance

return

end

if f$($b$)*$f$($c$)>0\%$ Check sign changes

b $=$ c; $\%$ Adjust the endpoint of interval

else

a $=$ c;

end

end