Question

An algorithm for the Bisection method function root Bisect ( x,, x, e, imax) while i s imax x' ←(x, +x.)/2 [or 1. ← f(x.) if f. = 0 or (x,-x,) x,+(x,-x,)/2] /r +x, then root ←x exit end if ii +1 if f, × f, < 0 then else end if end while root 'failed to converge"

Answer 1

%%%PART A,Bisect.m function file

function root=Bisect(xl,xu,eps,imax,f)
i=1;
fl=f(xl);
fprintf(' iteration approximation \n')
while i<=imax
xr=(xl+xu)/2;
fprintf('%6.0f %18.8f \n',i,xr)
fr=f(xr);
if fr==0||((xu-xl)/abs(xu+xl))<eps
root=xr;
return
end
i=i+1;
if fr*fl<0
xu=xr;
else
xl=xr;
fl=fr;
end
end
fprintf('failed to converge in %g iterations\n',imax)

Bisect.m 28 29 30 31 32 function root Bisect (xl, xu,eps, imax, f) fl-f (xl) fprintf (' iteration while i<=imax approximation \n') 35 - 36 37- fprintf ( %6 . 0f %18. 8f \n", i, xr) fr=f (xr) ; if fr-ol l ( (xu-x1) /abs (xu+x1)) <eps root-xr ; return end if frfl<o xuFX else 44 - 45 f1=fr ; end 47 - end fprintf ('failed to converge in %g iterations\n", imax) 49 50

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5

%%%%Part B ,function file

function f=F_v(h)
f=pi*h.^2*(3*4.1-h)/(3)-45;

%%%%%%OUTPUT

Command Window >>hl-Bisect (0,4.1,le-4,20,F_v) 2 iteration approximation 2.05000000 1.02500000 1.53750000 1.79375000 1.92187500 1.98593750 2.01796875 2.03398437 2.04199219 2.04599609 2.04799805 2.04699707 2.04749756 2.04724731 2.04737244 10 12 13 14 15 2.0474

%%%%%%%%%%%%%%PART C

%%%%%%FUNCTION FILE

function f=f_velocity(m)
c=13.5;
t=10;
g=9.81;
f=g*m*(1-exp((-c*t)/m))/c-40;

%%RESULT

Command Window >>[h] Bisect (1,100,1e-4,20,@f velocity) 6 iteration approximation 50.50000000 75.25000000 62.87500000 56.68750000 59.78125000 61.32812500 62.10156250 62.48828125 62.29492188 62.19824219 62.14990234 62.12573242 62.11364746 62.10760498 10 12 13 62.1076