(6)(6)> > > > > > > > > > > > (1)(1)> > (3)(3)> > > > (2)(2)> > > > > > (5)(5)(4)(4)Bisection methodBisection methodrestart:a[0]:=1:b[0]:=2:P[0]:=(a[0]+b[0])/2;e:=10^(-1):P

(1)

(6) (6)

>

(1) (1)

>

(3) (3)

>

(2) (2)

>

(5) (5) (4) (4) Bisection method

Bisection method restart:

a[0]:=1:b[0]:=2:P[0]:=(a[0]+b[0])/2;e:=10^(-1):

P₀ 3 2

f := unapply(x^3+4*x^2-10,x);

f x x³ 4 x² 10

for i from 1 to 100 do

if f(a[i-1])*f(P[i-1])<0 then

b[i]:=P[i-1];a[i]:=a[i-1]:P[i]:=(a[i]+b[i])/2:

else

a[i]:=P[i-1]:b[i]:=b[i-1]:P[i]:=(a[i]+b[i])/2:

if abs(P[i-1]-P[i])<e then break fi end if

end do;

printf(" n | a[n]| |b[n] | P[n] \n");

for n from 0 to 100 do printf("%2.1f| %1.11f |%1.11f

|%1.11f|%1.11f \n",n,a[n],b[n], P[n],abs(P[i-1]-P[i])) end do;

n | a[n]| |b[n] | P[n]

0.0| 1.00000000000 |2.00000000000 |1.50000000000|0.03125000000 1.0| 1.00000000000 |1.50000000000 |1.25000000000|0.03125000000 2.0| 1.25000000000 |1.50000000000 |1.37500000000|0.03125000000 3.0| 1.25000000000 |1.37500000000 |1.31250000000|0.03125000000 4.0| 1.31250000000 |1.37500000000 |1.34375000000|0.03125000000 5.0|

Error, (in fprintf) number expected for floating point format Fixed point

Fixed point restart:

a[0]:=1:b[0]:=2:P[0]:=(a[0]+b[0])/2;

P₀ 3 2 g := unapply(cos(x),x);

g x cos x

e:=10^(-4):

for i from 1 to 400 do P[i]:=evalf(g(P[i-1]));

if abs(P[i-1]-P[i])<e then break fi

(2)

>

(7) (7)

(11) (11)

>

(12) (12) (8) (8)

>

(9) (9)

>

(10) (10) od:

printf(" n | P[n] \n");

for n from 0 to 10 do printf("%2.1f| %1.11f \n",n, P[n]) end do;

n | P[n]

0.0| 1.50000000000 1.0| 0.07073720167 2.0| 0.99749916720 3.0| 0.54240499230 4.0| 0.85646970900 5.0| 0.65510880170 6.0| 0.79298164580 7.0| 0.70172416830 8.0| 0.76373031130 9.0| 0.72226108210 10.0| 0.75031288570 Newton method

Newton method restart:

a[0]:=1:b[0]:=2:P[0]:=(a[0]+b[0])/2;e:=10^(-4):

P₀ 3 2

f := unapply(x^3+4*x^2-10,x);fd:= unapply(diff(f(x),x),x);fd(1);

f x x³ 4 x² 10 fd x 3 x² 8 x

11 for i from 1 to 4 do

P[i]:=P[i-1]-f(P[i-1])/fd(P[i-1]):

if abs(P[i-1]-P[i])<e then break fi od:

printf(" n | P[n] \n");

n | P[n]

0.0| 1.50000000000 1.0| 1.37333333300 2.0| 1.36526201500 3.0| 1.36523001400 4.0|

Error, (in fprintf) number expected for floating point format Secant method

Secant method restart:

f := unapply(cos(x)-x,x);

f x cos x x

a[0]:=0:b[0]:=Pi/2:P[1]:=(a[0]+b[0])/2;e:=10^(-3):evalf(f(Pi/6)*f (Pi/4));

(3)

(12) (12)

>

(13) (13)

>

P₁ 4 0.02680905413

P[0]:=Pi/6;

P₀ 6 for i from 2 to 4 do

P[i]:=P[i-1]-f(P[i-1])*(P[i-2]-P[i-1])/(f(P[i-2])-f(P[i-1])):

if abs(P[i-1]-P[i-2])<e then break fi

Error, cannot determine if this expression is true or false: od:

(1/12)*Pi < 1/1000

printf(" n | P[n] \n");

n | P[n]

0.0| 0.52359877580 1.0| 0.78539816350 2.0| 0.73667993540 3.0|

Error, (in fprintf) number expected for floating point format