Метод дотичних

Так Ні

+ -

Так Ні

program metoddotichnih;

uses crt;

var a,b,c,x,x0,E:real;

function f(x:real):real;

begin

f:=exp(ln(2)*x)-4*x;

end;

function f1(x:real):real;

begin

f1:=exp(ln(2)*x)*ln(2)-4;

end;

function f2(x:real):real;

begin

f2:=exp(ln(2)*x)*ln(2)*ln(2);

end;

begin

clrscr;

writeln('vvedite konci otrezka a,b');

readln(a,b);

writeln('vvedite to4nistj ob4islennja E');

Readln(E);

if f(a)*f2(a)>0 then x:=a

else x:=b;

While abs(x-x0)>E do

begin

x0:=x;

x:=x0-(f(x0)/f1(x0));

end;

writeln(x,' korinj rivnjannja');

writeln('esli sleduyushee chislo prubluzno = 0, to rivnjannja rozvjazane virno');

writeln(f(x):1:3);

readln;

end.

К

program metoddotichnih;

uses crt;

var a,b,c,x,x0,E:real;

function f(x:real):real;

begin

f:=x*x*x-5*x+0.1;

end;

function f1(x:real):real;

begin

f1:=3*x*x-5;

end;

function f2(x:real):real;

begin

f2:=6*x;

end;

begin

clrscr;

writeln('vvedite konci otrezka a,b');

readln(a,b);

writeln('vvedite to4nistj ob4islennja E');

Readln(E);

if f(a)*f2(a)>0 then x:=a

else x:=b;

While abs(x-x0)>E do

begin

x0:=x;

x:=x0-(f(x0)/f1(x0));

end;

writeln(x,' korinj rivnjannja');

writeln('esli sleduyushee chislo prubluzno = 0, to rivnjannja rozvjazane virno');

writeln(f(x):1:3);

readln;

end.

од програми:

Код програми:

program metoddotichnih;

uses crt;

var a,b,c,x,x0,E:real;

function f(x:real):real;

begin

f:=x*x*x*x+x*x-2*(x+1);

end;

function f1(x:real):real;

begin

f1:=4*x*x*x-2*x;

end;

function f2(x:real):real;

begin

f2:=12*x*x+2;

end;

begin

clrscr;

writeln('vvedite konci otrezka a,b');

readln(a,b);

writeln('vvedite to4nistj ob4islennja E');

Readln(E);

if f(a)*f2(a)>0 then x:=a

else x:=b;

While abs(x-x0)>E do

begin

x0:=x;

x:=x0-(f(x0)/f1(x0));

end;

writeln(x,' korinj rivnjannja');

writeln('esli sleduyushee chislo prubluzno = 0, to rivnjannja rozvjazane virno');

writeln(f(x):1:3);

readln;

end.

Домашня робота:

2

program metoddotichnih;

uses crt;

var a,b,c,x,x0,E:real;

function f(x:real):real;

begin

f:=2*x*ln(X)-4;

end;

function f1(x:real):real;

begin

f1:=2*ln(x)+2;

end;

function f2(x:real):real;

begin

f2:=2/x;

end;

begin

clrscr;

writeln('vvedite konci otrezka a,b');

readln(a,b);

writeln('vvedite to4nistj ob4islennja E');

Readln(E);

if f(a)*f2(a)>0 then x:=a

else x:=b;

While abs(x-x0)>E do

begin

x0:=x;

x:=x0-(f(x0)/f1(x0));

end;

writeln(x,' korinj rivnjannja');

writeln('esli sleduyushee chislo prubluzno = 0, to rivnjannja rozvjazane virno');

writeln(f(x):1:3);

readln;

end.

xlnx-4=0

Метод ітерацій

Program metoditeraciy;

Uses Crt;

Function F(x:real):real;

Begin

F:=exp(ln(2)*x)-4*x;

Function F1(x:real):real;

Begin

F1:=exp(ln(2)*x)*ln(2)-4;

End;

end;

Function G(s,x:real):real;

Begin

G:=x-s*F(x);

end;

Var s,a,b,x,e,x0:real;

Begin

clrscr;

writeln ('Vvedit meji');

readln (a,b);

writeln ('Vvedit e');

readln(e);

if abs(F1(a))<abs(F1(b)) then

s:=abs(2/F(b))-0.001

else

s:=abs(2/F(a))-0.001;

repeat

x0:=x;

x:=G(s,x0);

Until

ABS(x-x0)<=e;

writeln ('x=',x:7:5);

Writeln('f(x)=',f(x):1:5);

readln;

end.

Program metoditeraciy;

Uses Crt;

Function F(x:real):real;

Begin

F:=x*x*x-5*x+0.1;

end;

function f1(x:real):real;

begin

f1:=3*x*x-5;

end;

Function G(s,x:real):real;

Begin

G:=x-s*F(x);

end;

Var s,a,b,x,e,x0:real;

Begin

clrscr;

writeln ('Vvedit meji');

readln (a,b);

writeln ('Vvedit e');

readln(e);

if abs(F1(a))<abs(F1(b)) then

s:=abs(2/F1(b)-0.001)

else

s:=abs(2/F1(a)-0.001);

repeat

x0:=x;

x:=G(s,x0);

Until

ABS(x-x0)<=e;

writeln ('x=',x:7:5);

Writeln('f(x)=',f(x):1:5);

readln;

end.

Program metoditeraciy;

Uses Crt;

Function F(x:real):real;

Begin

F:=x*x*x*x+x*x-2*x-2;

end;

Function G(s,x:real):real;

Begin

G:=x-s*F(x);

end;

Var s,a,b,x,e,x0:real;

Begin

clrscr;

writeln ('Vvedit meji');

readln (a,b);

writeln ('Vvedit e');

readln(e);

if F(a)<F(b) then

s:=abs(2/F(b)-0.001)

else

s:=abs(2/F(a)-0.001);

repeat

x0:=x;

x:=G(s,x0);

Until

ABS(x-x0)<=e;

writeln ('x=',x:7:5);

Writeln('f(x)=',f(x):1:5);

readln;

end.

Домашня робота:

2

Program metoditeraciy;

Uses Crt;

Function F(x:real):real;

Begin

F:=2*x*ln(x)-4;

end;

Function G(s,x:real):real;

Begin

G:=x-s*F(x);

end;

Var s,a,b,x,e,x0:real;

Begin

clrscr;

writeln ('Vvedit meji');

readln (a,b);

writeln ('Vvedit e');

readln(e);

if F(a)<F(b) then

s:=abs(2/F(b)-0.001)

else

s:=abs(2/F(a)-0.001);

repeat

x0:=x;

x:=G(s,x0);

Until

ABS(x-x0)<=e;

writeln ('x=',x:7:5);

Writeln('f(x)=',f(x):1:5);

readln;

end.

xlnx-4=0