Matematica

TAREA DOMICILIARIA N°4

1)
function y=f(x)
y=sin(x)-2*cos(x)+x^2-((3.14^2)-2);

function y =df(f,x)
e=0.00001;
y=(feval(f,x+e)-feval(f,x-e))/(2*e);
>>x=0
x=
  0
>>f(x)
ans=    -9.8696
>>df(@f,x)
ans=
    1

2)
function y=f(x)
y=sin(x)-2*cos(2x)+x^2-((pi^2)-2);

function y=f1(x)
y=cos(x)+4*sin(x)+2*x;

function y=newt(f,f1,x)
x1=x;
error=1;emin=0.00001;
while error>emin
    x2=x1-(feval(f,x1)/feval(f1,x1));
    error=abs(x2-x1);
    x1=x2;
end
y=x1;
 x=pi

x =

    3.1416

>> f(x)

ans =

   -9.8996

>> g1(x)ans =

 1

>> newt(@f,@f1,x)

ans =

    3.1308

3)
function y=f(x)
y=sin(x)-2*cos(2x)+x^2-((pi^2)-2);

function y=raiz(f,x)
x1=x;
e=0.0001;
error=1;
emin=0.00001;
whileerror>emin
    x2=x1-(feval(f,x1)*e*2/(feval(f,x+e)-feval(f,x-e)));
    error=abs(x2-x1);
    x1=x2;
end
y=x1;
 f(x)

ans =

  -9.8696

>> raiz(@f,x)

ans =

    3.1308
4)function y = f(x)
y = sin(x)-2*cos(2*x)+x^2-(pi^2-2);

function y= f2(a,b,n,f)
x=linspace(a,b,n+1);
suma=0;
for i=1:n
area=(x(i+1)-x(i))*(feval(f,x(i+1))+feval(f,x(i)))/2;
suma=suma+area;
endsuma

>> f2(pi,3*pi,101,@f)

suma =

219.2789

5)
function fxy = f (t,y)
fxy=0.235*(1-y)*(1+2*y)^2

function [t,y] = euler (f,a,b,yo,n)
h=(b-a)/n;
t(1)=a;
y(1)=yo;
for i=1:n
 t(i+1) = t(i) + h;
  y(i+1)= y(i) + h*feval(f,t(i),y(i));
end

[x,y]=euler(@ft,2,6,0,40)
x =
  Columns 1 through 8
         0    0.4000    0.8410    1.3250    1.8540    2.4300    3.0550    3.7310  Columns 9 through 16
    4.4600    5.2440    6.0850    6.9850    7.9460    8.9700   10.0590   11.2150
  Columns 17 through 24
   12.4400   13.7360   15.1050   16.5490   18.0700   19.6700  21.3510   23.1150
  Columns 25 through 32
   24.9640   26.9000   28.9250   31.0410   33.2500   35.5540   37.9550   40.4550
  Columns 33 through 40
   43.0560   45.7600   48.5690   51.4850   54.5100  ...