Nama : Hasna Nabila Khansa

NPM : 140 110 1200 74

1.

Deret Taylor

Penguraian Deret Taylor untuk di adalah:

Untuk mencari F(0,5) digunakan iterasi: Iterasi I

Iterasi II

Iterasi III

Iterasi IV

Iterasi V

-->exec('faktorial.sci')

-->function [hasil]=faktorial(x)

--> if (x else hasil=x*faktorial(x-1);

--> end

-->endfunction

-->exec('iterasi.sci')

-->function it=iterasi(n,x)

--> it=2^(n-1)*x^(n-1)/faktorial(n-1)

--> if (n==1) then it=1;

--> elseif (n==2) it=1+18*x;

--> else it=1+18*x;

--> for i=2:(n-1)

--> it=it+2^i*x^(i)/faktorial(i);

--> end

--> end

-->endfunction

-->iterasi(1,0.5)

ans =

1.

-->iterasi(2,0.5)

ans =

10.

-->iterasi(3,0.5)

ans =

10.5

-->iterasi(4,0.5)

ans =

10.666667

-->iterasi(5,0.5)

ans =

10.708333

-->galat21=abs((iterasi(2,0.5)-iterasi(1,0.5))/iterasi(2,0.5))*100

galat21 =

90.

-->galat32=abs((iterasi(3,0.5)-iterasi(2,0.5))/iterasi(3,0.5))*100

galat32 =

4.7619048

-->galat43=abs((iterasi(4,0.5)-iterasi(3,0.5))/iterasi(4,0.5))*100

galat43 =

1.5625

-->galat54=abs((iterasi(5,0.5)-iterasi(4,0.5))/iterasi(5,0.5))*100

galat54 =

0.3891051

2.

Deret Taylor

Penguraian Deret Taylor untuk di adalah:

Untuk mencari F(0,5) digunakan iterasi: Iterasi I/2

Iterasi II

Iterasi III

Iterasi IV

Iterasi V

-->exec('faktorial.sci')

-->function [hasil]=faktorial(x)

--> if (x else hasil=x*faktorial(x-1);

--> end

-->endfunction

-->exec('iterasi2.sci')

-->function iter=iterasi2(n,x)

--> iter=3^(n-1)*x^(n-1)/(2*faktorial(n-1))

--> if (n==1) then iter=0.5;

--> elseif (n==2) iter=0.5+1.5*x;

--> else iter=0.5+1.5*x;

--> for i=2:(n-1)

--> iter=iter+3^(i)*x^(i)/(2*faktorial(i));

--> end

--> end

-->endfunction

-->iterasi2(1,0.5)

ans =

0.5

-->iterasi2(2,0.5)

ans =

1.25

-->iterasi2(3,0.5)

ans =

1.8125

-->iterasi2(4,0.5)

ans =

2.09375

-->iterasi2(5,0.5)

ans =

2.1992188

-->galat21=abs((iterasi2(2,0.5)-iterasi2(1,0.5))/iterasi2(2,0.5))*100

galat21 =

60.

-->galat32=abs((iterasi2(3,0.5)-iterasi2(2,0.5))/iterasi2(3,0.5))*100

galat32 =

31.034483

-->galat43=abs((iterasi2(4,0.5)-iterasi2(3,0.5))/iterasi2(4,0.5))*100

galat43 =

13.432836

-->galat54=abs((iterasi2(5,0.5)-iterasi2(4,0.5))/iterasi2(5,0.5))*100

galat54 =

4.7957371