% Write a program to solve t aylor series expan sion from zero to third % order

Question

% Write a program to solve taylor series expansion from zero to third

% order to predict f(3) for: f(x)= 25x^3+ 6x^2 - 7x-88

% Display results in array

x= 1;

z= 3;

h= z-x;

n(1)= 1;

f_n(1)= 25* x^(3)- 6*x^(2)+7*x- 88;

f_n(2)= 75* x^(2)- 12*x^(1)+7;

f_n(3)= 150*x-12;

f_n(4)= 150;

exact = 25*3^(3)-6*3^(2)+7*3-88;

array=0;

for i=1:4

    Taylor=(f_n(i)/ factorial(i-1))*(h^(i-1));

    n(i+1)= Taylor + n(i);

    error= ((exact- n(i+1))/ (exact))*100;

    approx= abs((n(i+1)-n(i))/n(i+1))* 100 ;       

end

L=[f_n() n(i+1) error];

fprintf ('  Function Value       Exact Value       True Percent Error ');

fprintf ('  %4.0f                %4.0f              %4.0f n',L);

disp (approx)

Problem: not all the results are displaying, please help.

Explanation / Answer

% Write a program to solve taylor series expansion from zero to third

% order to predict f(3) for: f(x)= 25x^3+ 6x^2 - 7x-88

% Display results in array

clear all

close all

clc

x=1;

z= 3;

h= z-x;

n(1)= 1;

f_n(1)= 25* x^(3)- 6*x^(2)+7*x- 88;

f_n(2)= 75* x^(2)- 12*x^(1)+7;

f_n(3)= 150*x-12;

f_n(4)= 150;

exact = 25*3^(3)-6*3^(2)+7*3-88;

array=0;

for i=1:4

Taylor=(f_n(i)/ factorial(i-1))*(h^(i-1));

n(i+1)= Taylor + n(i);

error= ((exact- n(i+1))/ (exact))*100;

approx= abs((n(i+1)-n(i))/n(i+1))* 100 ;

end

%L=[f_n() n(i+1) error];

fprintf (' Function Value Exact Value True Percent Error approx ');

fprintf (' %8.3f %8.3f %8.3f %8.3f ',exact,n(i+1),error,approx);

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