Question

Write a matlab program to apply Horner's algorithm to evaluate the sum of the first four nonzero terms of the Taylor series for sin(x) with c=0. Your program should not use any arrays, the exponentiation operator or the factorial function. Print out your program and include the output upon execution for the special case where x = 1. How many nonzero terms of the above Taylor series are needed to guarantee that the sum approximates sin(x) to within .0001 for any x with -π /2 < x < π /2. Show your computations.

Answer 1

Below is the code for your question:

clc%clears console
clear all%clears the history
close all;
syms f(x)
f(x)=sin(x);
F=f;
count=0;
j=0;
while(count~=4)
F=diff(F);
if(F(0)~=0)
count=count+1;
end
j=j+1;
end
sum=0;
for i=j:-1:0
sum=sum*x/(i+1)+(F);
F=int(F);
end
disp(sum)
fprintf('Taylor series with fith first 4 non zero sums of sinx at x=1 is: %.10f',eval(sum(1)));

execution:

------------------------------------------------------Thank you-------------------------------------------------------