i was asked to develop a program that will evaluate a function for -0.9<x<0.9 in steps of 0.1 by arithmetic statement, and series allowing as many as 50 terms. however, end adding terms when the last term only affects the 6th significant in answer

the function and its series expansion is

f(x)=(1+x^2)^(-1/2)=1-1/2*(x^2)+(1*3)/(2*4)*(x^4)-(1*3*5)/(2*4*6)*(x^6)+...-....

Answer 1

[Youssef Khmou]

Developing Taylor requires to compute the derivative :

      x=-.9:.1:.9;
      f=1./sqrt(1+x.^2);
      g=1-1/2*(x.^2)+(1*3)/(2*4)*(x.^4)-(1*3*5)/(2*4*6)*(x.^6);
      plot(x,g,x,f,'+r')

Answer 2

[Roger Stafford]

You can use a for-loop with a 'break' to generate successive terms and their sum. For each value of x you are required to use, get the corresponding f with

   f = 1;
   t = 1;
   for k = 1:50
     t = -(2*k-1)/(2*k)*x^2*t; % Iteratively compute successive terms
     f = f + t; % Update the sum of the series
     % Exit the for-loop when the current term, t, is too small
     if abs(t) < ????
       break
     end
   end