Shaddy-Ethical-hacking: A C - PROGRAM TO FIND THE VALUE OF exp(0.5) USING TAYLOR SERIES

Sunday, 26 May 2013

0 A C - PROGRAM TO FIND THE VALUE OF exp(0.5) USING TAYLOR SERIES

TAYLOR SERIES

The Taylor series of a real or complex-valued function ƒ(x) that is infinitely differentiable in a neighborhood of a real or complex number a is the power series

$f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots.$

$1 + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \frac{x^5}{5!}+ \cdots = 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24} + \frac{x^5}{120} + \cdots\! = \sum_{n=0}^\infty \frac{x^n}{n!}.$

THE PROGRAM :

#include<stdio.h>
#include<math.h>
#include<float.h>
#include<conio.h>
void main()
{
    double x=0.5,e=1.0,term=1.0,fact=1.0;
    int i;
    for(i=1;term>=FLT_EPSILON;i++)
    {
        fact=fact*i;
        term=pow(x,i)/fact;
        e=e+term;
    }
    printf("\n Sum without using library function exp(%lf) = %lf \n",x,e);
    printf("\n Sum using library function exp(%lf) = %lf \n",x,exp(x));
    getch();
}

Just copy and paste into your Microsoft Visual C++ or Turbo C (these are program developing software)

Or else you can try this demo file and use it ...
Click HERE to download this file.
(Press ctrl+z and hit Enter to end the program)..
~NOTE~ : While executing if you get any warning then just ignore it and continue with your program...

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