find e^x with out using exp(x)

[sniper6560]

#include<iostream>// e^x    with factorial function
using namespace std;
#include<cmath>
double factorial(double);
int main ()
{
	int i=1;
	 double x, a=1, j,  y, z, E=0.0000000001;//E is error rate
	cout<<"enter x to get e^x : "<<endl;
	cin>> x;
	y=x;
	for(    ;    ;    )
	{
		j=factorial(i);
		z=y/j;
		if( fabs(z)<E)
			break;
		else
		{
			a=a+z;   
			y=x*y;
			i++;}
	}cout<<"e ^x = "<<a<<" exact = "<<exp(X)<<" error rate "<<exp(x)-a <<endl;
	return 0;
}
	double factorial (double n)
	{
		double fact=1;
		if((n==0)||(n==1))
			fact=1;
		else{
			for(int j=2; j<=n; j++)
			{
				fact*=j;
			}
		}
		return fact;
	}

[VernonDozier]

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