// this program approximates the function e raised to the x power
// using one, two, three, an four terms of an approximating 
// polynomial
#include <iostream.h>
#include <iomanip.h>
#include <math.h>

int main()
{
  float x, funcvalue, approx, difference;

  cout << "\nEnter a value of x: ";
  cin  >> x;

    // print two title lines
  cout << " e to the x       Approximation      Difference\n";
  cout << "-------------     -------------     -------------\n";

  funcValue = exp(x);      // use the library function

    // calculate the first approximation
  approx = 1;
  difference = fabs(funcvalue - approx);
  cout << setw(10) << setiosflags(ios::showpoint) << funcvalue
       << setw(18) << approx
       << setw(18) << difference << endl;

    // calculate the second approximation
  approx = approx + x;
  difference = fabs(funcValue - approx);
  cout << setw(10) << setiosflags(ios::showpoint) << funcValue
       << setw(18) << approx
       << setw(18) << difference << endl;

    // calculate the third approximation
  approx = approx + pow(x,2)/2.0;
  difference = fabs(funcvalue - approx);
  cout << setw(10) << setiosflags(ios::showpoint) << funcvalue
       << setw(18) << approx
       << setw(18) << difference << endl;

    // calculate the fourth approximation
  approx = approx + pow(x,3)/6.0;
  difference = fabs(funcValue - approx);
  cout << setw(10) << setiosflags(ios::showpoint) << funcValue
       << setw(18) << approx
       << setw(18) << difference << endl;

  return 0;
}