C#: Calculate the Exponential Function exp(x) using Taylor Expansion

gistfile1.cs

using System;

namespace EulerNumberTaylorExpansion
{
	class Program
	{

		/// <summary>
		/// See: http://en.wikipedia.org/wiki/Exponential_function
		/// See: http://en.wikipedia.org/wiki/Taylor_expansion
		/// </summary>
		/// <param name="args"></param>
		static void Main( string[] args )
		{

			// Print Banner
			Console.WriteLine(
				"\nCSC 340 Scientific Computing\n" +
				"Calculate exp(3.7) using Taylor's Expansion\nAndrew M. Barfield\n" +
				DateTime.Now.ToLongDateString() + "\n" +
				DateTime.Now.ToLongTimeString() +
				"\n\n" );

			Console.WriteLine( "exp(3.7) = " + CalculateExp( 3.7 ).ToString("##.###") );

			Console.Read();
		}


		/// <summary>
		/// Calculate exp(x) using Taylor Expansion
		/// </summary>
		/// <param name="x">Exponent for Euler's Number</param>
		/// <returns>Returns exp(x)</returns>
		static double CalculateExp( double x )
		{
			
			// Holds and returns final answer
				double answer = 0;

			// Holds previous answer and is used to stop Taylor Expansion
				double oldanswer = 0;

			// Summation index variable
				double k = 0;


			// Refine the solution by adding more terms to the Taylor Expansion.
			// Stop when the answer doesn't change.
				while ( true )
				{

					answer += Math.Pow( x, k ) / Factorial( k );

					if ( answer == oldanswer )
					{
						break;
					}
					else
					{
						oldanswer = answer;
						k++;
					}

				}


			// Write directly to the console here to avoid global variable
				Console.WriteLine( "Answer calculated in " + k.ToString() + " iterations." );


			// Return solution to caller
				return answer;
		}


		/// <summary>
		/// Calculate the factorial for x
		/// </summary>
		/// <param name="x"></param>
		/// <returns></returns>
		static double Factorial( double x )
		{

			double answer = 1;
			double counter = 1;

			while ( counter <= x )
			{
				answer = answer * counter;
				counter++;

			}

			return answer;
		}

	}
}

Output.txt

CSC 340 Scientific Computing
Calculate exp(3.7) using Taylor's Expansion
Andrew M. Barfield
Thursday, January 15, 2009
1:56:36 PM

Answer calculated in 29 iterations.
exp(3.7) = 40.447