function errors_test29 ( )

%*****************************************************************************80
%
%% errors_test29() compares the exponential Taylor series for small argument.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    10 May 2024
%
%  Author:
%
%    John Burkardt
%
  fprintf ( 1, '\n' );
  fprintf ( 1, '+=============================================+\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|  Exercise 29                                |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|  f(z) = ( e^x - 1 - x ) / x^2               |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|  Evaluate f(x) at:                          |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|    x = 10^(-8)                              |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|  The correct answer:                        |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|    f(x) approx 0.5                          |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '+=============================================+\n' );

  x = 1.0E-08;
  f = ( exp ( x ) - 1.0 - x ) / x^2; 

  f_exact = 0.50000000166666667;

  fprintf ( 1, '\n' )
  fprintf ( 1, '  Computed result = %g\n', f );
  fprintf ( 1, '  Correct result  = %20.16g\n', f_exact );

  return
end
