function value = p01_fun ( x )

%*****************************************************************************80
%
%% P01_FUN evaluates the function for problem 1.
%
%  Discussion:
%
%    This is a famous example, due to Runge.  If equally spaced
%    abscissas are used, the sequence of interpolating polynomials Pn(X)
%    diverges, in the sense that the max norm of the difference
%    between Pn(X) and F(X) becomes arbitrarily large as N increases.
%
%  Dimension:
%
%    N = 1
%
%  Interval:
%
%    -5 <= X <= 5
%
%  Function:
%
%    1 / ( X * X + 1 )
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    24 August 2011
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, real X, the point at which the function
%    is to be evaluated.
%
%    Output, real VALUE, the value of the function at X.
%
  value = 1.0 ./ ( x .* x + 1.0 );

  return
end
