% Script deriv3.m
% The derivative approximations get better for awhile
% since the error in last column decreases and then
% they get worse.

% Eventually the derivative approximation becomes zero.
% The reason is that, as h gets closed to 0, 0.5+h will
% be 0.5 for some small non-zero value of h.

% For this h and any smallre ones the numerator in the
% calculation of the ratio r becomes exactly zero.


% try 30 iterations
num_iter = input('Enter number of iterations ');

exact = log(1.1);
fprintf('Exact value = %.10e\n', exact);
fprintf('%5s %18s %18s %18s\n','n','h','r','err');
h = 1.0;
for n = 1 : num_iter
   r = (log(1.1+h) - log(1.1)) / h;
   err = exact - r;
   fprintf('%5d %18.10e %18.10e %18.10e\n',n,h,r,err);
   h = h / 4.0;
end