% Script deriv.m
% Uses the limit formula from calculus for estimating the
% derivative of a function cos(x) at x = 0.5
%
% Why does this eventually fail?

num_iter = input('Enter number of iterations ');

exact = cos(0.5);
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 = (sin(0.5 + h) - sin(0.5)) / h;
   err = exact - r;
   fprintf('%5d %18.10e %18.10e %18.10e\n',n,h,r,err);
   h = h / 4.0;
end