% truncation_example_1.m
% Truncation error example #1
% Reducing "h" to make the secant slope a better approximation 
% to the derivative which is the mathematical limit of secant slopes.

x = 1;    % point at which we are approximating the derivative
fprintf('\nTrying to approximate slope of sin at %f\n',x);
true_slope = cos(x) % (here we happen to know the derivative exactly)
n = 8;
fprintf('             h                  secant slope               error\n');
for i = 1:n
  h=10^-i;
  secant_slope = ( sin(x+h) - sin(x) ) / h;
  the_error = secant_slope - true_slope;
  fprintf('%23.15f %23.15f %23.15f\n',h,secant_slope,the_error);
end