diffquot[f_, x_, h_]  :=  (f[x + h] - f[x])/h

g[x_]  :=  x^2

\(\(\(xi\)\(\ \)\(=\)\(\ \)\(Interval[{N[1], N[1]}]\)\(
\)\)\)

\(Do[
	\ \ \ \ {\ 
        h\  = \ N[1/3. ^i], 
		\ \ \ \ Print[i, \ " ", \ 
          h, \ " ", \ 
          diffquot[Cos, Interval[{N[Pi/4], N[Pi/4]}], h]]
	\ \ \ }, 
{i, 
        40}]\)

N[Cos[Pi/4], 20]