(* V on [0.4, 0.75] *)
V[t_]:= 2(810447 - 5630400 t + 14463600 t^2 - 15640000 t^3 + 6120000 t^4)/1127;
(* Verify that this agrees with Appendix 2B *) Expand[V[t]]

(* Calculate V[t+h] *) V[t+h]

(* Calculate Diff(V,[t,t+h] *) V[t+h] - V[t]

(* Simplify the above expression *) Expand[V[t+h]-V[t]]

(* Calculate DQ(V,[t,t+h] *) DQ = Expand[(V[t+h]-V[t])/h]

(* Extract the leading term *) Vprime = Coefficient[DQ,h,0]

(* Find the error term *) epsilon = DQ - Vprime