Imaginable Calculus

The two new rules limΔx→0[(ΔA_r1+Δ A_r2+ ... +Δ A_rm)/(Δ A₁+Δ A₂+ ... +Δ A_m)] and limΔx→0[(Δ y_t1+Δ y_t2+ ... +Δ y_tm)/(Δ y₁+Δ y₂+ ... +Δ y_m)] are developed in this book. Based on these two new rules, the Fundamental Theorem of Calculus that is the most important theorem in calculus can be developed in an imaginable way. The new rule limΔx→0[(Δ l_t1+Δ l_t2+ ... +Δ l_tm)/(Δ l₁+Δ l₂+ ... +Δ l_m)] is also developed in this book. Based on it, the formula for the length of a curve can be developed in an imaginable way. The more imaginable calculus is, the more understandable it will be. All these innovations and new developments make calculus easier to understand.