Give a class of differential intermediate value theorem, and obtain the asymptotic behavior of mediant for the theorem.

给出了一类微分中值定理，并得到了该定理中间点的渐近性质。

Focused on the asymptotic behaviour of mediant for fourth order Lagrange's mean value theorem and obtained the main results as followed (The equation is abbreviated).

对四阶拉格朗日中值定理中间点的渐近性质进行了研究，得到的主要结果是（方程式略）。

The right rectangle formula was generalized, the asymptotic behaviour of mediant for the right rectangle formula and the generalized right rectangle formula were given.

本文得到推广的右矩形公式，并给出了右矩形公式和推广的右矩形公式中间点的渐近性质；