在此基础上通过构造区间套依次证明了罗尔中值定理、拉格朗日中值定理和柯西中值定理。
On the basis of these theories, Rolle mean value theorem, Lagrange mean value theorem and Cauchy mean value theorem are proved by constructing nested interval.
其证明方法关键在于构造一个辅助函数，再应用罗尔中值定理推出拉格朗日中值定理的结论。
Its key proof is to construct an auxiliary function, which is used by Roll's theorem to reach a conclusion of Lagrange's theorem.
本文将微积分中的罗尔定理从有限闭区间推广到了半无限区间和无限区间，有助于对罗尔中值定理的理解。
The author generalizes the theorem of Rolle in the calculus from closed interval to semi-infinite interval and infinite interval , which is useful for students to understand theorem of Rolle better.
利用罗尔中值定理给出了函数与其拉格朗日插值函数间的关系，得到中值定理的另外一种形式，并给出了它的应用。
Another form about the median theory and its application is put forward according to the relation between the function and its Lagrange interpolation function in accordance with Rolls median theory.
本文根据区间套的方法，证明柯西中值定理，而把罗尔定理和拉格朗日中值定理作为它的推论。
Cauchy's theorem of the mean is proved by means of nested intervals, with Rolle's and Lagrange's theorems of the mean as its corollaries.
由此可见罗尔微分中值定理可以是实数的完备性的直接推论。
This implies that Rolles Theorem is the direct consequence of completeness of real numbers.
中值定理包括罗尔定理、拉格朗日定理和哥西定理。
The middle value theorem consists of Roue. Lagrang and Cauchy theorem.
中值定理包括罗尔定理、拉格朗日定理和哥西定理。
The middle value theorem consists of Roue. Lagrang and Cauchy theorem.
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