Cauchy定理及L''''hopital法则的推广

本文通过对Lagrange中值定理的证明中辅助函数的分析入手,描述了其构造特征。尤其通过选择新的辅助函数减弱了Cauchy定理的条件,推广了Cauchy定理并相应在L'hopital法则的定理证明中减弱了定理的适用条件,随之推广了L'hopital法则,可以使用L'hopital法则求取更多未定式形式的极限。

Some Improvement on the Proving of Mean Value Theorem, and L''''Hopital''''s Rule

We research careflly on the function used in the proving of Mean Value Theorem and Cauchy' Theorem and we found that we can give another theorem which need less condition and correspondently we can use it to reach the result that we need in the proving of L'Hopital's Rule without the strict condition needed before, and thus we can widen the area where L'Hopital's Rule works.