以下为句子列表：
英文: And based on this conclusion, Darboux theorem on open interval is also given.
中文: 在此基础上给出有限开区间上的达布定理。
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英文: Lagrange and Cauchy differential mean value theorem on open interval are obtained based on generalized Roll's theorem, which make it more expedient to study general character of function defined on open interval by means of derivative.
中文: 摘要基于推广的罗尔中值定理，得到有限开区间上的拉格朗日中值定理及柯西中值定理，使得利用导数研究开区间上函数的整体性态更为方便。
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