以下为句子列表：
英文: Based on the Rolle mid-value theorem, by using determinant method, the Lagrange mid-value theorem and Cauchy mid-value theorem are obtained, and some new results are discovered.
中文: 本文从罗尔中值定理出发，这用行列式理论，不仅证明了拉格朗日中值定理和柯西中值定理，还发现了一些新的结论。
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英文: The mid-value theorems is the basic theorems in the calculus.
中文: 摘要微分中值定理是微分学中的基本定理。
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