Cauchy mean value theorem is one of the three theorems of differential mean value theorem, and its Birol theorem and Lagrange mean value theorem are more general.

However, most advanced mathematics textbooks only introduce Cauchy's mean value theorem and its proof, and the application of this theorem is less involved, which is not conducive to students' understanding of this theorem and its application value. The following introduces the application of Cauchy mean value theorem in finding the limit.

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One of the most important applications of Cauchy's mean value theorem is to derive the most effective method to calculate the limit of undetermined type-Lobida's rule. L'H?pital's law is to find the limit of two infinitesimals or the ratio of two infinitesimals.

Mean value theorem is a basic theorem in calculus, which consists of four parts. The content is that there must be a point on a continuous smooth curve, and its slope is the same as the average slope of the whole curve. The mean value theorem is also called the basic theorem of differential calculus, Lagrange theorem, Lagrange mean value theorem and finite change theorem.

Baidu encyclopedia-mean value theorem

Baidu encyclopedia-Cauchy mean value theorem