The proof of the limit of sequence is the focus of number one and number two, especially the number two has been tested very frequently in recent years, and several big proof questions have been tested. The big problem generally involves the proof of the limit of sequence, and the method used is monotone bounded discrimination.

Second, the relevant proof of differential mean value theorem

The proof of differential mean value theorem has always been a difficult point in postgraduate entrance examination. Its examination is comprehensive and involves a wide range of knowledge. There are three kinds of theorems for equations involving the average value:

1. Zero theorem and intermediate value theorem;

2. Differential mean value theorem;

Including Rolle's theorem, Lagrange's mean value theorem, Cauchy's mean value theorem and Taylor's theorem, in which Taylor's theorem is used to deal with the related problems of higher-order derivatives and investigate the frequency base, so the first two theorems are the main ones.

3. Differential mean value theorem

The function of integral mean value theorem is to remove the integral symbol.

In the exam, three kinds of theorems are generally tested in two combinations, so it is necessary to summarize the questions tested so far.

Third, the problem of equation roots

Include that uniqueness of the equation root and the number of the equation root.

Fourth, the proof of inequality

Proof of definite integral equality and inequality of verb (abbreviation of verb)

The main methods involved are differential calculus: constant variation method; Integral method: method of substitution and distributed integral method.

Six, five equivalent conditions of path-independent integral