Pseudo-coercion theorem is the most commonly used calculation method in calculus, which is divided into pinching theorem of function limit and pinching theorem of sequence limit. If we want to use this theorem correctly, the most important thing is to understand that pinching theorem is used to calculate the limit, not to judge whether there is a limit. If the limit of function can be calculated by this method again, it shows that the limit of sequence exists, but it cannot be inferred. If the limit already exists, pinching theorem can be used, which is wrong.

2. Monotone bounded convergence theorem

Monotone bounded convergence theorem is also a main method in higher mathematics, which is used to calculate the limit problem of sequence. Generally speaking, the application scope of this theorem is fixed, and the monotone bounded convergence theorem can only be used in specific topics. In this way, two important conclusions can be proved. Firstly, it is proved that the sequence is bounded, and secondly, it is proved that the sequence is monotonous. In the study of advanced mathematics, there are nearly 20 other important theorems besides the above two theorems. Students need to understand the reasoning process of theorems. Only when users have a reasonable understanding of theorems can we ensure the efficiency of solving problems in the learning process of advanced mathematics.