The basic concept of calculus, the generalized "limit" is "infinitely close, never reaching".

The "limit" in mathematics means that a variable in a function gradually approaches a certain value A in the process of getting bigger (or smaller), and "it can never coincide with A" ("it can never be equal to A").

The change of this variable is artificially defined as "always approaching", and it has a "tendency to approach point A".

1, Introduction

Limit thought is an important thought in modern mathematics, and mathematical analysis is a subject that studies functions with the concept of limit and limit theory (including series) as the main tools.

The so-called limit thought refers to "a mathematical thought that uses the concept of limit to analyze and solve problems".

The general steps to solve problems with extreme ideas can be summarized as follows:

For the unknown quantity under investigation, first try to correctly conceive another variable related to its change, and confirm that the trend result of the' influence' of this variable through the infinite change process is very accurate and approximately equal to the unknown quantity sought; The result of the unknown quantity under investigation can be calculated by the limit principle.

The idea of limit is the basic idea of calculus and a series of important concepts in mathematical analysis, such as continuity of function, derivative (finding the maximum or minimum value of 0), definite integral and so on. These are all defined by the way of limit.

If you want to ask, "What is the theme of mathematical analysis?" Then it can be simply said: "Mathematical analysis is a subject that studies functions with limit thought, and the error of calculation results is too small to imagine and can be ignored.

2. Extreme thinking to solve problems

The method of "extreme thinking" is an indispensable and important method for mathematical analysis and even all higher mathematics, and it is also the development of "mathematical analysis" and "elementary mathematics" with continuity and further thinking.

Mathematical analysis can solve many problems that elementary mathematics can't solve (such as finding instantaneous velocity, curve arc length, curved edge area, surface volume, etc.). ), it is precisely because it adopts the thinking method of "limit" and "infinite approximation" that it can get extremely accurate calculation answers.