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 (maximum value is 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.
Extreme thinking to solve problems:
Extreme thinking method is an indispensable and important method in 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.
People can scientifically determine the extremely accurate value of a certain quantity by investigating a series of countless more and more accurate approximation trends of some functions, which requires the use of the concept of limit and the thinking method of the above limit. It is considered that it is scientific to use the thinking method of limit, because extremely accurate conclusions can be obtained through the function calculation method of limit.
Refer to the above? Baidu encyclopedia-limit