Extreme operation

Limit is one of the most basic concepts in other branches of calculus and mathematical analysis, and the concepts of continuity and derivative are defined by it. It can be used to describe the changing trend of element properties in a sequence when the exponent of a sequence is getting larger and larger, and it can also be used to describe the changing trend of the corresponding function value when the independent variable of a function approaches a certain value.

When solving problems with the concept of limit, we should first establish a function (calculation formula) with traditional thinking and constant thinking of' low mathematical thinking', then try to deform the total area of the image and find out the limit of a corresponding variable, so that the problem can be solved. Finding the limit value in this "identity" transformation is an important move for mathematics to be applied to the calculation of actual variables. The above-mentioned partial sum method, average velocity method and regular polygon inscribed circle area method are the most accurate approximation methods among infinite series corresponding approximation value, instantaneous velocity method and circle area method respectively. Using the limit idea, we can get the corresponding extremely accurate conclusion value. This is all with the help of extreme thinking method, and people can also achieve accurate calculation results through' infinite approximation'. This new method, the limit idea of calculus, can satisfactorily solve the problem of' directly using constant method to calculate variable function, but there is no ready-made formula available, and the calculation result has a big error'.