The analysis of the method on the one variable function’s limit

Abstract

The limit of one variable function is an important problem in Higher Mathematics, it is a basic method to study the relationship between the function of variables. This template describes some important method about counting the limit, and gives the solving skills. Introduction The concept of limit is produced in order to solve some practical problems of precise. In the third Century A.D. China's well-known mathematician Liu Hui used the method of cyclostome. Surgery, and used the regular polygon inscribed in a circle to approximated the area of a circle, this is the estimating thinking. Liu hui starts from the hexagon inscribed in a circle, does the Inscribed regular twelve sided in shape, twenty-four polygon etc., doubles the number of edges every time. So we get a series of inscribed regular polygon areas 1 A 2 A 3 A ..., n A ....Imagine n infinite increase, and the number of edges inscribes regular infinite increase. In this process, inscribed regular infinite closes to a circle. At the same time, n A inhibiting closes to a determined value, the determined values can be understood as the area of a circle. This is the origin of the conception of limit. The limit of one variable function is an important problem in Higher Mathematics. Limit method is a basic method to study the relationship between the function of variables, it is an important basis for the limit of function of many variables, the derivative, differential and integral calculus. The limit is an important foundation of calculus, it is necessary to make a summary and analysis for the method of solving the limit, prepare for Calculus Learning. The various method of finding the limit of various Calculation of limit by using using the concept Definition 1 assuming the function ( ) f x at the point 0 x of a deleted neighborhood has a definition. If there exists a constant A , for any positive number, there is always a positive number, when 0 0 x x δ 0 0 lim t t t t → = . Prove 0 e ∀ > as: 0 0 0 0 0 1 t t t t t t t t t − − = ≤ − + ,