1. One is the common limit extension, such as lim (x->; 0)( 1+x)^ 1/x=e,lim(x->； 0)sinx/x= 1. Limit theory is the basis of mathematical analysis, and the limit problem is one of the main problems in mathematical analysis. There are two central problems: one is to prove the existence of limit, which is one of the difficult problems in mathematical analysis; The second is to find the limit value.

2. Secondly, Robida's law, such as 0/0, oo/oo type, can be transformed into the above two kinds of problems. These two problems are closely related: if the value of limit is found, the existence of natural limit is proved.

3. Thirdly, Taylor expansion, sinx, cosx, ln( 1+x) and other topics can all be expanded into polynomials about X by mclaughlin. On the contrary, proving existence often paves the way for calculating the limit. This paper mainly summarizes some commonly used methods to find the limit value, and more methods depend on people's specific analysis and treatment according to specific conditions.

4. Equivalent infinitesimal transformation, (it can only be used in multiplication and division, but it doesn't mean that it can't be used in addition and subtraction, but it must be proved that the limit still exists after splitting). The x power of e-1 or the a power of (1+x)-1 is equivalent to Ax and so on. When x approaches infinity, it reverts to infinitesimal.

5. We know the relationship between Xn and xn+ 1. When the limit of Xn exists, the limit of Xn is the same as that of Xn+ 1, and the limit value of the finite term should be removed for the limit.