A new method of determining the dividing point about fatigue crack initiation and propagation for the notch specimens is introduced according to elastic plastic theory.

By defining dividing point,we can differentiate each of the breaking points defined by Nguyen S.

It is possible that some dividing points included in the original breaking set defined by Nguyen S.

After the functional relation between designed flow rate and water demand unit is analyzed, the concept of demarcation point of water supply is put forward, which is convenient for actual .

On the basis of method of derivative on the left and the right of separable function,the derivability of separable function on demarcation point was simply distinguished,and derivative continuity on demarcation point discussed.

By making use of the definition of derivative ,one can calculate the derivative of demarcation point,the derioative of the special elementary function,the derivative of parametric equation.

This paper proposes a new method of seeking the derivation of a fragmental function at the point of demarcation.

Discussing the limit,Continuity and Derivative at the Boundary of Section Function;

This text will talk about some new methods about the limit of disjunction function in the boundary and the operation of lead number and definite integral.