多元函数的Cauchy中值定理及L′HOSPITAL法则

CAUCHY'S MID-VALUE THEOREM AND L'HOSPTAL OF MULTIPLE VARIABBLE FUNCTION

本文借助于一元函数的拉格朗日中值定理及一元函数的 Cauchy 中值定理,给出了二元函数的 Cauchy中值定理及 L'HOSPITAL 法则,这种方法具有一般的意义,可以推广到多元函数。

In this paper,We discussed the Cauchy's mid-value theorem ahd L'Hospital of multiple-vari- able functrn.We gave some theorems and reference.By use of them,We solved f(x,y)→0,g(x,y) →0,Limf(x,y)/g(x,y),f(x,y)→0,g(x,y)→0,Limf(x,y)/g(x,y),and Limf(x,y)→0,g(x,y) →0,Limf(x,y)/g(x,y)