二元函数的柯西中值定理及罗必达法则

CAUCHY MEAN VALUE THEOREM AND I'HOPITAL'S RULE FOR TWO VARIABLES

本文首先给出二元函数的柯西中值定理,并通过代换转化为一元函数的柯西中值定理加以证实。在此基础上,推导出二元函数的罗必达法则,从而比较方便地解决了一些“不定式”的极限问题。

First, the cauchy Mean Value Theorem fro two- variables is given and then it is proved by transforming the two- variable function into one variable by using the Cauchy Mean Value Theorem for- one- variable- Based on the result, the I'Hopital's rule for two- variables is deduced .Therefore, some limit problcmes of indefinite forms can be resolved smoothly.