由一个重要极限引发的问题

A problem from an important limit

将是否可以用洛比达(L′Hospital)法则求解极限limx→0sinxx的问题,归结为导数公式(sinx)′=cosx是否必须利用limx→0sinxx=1这一结果才能得到.给出了另一种推导三角函数导数公式的方法.

In this paper,the problem whether the limit,(lim)x→0sinxx can be solved with the rule of L′Hospital is changed to whether the derivative formula of sinx must be obtained by using the result (lim)x→0sinxx=1.A new derivation method for the derivative formula of trigonometric functions is given.At last,it manifests that the describing order of the text book is not the only representation of the development of the differential and integral calculus.