关于洛必达法则求函数极限的分析与研究

Analysis and Study of Functional Limits by Employing L'hospital Rule

首先对洛必达法则的适用条件和常见的误区进行了详细分析,探讨了法则适用函数极限类并举例说明其应用,将法则的应用推广至求数列极限以扩大法则的适用范围;然后分析法则的不足(失效)之处;最后通过实例说明可以将法则和其他求极限方法结合起来使用,显示了该法则在极限计算中的重要作用.

We made a detailed analysis to the conditions and erroneous areas of applying the L＇ hospital Rule, and clarified the types where the rule can be employed to get functional limits. We proceeded to exemplify its applications and extend the rule to get sequence limits so as to enlarge its range of application. Besides, we analyzed its insufficiency （failure）. On such a basis, we proposed to combine the rule with other approaches to get functional limits by exemplifications, pointing out the precautions therein and highlighting the rule＇s significance in the calculation of getting functional limits.