求解0·∞型极限的方法分析

Methods for Solving the Undetermined Limit in the Form of 0·∞

0·∞型极限是一种常见的待定型极限,洛必达法则是计算这种待定型极限的有效方法。在应用洛必达法则之前,必须把0·∞型变形成0/0型或∞/∞型。文章通过大量典型例题的分析,推导出计算0·∞型极限的方法,应用这些方法能快速而方便地求出0·∞型的极限。

The limit in the form of 0·∞ is a common type of undetermined limit.L’Hospital’s Rule is an effective method to calculate this kind of undetermined limit.Before we can apply L’Hospital’s Rule,we have to change the form of 0·∞ to the form of either 0/0 or ∞/∞,which is a tricky process.In this paper,a number of typical examples are given to deduce some methods of calculating the limit in the form of 0·∞.Using these methods we can quickly and easily solve the undetermined limit in the form of 0·∞.