等价无穷大在未定式计算中的应用

Application of Equivalent Infinite in Indeterminate Calculation

由等价无穷小的概念类似得到了等价无穷大的概念,并且同时总结出一些常见的等价无穷大.等价无穷大有着等价无穷小类似的特性.通过应用极限的四则运算法则证明得到这样的结论:在0·∞,∞/∞,∞-∞,∞0,1∞型未定式的计算中等价无穷大也可以做到有条件的替换.掌握这些常见的等价无穷大与在未定式计算中的等价替换条件可以有效的减少计算量,在一定程度上比洛必达法则求解问题更加的简捷.

In this paper, not only the definition of equivalent infinite is given by the equivalent infinitesimal, but also some common equivalent infinite is given. Equivalent characteristics similar with equivalent infinitesimal. Through the application of four arithmetic definition of infinite has operations limit, a conclusion is proved in this paper. In indeterminate calculation of 0·∞,∞/∞,∞-∞,∞0,1∞, the equivalent infinite replacement can be conditional. Mastering these common equivalent infinite and equivalent replacement conditions in indeterminate calculation can effectively reduce the amount of calculation. In the process of problem solving,it is more simple than L＇Hospital Rule.