一类未定式的计算方法探究  

Study of Computing Methods of a Kind of Indefinite Formulas

作　　者：龚东山[1] 周志贵[2] 

机构地区：[1]兰州大学数学与统计学院,甘肃兰州730000 [2]兰州大学大气科学学院,甘肃兰州730000

出　　处：《湘南学院学报》2008年第5期35-37,共3页Journal of Xiangnan University

基　　金：国家自然科学基金对外交流与合作项目(40640420072)

摘　　要：未定式的计算是极限计算的重要组成部分．对于未定式1^∞，在满足一定条件下，可通过适当变换后再运用洛必塔法则直接计算．但洛必塔法则求解未定式既非万能，也非最佳。当该条件不满足时，洛必塔法则不能直接使用，可借助高等数学中的重要极限，选择凑构法、等价无穷小替换法及泰勒式展开法等来计算，从而巧妙地得到问题的解．Computation of indefinite formulas is main part of limit. We are able do directly by using L＇ Hospital after proper transform in some conditions, but the method of L＇ Hospital isn＇ t omnipotent, nor the best. When the condition isn＇ t satisfied, L＇ Hospital can＇ t be used at first hand. After using of some important limits in Advanced Mathematics, we may choose one of the methods in computation, such as method of improvisation and method of replacement with equivalent infinitesimal and method of Taylor expansion, to get the answer of questions skillfully.

关 键 词：未定式 洛必塔法则 重要极限 凑构法 等价无穷小替换法 泰勒式展开法 

分 类 号：O172.1[理学—数学]