一类与积分∫baf^n(x)dx相关的极限

Limit of a Sequence Involving the Integral ∫baf^n(x)dx

针对第九届中国大学生数学竞赛(数学类)预赛的一道题进行拓广.通过对该竞赛题解答的关键步骤的分析,得到在较一般的情形下,与积分∫baf^n(x)dx相关的一类数列极限的简洁计算方法,给出相应函数类.

A generalization of a problem in the Ninth National Mathematics Competition is given.By analyzing the key steps for the solution of the problem,we present a simple way to find the limit of a sequence involving term like ∫b af^n（x）dx under more general conditions,and give two kinds of corresponding functions.