分段拟合法在求解函数列问题中的重要应用
The Important Application of the Piecewise Fitting Method in Solving the Sequence of Functions Problems

数学分析中部分求解函数极限的问题，实质上就是求解函数列积分的极限。分段拟合法作为一种研究函数极限的关键方法，同样在研究函数列问题中发挥着重要作用。本文将借助分段拟合的思想，讨论研究$\underset{n\to \infty }{lim}{\displaystyle {\int }_a^b{f}_n\left(x\right)g\left(x\right)dx}$ 这类极限问题以及迭代函数列的相关问题。
In mathematical analysis, partially solving the function limit problem is essentially solving the limit of the sequence of functions integral. As a key method to study the limit of function, piecewise fitting method also plays an important role in the study of function sequence. In this paper, we will discuss the limit problem of $\underset{n\to \infty }{lim}{\displaystyle {\int }_a^b{f}_n\left(x\right)g\left(x\right)dx}$ and the related problems of iterative function sequence by means of the idea of piecewise fitting.