【摘要】 针对一类因含扰动项而不满足积分和标准形式的极限问题,对扰动项有界和无界的情况进行了归纳。无界扰动的情况下,当扰动项趋于无穷的速度快慢不同时,扰动项对整个结果的影响也不同。首先利用夹逼原理对扰动项进行放缩,将扰动项放缩成与求和对象i无关的结构,从而把求和的部分凑成积分和因子与一个跟求和对象i无关因式的乘积,再将与求和对象i无关的因式置于求和符号外,然后基于乘积的极限运算法则和定积分定义求解经处理后的极限问题。对扰动项趋于无穷的速度与nα进行比较,分别给出了α<1和α>1这2种情况下的结果,该结果为处理该类问题的一般性结论。最后通过算例说明该方法的有效性。更多还原

【Abstract】 The bounded and unbounded perturbations,for a class of limit problem which is no in standard form of integral sum,are discussed in this paper. Under unbounded perturbations,the influence on the total result varies for the different velocities,the perturbations move toward infinite. At first,the perturbations are enlarged and narrowed into a form independent of integral sum,by utilizing theorem of clamp approximation. And then the perturbations may be taken out from the integral sum,the limit problem would be solved in the utilization of definite integral and the law of limit operation. In consideration of the velocity of the perturbations,compared with nα,where α < 1 or α > 1,the paper comes to general conclusions for this kind of problem. Finally,examples are given to illustrate the effectiveness of the conclusions drawn in this paper.更多还原