“3、8、8链式整体因式优先法则”在极限计算中的应用

Application of“3,8,8 Chain Integral Factor Priority Rule”in Limit Calculation

本文结合高等数学中经常出现的极限计算问题,分类、归纳、总结出一种比较简便且实用的求极限法则——“3、8、8链式整体因式优先法则”.具体阐述为:初学者求极限要分“三步走”,掌握“八种题型”,熟练应用“八种无穷小代换”.“链式整体”是在求极限的过程中,可以把某些代数式看成一个个“整体”,依据“整体”的取值,运用基本初等函数图像思维,一步步推导出最终结果,整个过程像“一条链子”.“因式优先”是在极限的计算过程中,只要是能求出极限的“因式”,为了方便后续计算极限,优先计算出此因式的极限.

This paper introduces the“3,8,8 Chain Integral Factor Priority Rule,”a practical method for calculating limits in advanced mathematics.This method involves three steps,eight problem types,and eight infinitesimal substitutions.The“chain integral”concept treats certain algebraic expressions as“integrals,”enabling step-by-step limit calculations using basic function visualization.The“factor priority”rule advises prioritizing the evaluation of certain factors to simplify the overall limit calculation,making the process more intuitive for beginners.