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等价代换在数学分析中具有十分重要的作用。本文在已有文献的基础上,分析了加减运算下等价代换的错误根源,讨论了加减运算下的等价无穷大量代换,乘除运算下的等价无穷大量代换以及乘方运算下的等价代换,并通过一些具体的例子分析它们的应用。本文所得到的结果是对等价代换理论的进一步丰富与完善,也是对现有文献中一些相应结论的改进与推广。
Equivalent substitution plays a very important role in mathematical analysis. Based on the existing literature, this paper analyzes the error sources of equivalence substitution under the addition and subtraction operations, discusses the infinite equivalent substitutions under the addition and subtraction operations, the equivalent infinite mass substitutions under the multiplication and division operations, Equivalent substitution under the operation, and through some specific examples of their application. The result obtained in this paper is to further enrich and perfect the equivalence substitution theory and to improve and popularize the corresponding conclusions in the existing literature.