英语翻译微积分学可以说是一门极限的科学,而无穷小是一类特殊的极限为零的函数.本文首先介绍了无穷小的出现在历史上的作用等价无穷小是数学中求解极限问题的一个极好工具,本文归纳

Question

英语翻译
微积分学可以说是一门极限的科学,而无穷小是一类特殊的极限为零的函数.本文首先介绍了无穷小的出现在历史上的作用等价无穷小是数学中求解极限问题的一个极好工具,本文归纳总结了等价无穷小在求解各类极限问题中的应用.由于初学者在运用等价无穷小的替换中总是会出现这样那样的错误,我们又对出现这些错误的根源进行了剖析,另外也将等价无穷小拓展到幂指函数、变上限积分以及二元极限函数
等价无穷小：infinitesimal quantity 或者 eqvivalent infinitesimal
幂指函数 ：power-exponential function
变上限积分：variable upper limit integral
二元极限函数：limit function of two variables

Answer 1

本人手工正确翻译如下：
Calculus can be called a subject about limitation,and infiniteness is a special kind of function for which the limitation is zero.This paper first introduces effect of the appearance of infiniteness in history.Infinitesimal quantity is a great tool to solve the limitation questions.And we summarize the application of Infinitesimal quantity in solving various limination questions.Since the beginners always make this or that kind of mistakes in using the substitute of Infinitesimal quantity,we furthermore analyaze the root of these mistakes.And we also extend the Infinitesimal quantity to power-exponential function,variable upper limit integral,and limit function of two variables.