“以学员为中心”理念下一道求函数极限题目的解法探讨

Research on Solutions to One Limit with Concept of“Learning-Centered”

基于“以学员为中心”的教学理念,设计一道一元函数极限的题目,并对其求解方法进行探讨,提出7种解法,即可以先利用对数函数的性质进行化简再利用等价无穷小代换求解,也可以直接利用洛必达法则求解,还可以利用泰勒公式求解等,进而培养学员的发散思维。

Designed a limit with the concept of“learning-centered”,and discussed the solutions to the limit and proposed seven methods to calculate it in order to cultivate the divergent thinking of students.The methods included using of the properties of logarithmic function and then the replacement of equivalent infinitesimals,use of L’Hospital’s rule,and use of Taylor’s formula and so on.