由一道求极限题谈不等式思维培养

On the training of inequality thinking based on a problem of computing limit

在高校公共数学课的教学中,不等式思维的培养很有意义.在利用夹逼准则求函数极限时,如何运用不等式思维进行适度放缩是关键所在,也是一个难点.通过一道极限题的教学案例,展示完整的分析过程.通过灵活运用不等式思维对研究对象进行放缩的训练,学生的数学思维能力可以得到很好的提升.

In the teaching of public mathematics in universities,the cultivation of inequality thinking is of great significance.In the squeeze theorem of calculating the limit of a function,how to appropriately scale the function is a fundamental and difficult problem.Through a teaching case of computing limit,the complete analysis process is shown.Through the practice of using inequality thinking flexibly to scale the research object,students′mathematical thinking ability can be improved.