论“lnarccosx”与-lnarctanx的不等:一道训练学生判断两个函数是否相同的好题例  

On Determining Function f(x)=lnarccosx and Function g(x)=-lnarctanx are not the Same:A good Instance to Train Students'Skill of Determining Whether Two Functions are the Same

作　　者：张永林[1] ZHANG Yong-lin(Basic Teaching Department,Qingdao Technical College,Qingdao,Shandong 266555,China)

机构地区：[1]青岛职业技术学院基础教学部,山东青岛266555

出　　处：《教育教学论坛》2020年第39期156-157,共2页Education And Teaching Forum

摘　　要：高等数学中判断两个函数是否相同或能否相同的问题,是检验学生对函数概念是否准确把握,是否会运用函数二要素进行逻辑推证的一类基础性问题。“判断函数f(x)=lnarccosx与函数g(x)=-lnarctanx能否相同”,是笔者构造的一道属于这类问题的题例,并给出详细的论证,对学生理解反三角函数、理解对数函数、理解复合函数,训练学生掌握判断两个函数是否相同具有较好的促进作用。In advanced mathematics,to determine whether two functions are the same or can be the same is a barometer to examine whether students can accurately grasp the concept of function as well as whether they can use the two elements of function for logical reasoning."To determine whether function f(x)=lnarccosx and function g(x)=-lnarctanx are the same''is such an instance used by the author,which is demonstrated and argued in detail in this article.It's beneficial for students to understand the anti-trigonometric function,the logarithmic function as well as the compound function.It would also help students to master the skill of determining whether two functions are the same.

关 键 词：高等数学 函数 反三角函数 解题研究 

分 类 号：G642.46[文化科学—高等教育学]