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中值等式问题证明的方法探究

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文章以历届全国研究生入学考试高等数学考题及历届全国大学数学竞赛真题(含某些省市的竞赛试题)为例,对中值等式问题的证明作了比较详尽的分析.得出结论:在中值等式问题的证明中,一般需要构造辅助函数,而辅助函数的构造可以用间接积分的方法得到,而且此方法坡度小、难度低,学生容易掌握.
Exploration of Methods for Proving Median Equality Problems
Absrtact:The paper provides a detailed analysis of the proof of the median equality problem by taking the advanced mathematics exam questions of previous national postgraduate entrance exams and the real questions of previous national university mathematics competitions(including competition questions of certain provinces,cities and universities)as examples.It is pointed out that in the proof of median e-quality problems,auxiliary functions are generally constructed,and the construction of auxiliary functions can be completely obtained by the method of indirect integration,which has the advantages of small slope and low difficulty,and it is easy for students to master.

median problemmedian theoremauxiliary functionsintegral method

张锐、詹紫浪

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兰州城市学院信息工程学院,甘肃兰州 730070

兰州城市学院学报编辑部,甘肃兰州 730070

中值问题 中值定理 辅助函数 间接积分法

2024

甘肃高师学报
甘肃民族师范学院 定西师范高等专科学校,陇南师范高等专科学校 兰州城市学院

甘肃高师学报

CHSSCD
影响因子:0.173
ISSN:1008-9020
年,卷(期):2024.29(2)