第7届全国数学“希望杯”高二年级赛题中有这样一道题目:已知函数 f(x)=(sinx)/x,试证 f(x)在 x∈(0,π/2)上为减函数.答案是用微积分的有关知识来证的.由于现行高中教材还未把微积分列入必学考查内容,这种证法虽然简洁自然,但对许多考生来说可望而不可及,文[1]曾给出一个初等证法,其中用到三 The title of the 7th National Mathematics “Hope Cup” Senior Year competition title is: Known function f(x)=(sinx)/x, test f(x) on x∈(0,π/2) In order to reduce the function, the answer is proved by the knowledge of calculus. Since the current high school textbooks have not included calculus in the content to be studied, the evidence is concise and natural, but it is not expected for many candidates. And, the text [1] has given an elementary proof method, which uses three