最小正周期的证明与求法

• 作 者: 郝君方
• 机 构: 天津市二十三中学,
• 出 处: 中等数学
• 发表日期: 1985年03期
• 关键词: 最小正周期 常数函数 非零常数 主周期 余切函数 余弦函数 多项式函数 正有理数 士少 七势

连续周期函数(常数函数除外)必有最小正周期,求出它的最小正周期是有实际意义的:其一,知道了周期函数的最小正周期,就可把握住它的所有周期(见下面性质3);其二,知道了周期函数的最小正周期,就可在小的取值范围内研究函数的性态。对于函数f(x),其定义域为M.如果存在一个非零常数T,x±T∈M,并且对于

The continuous period function (except the constant function) must have the minimum positive period, and finding its minimum positive period is of practical significance: First, knowing the minimum positive period of the period function, you can hold all the periods of it (see below Property 3); Second, knowing the minimum positive period of the periodic function, the behavior of the function can be studied within a small range of values. For the function f(x), its domain is defined as M. If there is a non-zero constant T, x±T∈M, and for