另类“夹逼法”——切线“夹逼法”

• 作 者: 朱传美
• 机 构: 江苏省兴化市戴南高级中学,
• 出 处: 数学通讯
• 发表日期: 2016年05期
• 关键词: 构造函数 模拟题 恒成立 高考题 求值 分类讨论 参考答案 单调递增 单调递减 代数的

我们知道:x~2≤0(x∈R)■x=0,这就是一个简单的夹逼法.“夹逼法”能很巧妙地处理一些实数求值问题,在高考题或模拟题中多有体现.在解题中,笔者发现:在某些函数试题中,切线同样体现着“夹逼法”的思想,收到意想不到的解题效果.例1已知lnx≤a(x-1)对一切x>0恒成立,则a的取值范围为.变量分离是处理此类问题的常用方法,直接移项,构造函数h(x)=lnx-a(x-1),即得如下

We know that: x ~ 2≤0 (x∈R) ■ x = 0, which is a simple nip method. “Nip” method can deal with some real numbers skillfully, In the problem-solving, the author found that: in some function test questions, tangent also reflects the idea of ​​“pinch law”, received an unexpected problem solving effect.Example 1 Known lnx≤ a (x-1) for all x> 0 holds, then a range of values. Variable separation is a common method to deal with such problems, the direct transfer, the constructor h (x) = lnx-a 1), that is as follows