题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231255-96402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231256-76875.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231256-66679.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231256-25416.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231256-91021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231256-62644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231257-96013.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231257-90089.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231257-58757.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231257-94987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231257-29498.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231257-96526.gif)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231257-96526.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231258-33817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231258-69765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231258-19620.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231258-65515.gif)
(2)根据
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231257-96526.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231258-65515.gif)
![]() |
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-26576.gif)
(2)当k=1时,定义域为{x|x>
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-87219.gif)
当0<k<1时,定义域为{x|
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-46351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-67539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231300-72301.gif)
当k>1时,定义域为{x|
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-46351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-67539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231300-64531.gif)
解析
则|OM|=
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231300-71449.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231300-56373.gif)
由动点P在∠AOx的内部,得0<y<kx.
∴|PM|=
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231300-46781.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231301-49497.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231301-54016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231301-32274.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231301-25454.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231301-19931.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231301-19931.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231301-19931.gif)
∴k(a+b)x-( a -b)y=2k ①
又由kPM= -
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231302-28676.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231302-92330.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231302-28676.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231302-76611.gif)
分别解得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231302-44093.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-83351.gif)
∵y>0,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-26576.gif)
(2)由0<y<kx,得 0<
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-39255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-40106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-73441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-40106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-88012.gif)
当k=1时,不等式②为0<2恒成立,∴(*)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-40106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-35094.gif)
当0<k<1时,由不等式②得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231304-92939.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231304-84539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-40106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-46351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-67539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231304-58912.gif)
当k>1时,由不等式②得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231304-62704.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231304-94159.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231303-40106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231305-24427.gif)
但垂足N必须在射线OB上,否则O、N、P、M四点不能组成四边形,
所以还必须满足条件:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231305-37403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231305-20735.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-46351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-67539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231300-64531.gif)
综上:当k=1时,定义域为{x|x>
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-87219.gif)
当0<k<1时,定义域为{x|
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-46351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-67539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231300-72301.gif)
当k>1时,定义域为{x|
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-46351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231259-67539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231300-64531.gif)
核心考点
试题【如图,已知:射线为,射线为,动点在的内部,于,于,四边形的面积恰为.(1)当为定值时,动点的纵坐标是横坐标的函数,求这个函数的解析式;(2)根据的取值范围,确定】;主要考察你对导数的意义等知识点的理解。[详细]
举一反三
20.已知
(m为常数,且m>0)有极大值
,
(Ⅱ)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231245-79959.gif)
设总造价为S元,AD长为xm,试建立S与x的函数关系;
当x为何值时,S最小?并求这个最小值。
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231239-42631.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231226-68868.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231222-45342.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231223-91401.gif)
A.![]() | B.![]() | C.![]() | D.以上都不是 |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231214-44690.gif)
(I)求函数一份(x))的单调递增区间;
(Ⅱ)当k为偶数时,数列{
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231214-89579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231214-22389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231214-19742.gif)
不存在成等差数列的三项;
(Ⅲ)当后为奇数时,证明:对任意正整数,n都有
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017231214-27718.gif)
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