【题文】已知函数,集合,集合,则集合M ∩ N的面积是( )A.B.C.πD.2π
题型:难度:来源:
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155353-52178.png)
,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155353-99221.png)
,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155353-13588.png)
,则集合M ∩ N的面积是( )
A.![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155354-96396.png) | B.![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155354-48403.png) | C.π | D.2π |
答案
【答案】A
解析
【解析】
试题分析:因为,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155354-88749.png)
,
则
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155354-67143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155355-40419.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155354-67143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155355-68921.png)
.
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155355-94449.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155356-19123.png)
.
故集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155356-22439.png)
所表示的区域为两个扇形,其面积为圆面积的一半,即为
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155356-60113.png)
;故选C.
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155357-67735.png)
考点:线性规划的应用.
举一反三
【题文】设集合M={x|x
2-x-12=0},N={x|x
2+3x=0},则M∪N等于
A.{-3} | B.{0,-3, 4} | C.{-3,4} | D.{0,4} |
【题文】设集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155259-90863.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155300-98309.png)
【题文】已知集合A=
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155255-32744.png)
-2,3,4
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155255-78569.png)
-4
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155255-45338.png)
,集合B=
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155255-32744.png)
3,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155255-86374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155255-45338.png)
.若B
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155255-15902.png)
A,则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322155255-78569.png)
=
.
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