题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021959-53156.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-11634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-12493.png)
(III)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-55400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022001-82148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022001-23998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022001-96844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-55400.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021959-53156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022001-79403.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022002-51150.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022002-10077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022002-93932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022002-50404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022003-92356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022003-30275.png)
故函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022003-65399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022003-64178.png)
(Ⅱ)由(Ⅰ)知,函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022003-65399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022003-64178.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022003-74243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-12493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022004-88338.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022004-19862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022004-23110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022004-93248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022005-33385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-12493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022005-28385.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-76189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-12493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022005-30349.png)
(Ⅲ)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022001-96844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022000-55400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022005-46124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022001-79403.png)
该方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022005-77117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022006-57460.png)
只需讨论方程
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022006-39793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022001-79403.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022006-54897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022006-92402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022007-82949.png)
因
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022007-31087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022007-94037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022007-85442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022007-76487.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022008-76185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022008-99441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022008-73331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022008-55589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022009-50592.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022009-73409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022009-49521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022009-90996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022009-65765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022010-69796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022010-56395.png)
如图构造
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022010-29944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022010-44040.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022011-44734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022011-39806.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022011-57150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022011-37982.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022012-63192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022012-75535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022012-58331.jpg)
解析
(II)在第(I)问的基础上对a进行讨论求极值,最值.
(III)可以构造函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019022012-99317.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021954-40898.png)
A.3 | B.2 | C.1 | D.0 |
(1)设半圆的半径OA=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021945-67484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021945-67484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021945-67484.png)
(2)由于条件限制
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021946-10884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021945-67484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021946-53387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021931-33453.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021932-79723.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021932-79723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021932-24531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021925-52241.png)
(Ⅰ)计算
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021925-91043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021925-17117.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021925-91043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021902-68969.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021902-21781.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021902-51775.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019021903-73619.png)
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