题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172107-63004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172108-89189.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172108-49769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172108-79905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172109-86183.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172109-53691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172110-95474.png)
(Ⅲ)证明:对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172110-19235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172110-89686.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172110-49856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172111-23944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172111-77332.png)
所以曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172111-63807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172109-86183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172111-82682.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172112-20100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172112-94398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172112-39208.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172112-54593.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172113-89503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172113-96098.png)
![]() | ![]() | ![]() | ![]() |
![]() | + | ![]() | + |
![]() | ![]() | ![]() | ![]() |
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172110-95474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172115-89955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172114-81556.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172116-59074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172113-64455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172113-96098.png)
![]() | ![]() | ![]() | ![]() |
![]() | + | ![]() | + |
![]() | ![]() | ![]() | ![]() |
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172110-95474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172116-50485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172117-65329.png)
(Ⅲ)由(Ⅱ)可知,当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172117-52536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172110-95474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172117-45960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172116-98844.png)
以下分两种情况讨论:
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172117-74564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172110-95474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172118-42222.png)
所以对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172118-85817.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172118-88508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172110-95474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172117-45960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172118-19554.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172119-49624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172119-71191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172119-29655.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172119-44023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172119-10400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172120-74249.png)
所以,对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172120-33526.png)
综上,对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017172120-96498.png)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171933-96921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171933-11502.png)
(Ⅰ) 求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171933-87259.png)
(Ⅱ)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171934-58800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171934-98669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171934-36057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171934-42073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171934-58800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171935-38811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171934-42073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171943-24547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171943-64358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171943-60586.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171830-15833.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171831-58580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171831-56119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171831-88537.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171831-56119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171831-22900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171831-56119.png)
(Ⅲ)是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171832-25200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171831-56119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171832-44355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171832-25200.png)
若不存在,说明理由.
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171817-28855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171818-97660.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171818-95812.png)
(2)当b=1时,若方程
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171818-86897.png)
(3)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171819-82421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171819-59547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171612-11152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171612-45950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017171613-65367.png)
A.150毫克/升 | B.300毫克/升 |
C.150ln2 毫克/升 | D.300ln2毫克/升 |
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