题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120259-49031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120259-23216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120259-68576.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120300-37978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120300-61942.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120300-71104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120300-31853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120301-18712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120301-30292.png)
(3)证明当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120300-37978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120301-63742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120301-58408.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120302-55874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120302-14629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120300-31853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120302-20909.png)
解析
试题分析:(1)一般地,曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120300-61942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120302-60813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120303-22943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120300-61942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120303-29319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120303-75715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120301-30292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120303-32614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120304-61906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120304-84405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120303-75715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120301-30292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120304-61906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120301-58408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120304-20403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120304-67633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120304-81814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120305-21877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120305-21877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120305-37586.png)
试题解析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120305-32868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120305-50506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120302-55874.png)
若切点不是原点,设切点为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120305-93890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120306-95846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120306-80534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120306-42921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120306-19063.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120306-49110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120302-14629.png)
综上所述,所求切线有两条,方程分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120302-55874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120302-14629.png)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120307-70899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120307-71005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120307-20215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120307-92753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120308-79718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120308-40508.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120308-56496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120308-38127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-86383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-61125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-49036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-49036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-47197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120308-79718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-74069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120310-68355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-49036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120310-22912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-74069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120310-96683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-49036.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120310-30262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120311-97317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-86383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120311-17086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120311-87896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120311-79132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120312-28963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120311-79132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120307-92753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120312-25482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120312-12000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120312-69470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120307-71005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120312-19372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120309-49036.png)
综上所述,所求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120313-97847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120302-20909.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120300-37978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120305-21877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120313-50004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120313-52294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120313-16911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120305-21877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120305-37586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120314-89115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120313-52294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120314-23193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120314-77917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120313-52294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120304-81814.png)
在此不等式中依次取
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120314-99331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120314-15947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120315-57635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120315-39839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120315-62443.png)
…………………………
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120315-85762.png)
将以上不等式相加得:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120304-20403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120301-58408.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120246-55321.png)
(Ⅰ)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120246-18089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120247-14895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120247-74231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120247-68502.png)
(Ⅱ)记
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120247-67208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120248-62867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120248-93505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120248-55349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120241-21352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120241-31058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120241-30402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120242-78889.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120233-13137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120234-64899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120234-38565.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120224-26101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120225-62932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120225-45085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120224-26101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120225-45085.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120215-72279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120216-11844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120216-69468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120216-11196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017120217-58196.png)
A.1 |
B.2 |
C.-3 |
D.-4 |
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