解题方法
1 . 已知函数
,且
在
处的切线方程是
.
(1)求实数
,
的值;
(2)求函数
的单调区间和极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082ece762ffbf92921f4685d45f5166d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f31cba6e8a2a234dfb5b2f7e909b3a.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2 . 在平面直角坐标系
中,已知点
,点
(不位于
轴左侧)到
轴的距离为
.
(1)求点
的轨迹方程
;
(2)若圆
与点
的轨迹有且仅有一个公共点,求
的最大值;
(3)在(2)的条件下,当
取最大值,且
时,过
作圆
的两条切线,分别交
轴于
两点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9fb2f88c1d5ed038af2850f1a33ed6.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449c818c491f1907a27c40ab72cae85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c12244af190b0a9c8386810593f419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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名校
3 . 已知函数
.
(1)讨论
的单调性;
(2)
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33a528e46c7a1abf32635b8bc67bcd9.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ccb692a97ea01b9847bb3401f8a6e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6bfacfdb31f83a264ecb79589b16e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
4 . 已知
,
为椭圆
(
)的左、右焦点,过
的直线
与
相交于
,
两点,且
的最大值为
.特别地,当
垂直于
轴时,
.
(1)求
的方程;
(2)当
与
轴不重合时,直线
与直线
交于点
,若直线
恒过
轴上的定点
,求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c147acf65224d68727a7ca62ba38b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a0387fc1258f31e44a10068c0ccfd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2443bacdbf97c978557ffdf3d691e2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
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5 . 已知函数
.
(1)若
,求
在
处的切线方程;
(2)讨论
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7391742ac948de1b5109c366fadaf4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d06e33d079ac1649ee5eea8f61de7cf.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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名校
解题方法
6 . 设函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
(1)已知
对任意
恒成立,求实数
的取值范围;
(2)已知直线
与曲线
,
分别切于点
,
,其中
.
①求证:
;
②已知
对任意
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b5178b7395ee353cb63df3028c51f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4197070db34f0419b6d85eed4cec9fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6270bb08b90f72d5671ab8225f356c43.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f61bb43900bfc8bf7760185b4e0bbb.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9268d9bfd0e22baf5956a2d6fb07ed6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153c6af699ce31b283e79b973e1927af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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7 . 动点
与定点
的距离和它到定直线
的距离的比是2,记动点
的轨迹为曲线
.
(1)求
的方程;
(2)过
的直线
与
交于
两点,且
,若点
满足
,证明:点
在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40460e97733a56b0b9963f8c641c47c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc07a297731dfc432de5eaad9361fcd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5648da2c6db0309ae8c6826a0f3d414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d2d9f1a9b44d59101fc96bd1c7631c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2024-05-26更新
|
558次组卷
|
4卷引用:河南省TOP二十名校2024届高三下学期5月联考猜题(一)数学试卷 (2)
河南省TOP二十名校2024届高三下学期5月联考猜题(一)数学试卷 (2)河南省TOP二十名校2024届高三下学期5月联考猜题(一)数学试卷(已下线)情境11 结论已知的证明命题(已下线)易错点8 圆锥曲线问题中未讨论直线斜率的特殊情况
8 . 已知函数
.
(1)求
的极值;
(2)若过点
可以作两条直线与曲线
相切,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153fd5ba2a1a36ea1a7aee469663ddbd.png)
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9 . 已知函数
,
为
的导函数.
(1)求曲线
在点
处的切线方程;
(2)求函数
的单调区间和极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165ae95d326428e2c444f283d9a5bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9e5b06cd549eda63382915caf44e19.png)
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10 . 已知函数
.
(1)当
时,求
的单调区间;
(2)当
时,设正项数列
满足:
,
①求证:
;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912db59acd9b73f98c01414f28eeabc5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4c78214e43a8b93f2a57072033cbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a6951c356414872ba8f6a7b7957be8.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985be3c4916ba2f93f943a58e09edb80.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2338c60e8d58771d3265d15ed7f555.png)
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