1 . 已知函数
,
的定义域为
.
(1)求
的极值点;
(2)讨论
的单调性;
(3)若函数
存在唯一极小值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270679f83d2f89307b9b7080cf81203a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9ee1df512f2ebc9e6cff9953b805b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df17d1b404651bf6dbc97b519d452e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559447f0f9d01acba3d220d9b6b90383.png)
(1)当
时,求
在
处的切线方程.
(2)设
分别为
的极大值点和极小值点,记
,
;
①证明:直线
与曲线
交于另一个点C;
②在①的条件下,判断是否存在常数
,使得
,若存在,求n;若不存在,说明理由.
附:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559447f0f9d01acba3d220d9b6b90383.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6470c6a4349ea591ce2bbcd93199f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d14d55cbbfe1f2b82c41efcae8efad1.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
②在①的条件下,判断是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0723ba7f3a8721cb1381d5be9dc12447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357924c44549675683398a0b7c9bcb26.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b7cfcc147916ae7eeb5d557fea945e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d90807e6a0085068ae47a101b7c87d6.png)
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名校
3 . 下列判断正确的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
4 . 已知函数
.
(1)讨论函数
的单调区间;
(2)当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc416d493e9d15c0b508114302a3438d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7927fb665ccd7d85a446a8927d250d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-28更新
|
1876次组卷
|
11卷引用:四川省凉山州民族中学2023-2024学年高二下学期3月月考数学试题
四川省凉山州民族中学2023-2024学年高二下学期3月月考数学试题山西省吕梁市2023-2024学年高二上学期期末数学试题湖南省长沙市麓共体2023-2024学年高二下学期第一次学情检测数学试卷(已下线)专题4 导数在不等式中的应用(讲)江苏省常州市武进高级中学2023-2024学年高二下学期3月学情调研数学试卷(已下线)专题3 导数在不等式中的应用(期中研习室)(已下线)导数专题:导数与不等式成立问题(6大题型)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)(已下线)2023-2024学年高二下学期期中复习解答题压轴题十七大题型专练(1)河北省石家庄二中2023-2024学年高二下学期3月月考数学试题河北省石家庄正中实验中学2023-2024学年高二下学期期中数学试题(已下线)专题01 一元函数的导数及其应用-4
解题方法
5 . 已知椭圆
的离心率是
,点
在
上.
(1)求椭圆
的标准方程;
(2)过直线
上一点
作椭圆的切线,切点为
,
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee80939187a84e1863eeb192a301c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab111a95c47709d6ece96552ee396b2e.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
解题方法
6 . 已知
,
是椭圆
的左、右焦点,椭圆
与双曲线
的焦点相同,
与
在第二象限的交点为P,若
的中点在双曲线
的渐近线上,且
,则椭圆的离心率是( )
![](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/3f071c0d662b2220ea1aeb81e40fa462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2427943a38dcd93c9ec9b735ffc9fe5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知椭圆
的右顶点
,过点
的直线
与椭圆
交于
,
两点(
,
异于点
),当直线
与
轴垂直时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/5772faf0-2aa5-4366-8bd5-84be3bc19289.png?resizew=135)
(1)求椭圆C的方程;
(2)求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd67f4ff7cb2455222ec40bc1d8bf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec0bc3a43265b63b6964476ca327fab.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](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/158db3f561cb7fc2cc6b4a884be80c93.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/5772faf0-2aa5-4366-8bd5-84be3bc19289.png?resizew=135)
(1)求椭圆C的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
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2024-01-23更新
|
607次组卷
|
4卷引用:四川省凉山州安宁河联盟2023-2024学年高二上学期期末联考数学试题
名校
解题方法
8 . 在直三棱柱
中,底面
为等腰直角三角形,且满足
,点
满足
,其中
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90e17995e2f71e297d94ae51c7e5b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea534e984a43f352055691305b73ec16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79296cd4046a71e163a8f3e647a176ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994fe2e2ccff825adfe4567a84e0fd79.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/2b17cb2d-c0e6-471f-bee5-098c40bde9df.png?resizew=145)
A.当![]() ![]() ![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
2023-12-29更新
|
500次组卷
|
4卷引用:四川省凉山州安宁河联盟2023-2024学年高二上学期期末联考数学试题
四川省凉山州安宁河联盟2023-2024学年高二上学期期末联考数学试题四川省广安市华蓥中学2023-2024学年高二上学期1月月考数学试题(已下线)期末精确押题之多选题(40题)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)(已下线)高二上学期期末考点大通关真题精选100题(1)
名校
解题方法
9 . 已知
是圆
上一点,过点
作垂直于
轴的直线,垂足为
,点
满足
.若点
,
,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb6e9693f41a982230a768aab99df9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb29c3477fde8d8c3c42c851a3636bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ada753580438fed0612f88d79b0ad4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b976243dd944629217f35588e5a7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0ed7bfe8dd774cfa5d432f108d88a3.png)
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2023-12-29更新
|
612次组卷
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4卷引用:四川省凉山州安宁河联盟2023-2024学年高二上学期期末联考数学试题
四川省凉山州安宁河联盟2023-2024学年高二上学期期末联考数学试题(已下线)期末精确押题之填空题(40题)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)河南省南阳市第一中学校2024届高三上学期期末模拟数学试题广东省中山市中山纪念中学2024届高三上学期第一次调研数学试题
名校
解题方法
10 . 已知
,
分别是椭圆
:
的左,右顶点,
为椭圆
上的点,直线
,
的斜率之积为
.
(1)求椭圆
的方程;
(2)直线
与椭圆
交于
,
两点,且直线
与
相交于点
,若点
在直线
上,证明:直线
过定点.
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea8a480a2fe03293cb8303da8837d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-12-14更新
|
145次组卷
|
5卷引用:四川省凉山州宁南中学2023-2024学年高二上学期期末模拟数学试题(二)