名校
1 . 已知函数
,
.
(1)当
时,求
的单调区间;
(2)当
时,记
的极小值点为
.
(ⅰ)证明:
存在唯一零点
;
(ⅱ)求证:
.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f385b23c5ed85f350ffa395cd860f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc0733cb65fb25e9096618fff3348.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697572b42c40f498ed398099c659df1f.png)
您最近一年使用:0次
2024-05-04更新
|
259次组卷
|
2卷引用:福建省厦门第一中学2023-2024学年高二下学期期中考试数学试卷
2 . 已知动圆
经过定点
,且与圆
:
内切.
(1)求动圆圆心
的轨迹
的方程;
(2)设轨迹
与
轴从左到右的交点为
,
,点
为轨迹
上异于
,
的动点,设
交直线
于点
,连接
交轨迹
于点
,直线
,
的斜率分别为
,
.
①求证:
为定值;
②证明:直线
经过
轴上的定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866502435d9ea08c6d3a5e304a8986c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8387b687579c4d5152175c9d19e24232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9811dd726ed27d28ad5a8e83fbb20ed6.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/dad2a36927223bd70f426ba06aea4b45.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/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef79861421b414b455a090a3ef04fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b51a4949896526cfc3c076ea8dec8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128147bd4834566a78b4e9d2a3b2139c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4a51e6728d354cc1c3d32e2d4368d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729d727db2181aca4e8a6455d10cfe28.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6b1769274eee3ce2896cb3513d50f8.png)
②证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024-01-11更新
|
625次组卷
|
11卷引用:福建省厦门双十中学2023-2024学年高二上学期期中考试数学试题
名校
3 . 如图,在四棱锥
中,PA
面ABCD,AB
CD,且CD=2,AB=1,BC=
,PA=1,AB
BC,N为PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/2e5070b6-be71-4ac1-8866-3db509d25ff4.png?resizew=190)
(1)求证:AN
平面PBC;
(2)在线段PD上是否存在一点M,使得直线CM与平面PBC所成角的正弦值是
?若存在,求出
的值,若不存在,说明理由;
(3)在平面PBC内是否存在点H,满足
,若不存在,请简单说明理由;若存在,请写出点H的轨迹图形形状(不必证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/2e5070b6-be71-4ac1-8866-3db509d25ff4.png?resizew=190)
(1)求证:AN
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)在线段PD上是否存在一点M,使得直线CM与平面PBC所成角的正弦值是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241a37fb1eff68a7133822b1b52d627e.png)
(3)在平面PBC内是否存在点H,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2da5312b15f602fcb8c0ffe9ea57a95.png)
您最近一年使用:0次
2022-11-18更新
|
819次组卷
|
3卷引用:福建省福州市八县(市)协作校2022-2023学年高二上学期期中考试数学试题
福建省福州市八县(市)协作校2022-2023学年高二上学期期中考试数学试题辽宁省大连市第八中学2022-2023学年高三上学期12月月考数学试题(已下线)第三章 空间轨迹问题 专题一 立体几何轨迹常见结论及常见解法 微点3 立体几何轨迹常见结论及常见解法综合训练【培优版】
名校
解题方法
4 . 已知椭圆
过点
,且离心率为
.设
,
为椭圆
的左、右顶点,
为椭圆上异于
,
的一点,直线
,
分别与直线
相交于
,
两点,且直线
与椭圆
交于另一点
.
(1)求椭圆
的标准方程;
(2)求证:直线
与
的斜率之积为定值;
(3)判断三点
,
,
是否共线:并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.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/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
(3)判断三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2022-10-11更新
|
1675次组卷
|
9卷引用:福建省莆田市第二中学2023-2024学年高二下学期返校考试数学试卷
名校
解题方法
5 . 已知函数f(x)
,g(x)=lnx-1,其中e为自然对数的底数.
(1)当x>0时,求证:f(x)≥g(x)+2;
(2)是否存在直线与函数y=f(x)及y=g(x)的图象均相切?若存在,这样的直线最多有几条?并给出证明.若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540547414909de221d530d7abb9d66bb.png)
(1)当x>0时,求证:f(x)≥g(x)+2;
(2)是否存在直线与函数y=f(x)及y=g(x)的图象均相切?若存在,这样的直线最多有几条?并给出证明.若不存在,请说明理由.
您最近一年使用:0次
2021-09-12更新
|
898次组卷
|
9卷引用:福建省泉州市泉港区第一中学2023-2024学年高二下学期3月月考数学试题
福建省泉州市泉港区第一中学2023-2024学年高二下学期3月月考数学试题江苏省南通市海安高级中学2022-2023学年高二下学期期中数学试题江苏省南通市海安市2021-2022学年高三上学期期初学业质量监测数学试题宁夏银川一中2022届高三上学期第二次月考数学(理)试题陕西省西安中学2021-2022学年高三上学期期中理科数学试题四川省南充高级中学2021-2022学年高三上学期月考四数学(理)试题(已下线)专题36 盘点导数与函数零点的交汇问题—备战2022年高考数学二轮复习常考点专题突破重庆市南开中学校2023届高三上学期期末数学试题重庆市荣昌中学校2024届高三上学期第一次月考数学试题
名校
解题方法
6 . 如图,在四棱锥
中,
,
,
,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/d8dee249-e133-4f35-aca8-f9cbba1cddcc.png?resizew=180)
(1)求证:
;
(2)已知二面角
的余弦值为
.线段PC上是否存在点M,使得BM与平面PAC所成的角为30°?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946470cef32a0bd769b3809351d8ee61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279e119eed905cf15026649a1b86502a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/d8dee249-e133-4f35-aca8-f9cbba1cddcc.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e18836bc7fee22f8f813a6f525d93.png)
(2)已知二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9f1e2b86f4eca37c72011d3dffb0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f1145c162038df3c7184d9201c628e.png)
您最近一年使用:0次
2021-01-13更新
|
974次组卷
|
5卷引用:福建省泉州市2021-2022学年高二上学期期中联考数学试题
名校
解题方法
7 . 椭圆
,
是椭圆
的左右顶点,点P是椭圆上的任意一点.
(1)证明:直线
,与直线
,斜率之积为定值.
(2)设经过
且斜率不为0的直线
交椭圆于
两点,直线
与直线
交于点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)设经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ee8669bc280bff4b20644cb82faf23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a06486e1a6eb37f1a65b1972e10ee55.png)
您最近一年使用:0次
2020-07-07更新
|
591次组卷
|
5卷引用:福建省建瓯市芝华中学2020-2021学年高二上学期第一次阶段考数学试题
名校
解题方法
8 . 已知函数
(
,
为自然对数的底数),
是
的导数.
(1)当
时,求证:
;
(2)是否存在整数
,使得
对一切
恒成立?若存在,求出
的最大值,并证明你的结论;若不存在,也请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc62bb186214f638ae7eb5600a90b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)是否存在整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91b7c3887ad1e4cc1d71a6c04645806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-03-22更新
|
427次组卷
|
4卷引用:福建省福鼎第一中学2021-2022学年高二下学期第一次月考数学试题
福建省福鼎第一中学2021-2022学年高二下学期第一次月考数学试题2020届福建省福州第一中学高三下学期教学反馈检测数学(理)试题(已下线)2020届高三3月第01期(考点03)(理科)-《新题速递·数学》安徽省芜湖市第一中学2020届高三下学期3月第五次线上考试数学试题
9 . 已知
(
).
(1)求证:
;
(2)若不等式
在
时恒成立,求最小正整数
,并给出证明..
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e46ecd051c92489c0d1d458932f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08fbc9665668df0e8e2dd9405760a45.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f3dbac1a9f2b1903d48cd94684e3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c29bfcb2e31e3c21967ede660eaa0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
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10 . 已知函数
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1a5f2533b8ea54b7022383f875666.png)
(1)讨论函数
的单调性;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ae859b52222aaf0b4d0950dba26e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1a5f2533b8ea54b7022383f875666.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a4d90664b71fad5b99fdfb2de4fd47.png)
您最近一年使用:0次
2024-01-13更新
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517次组卷
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2卷引用:福建省厦门双十中学2023-2024学年高二下学期第一次月考数学试题