1 . 已知抛物线
,焦点为
,点
在
上,直线
∶![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
与
相交于
两点,过
分别向
的准线
作垂线,垂足分别为
.
(1)设
的面积分别为
,求证:
;
(2)若直线
,
分别与
相交于
,试证明以
为直径的圆过定点
,并求出点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d939b804513036cd96fddce791ece09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dba5cc987db7f50f9b8e2d4544006d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936c47254c94f202e1c97ccb07d943ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613b2b516b04a9a06db7526f5b4d7a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7ded76162a594e556495aa0a56d54f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2 . 已知函数
,曲线
在点
处的切线为
,记
.
(1)当
时,求切线
的方程;
(2)在(1)的条件下,求函数
的零点并证明
;
(3)当
时,直接写出函数
的零点个数.(结论不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be6b7c590b12db1b6cbe451ad18c4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd817a1014876a72ad1971548ed6f52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db57c256dac51842864d269d5cdab520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909736dad505d81be43aef91e6309bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)在(1)的条件下,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a93aef9c6c4b64df420c39ef19d1551.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe8dc8e5def7d46b88535453ae1fd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
名校
解题方法
3 . 已知数列
满足
,
,
,
成等差数列.
(1)求证:数列
是等比数列,并求出
的通项公式;
(2)记
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2438f2272d7b7ab51dbbe587025a553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479c0564241789f8f52ac4fda26e9904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6197e2365d7f39507f8671acfc25a339.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef130855c8dc1accbff28762858f20bf.png)
您最近一年使用:0次
2024-06-09更新
|
551次组卷
|
2卷引用:江西省赣州市2023-2024学年高三下学期5月适应性考试数学试题
4 . 若某类数列
满足“
,且
”
,则称这个数列
为“
型数列”.
(1)若数列
满足
,求
的值并证明:数列
是“
型数列”;
(2)若数列
的各项均为正整数,且
为“
型数列”,记
,数列
为等比数列,公比
为正整数,当
不是“
型数列”时,
(i)求数列
的通项公式;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b781279c765cfbfb88b28bc5b6cfb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be613fff0421d9be9e8bb5eb8b07c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00cf22c8daa450289ffdce46b85024b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85726f99979d3793ea28b77a7708f4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07cefac60bb3fcde0bded804501c90b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(i)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15b6cf3d2cdd85baed3056ac375d3c.png)
您最近一年使用:0次
5 . 若定义在
上的函数
满足对任意实数
恒成立,则我们称
为“类余弦型”函数.
(1)已知
为“类余弦型”函数,且
,求
和
的值;
(2)在(1)的条件下,定义
,求
的值;
(3)若
为“类余弦型”函数,且对任意非零实数
,总有
,求证:函数
为偶函数.设有理数
满足
,判断
和
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc57d42b2adbff8dfa18f45a5eb69703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8492210fbc3ea3678bbc96c6b35240e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
(2)在(1)的条件下,定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8eb899087bfa2bf4a9a58105f72c849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207d8709a7dc0f5e85b64b8f0a1ab504.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caea9a696f22c76f8f4563ac45d124b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c983d456ac12b40aea1fd87e961c07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9769116ec47353514e6b7fb7b17216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542893790445d6d888d9ff91fd215c9c.png)
您最近一年使用:0次
6 . 已知
是由正整数组成的无穷数列,该数列前
项的最大值记为
,即
;前
项的最小值记为
,即
,令
(
),并将数列
称为
的“生成数列”.
(1)若
,求其生成数列
的前
项和;
(2)设数列
的“生成数列”为
,求证:
;
(3)若
是等差数列,证明:存在正整数
,当
时,
,
,
,
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d7fcd7b8817a82478bd872bc61a132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09b082619df0e06d2dcd83a3bc0fb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd9b9869da85bfffac7c01d7c34e35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414f4f53b4ae5085836107278784e3ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7f82f00fe6163833431241820687ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef1643721ad2b804d4ee2ba1a091a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b6a226d310f16ea311db851216e894.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c29bfcb2e31e3c21967ede660eaa0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39222f0687c9124bddb35544bcc7798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
您最近一年使用:0次
2024-04-17更新
|
1593次组卷
|
10卷引用:广东省梅州市2024届高三下学期总复习质检(二模)数学试题
广东省梅州市2024届高三下学期总复习质检(二模)数学试题(已下线)数学(广东专用02,新题型结构)(已下线)5.2 等差数列和等比数列(高考真题素材之十年高考)(已下线)第4套 新高考全真模拟卷(二模重组)(已下线)压轴题05数列压轴题15题型汇总-1(已下线)第六套 艺体生新高考全真模拟 (二模重组卷)湖北省荆州市沙市中学2024届高三下学期高考全真模拟数学试卷广西南宁市第三十六中学2024届高三下学期适应性训练数学试题(已下线)模块五 专题4 全真能力模拟4(人教B版高二期中研习)(已下线)模块三 专题2 新定义专练【高二下人教B版】
7 . 已知抛物线
上任意一点
满足
的最小值为
(
为焦点).
(1)求
的方程;
(2)过点
的直线经过
点且与物线交于
两点,求证:
;
(3)过
作一条倾斜角为
的直线交抛物线于
两点,过
分别作抛物线的切线.两条切线交于
点,过
任意作一条直线交抛物线于
,交直线
于点
,则
满足什么关系?并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac78092eec8d674c97589a30d687d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd1ac4958d35abc7a64812eca930d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5480c2dd9197e86d1989e70347f.png)
(3)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be563ee0cc1e5fe5abade7efbeda6a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a481f48bd003009e85fd18cc7e34ebe.png)
您最近一年使用:0次
8 . 在正项等比数列
中,
.
(1)求
的通项公式:
(2)已知函数
,数列
满足:
.
(i)求证:数列
为等差数列,并求
的通项公式
(ii)设
,证明:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963be18b37690c2a4cebefad320b1aaf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e688cc3939a9422a6433a0dc23d2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0060ba7c94a156f968c7e3dd7dc34975.png)
(i)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51da505ea6ab5a3f92e459c311304e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831de7531e4b51f836a5ef44c4791198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5475fe99ef8eb84ab937f54ac9cdcc75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c46b33730f3a29b9ec3024df71375.png)
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9 . 已知函数
.
(1)求
的单调区间;
(2)证明:
;
(3)若
,且
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e50ead3dafa710129bd59b727bfd756.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29772ffc1a200fb6cd2283aef27e2874.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea134f599285e3d32d2ab3e7186990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225a93c53ca692b1e0a7c9809bbb5326.png)
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10 . 已知函数
.
(1)求
在
处的切线方程
,并证明
的图象在直线
的上方;
(2)若
有两个不相等的实数根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4b35e41dfa9391bf5004948d4ed574.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b331497342e72895c306815d1cca62b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b222b256b37f83fa24a3a4b6527f58d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5dc5d64a9a86dd15c47e7d129fc622.png)
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