1 . 已知数列
满足
,
,其中
.
(1)设
,求证:数列
是等差数列.
(2)在(1)的条件下,求数列
的前n项和
.
(3)在(1)的条件下,若
,是否存在实数
,使得对任意的
,都有
,若存在,求出
的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cb570b2e190d3a0fc98dd2ec3a7dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb3133b7ca679c841508e1f9431ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)在(1)的条件下,求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c0b04ff1a24b233372000a40ff868a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a81b71e56323ce72c688c4e9e3e779b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c74164bcbb550600a8fe2946e5d9844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-02-28更新
|
1671次组卷
|
5卷引用:四川省成都市盐道街中学2020-2021学年高一下学期6月月考文科数学试题
四川省成都市盐道街中学2020-2021学年高一下学期6月月考文科数学试题天津教研联盟2023届高三一模数学试题江西省宜春市宜春一中、万载中学、宜丰中学2022-2023学年高二下学期期末考试数学试题江西省宜春市第一中学2022-2023学年高二下学期期末考试数学试题(已下线)专题01 数列(6大考点经典基础练+优选提升练)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)
名校
解题方法
2 . 如图,在三棱锥
中,平面
平面ABC,且
是正三角形,O是AC的中点,D是AB的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/21/7187490e-22af-4c45-9980-ed521fd109d1.png?resizew=189)
(1)
平面SBC;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78307cd417504554a4e2276fe24d1162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08c39e44b50d0cac4a10106f8d09339.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/21/7187490e-22af-4c45-9980-ed521fd109d1.png?resizew=189)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6748d9b9948485c5ba87ca8751c6e053.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea27e2052fcaae1f3312f62bd90f86.png)
您最近一年使用:0次
2022-12-20更新
|
263次组卷
|
4卷引用:四川省南充市2020-2021学年高一下学期期末数学试题
解题方法
3 . 在数列
中,
,
.
(1)证明:数列
是等差数列.
(2)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7584b4ad34cdc5240f0a0510ba79db35.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
解题方法
4 . 已知定义域为
的函数
是奇函数.
(1)求
的解析式;
(2)判断
单调性,并用单调性的定义加以证明;
(3)若不等式
对任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9f333cee2ccb2b215d93011a162f7a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3d3340eed3e13d74ed68876554b5d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-12-29更新
|
896次组卷
|
4卷引用:四川省仁寿县第一中学2021-2022学年高一上学期期末模拟考试数学试题
名校
5 . 如图,在
中,弦
相交于点
,连接
,已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/9c33a7d8-1233-4887-9e53-1f4e3ab5f82c.png?resizew=156)
(1)求证:
;
(2)如果
的半径为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2224f664af4189df83e42696ec8d51d5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/9c33a7d8-1233-4887-9e53-1f4e3ab5f82c.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c220eadc312101e2fb89dfe920f7b30d.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbcb44d8facf4d59924860a9153f9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
解题方法
6 . 如图,已知直三棱柱
中,D,E,F分别为AC,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/8ab0e165-a831-4131-a12c-7353ba064d71.png?resizew=158)
(1)求证:
平面ABC;
(2)若△ABC为等腰直角三角形,∠ABC=90°,且
.求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/8ab0e165-a831-4131-a12c-7353ba064d71.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a407b262c22419f73396170ecdc849.png)
(2)若△ABC为等腰直角三角形,∠ABC=90°,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d289a52b00154f78031af90afa02135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047da2786ecd6c3b0248908e72593c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
您最近一年使用:0次
7 . 如图,菱形ABCD的边长为2,BD=2,E、F分别是边AD,CD上的两个动点,且满足AE+CF=2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/cee83aff-4851-4eb3-acf2-76093ceabee0.png?resizew=176)
(1)求证:△BDE≌△BCF;
(2)判断△BEF的形状,并说明理由;
(3)设△BEF的面积为S,求S的取值范围.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/15/cee83aff-4851-4eb3-acf2-76093ceabee0.png?resizew=176)
(1)求证:△BDE≌△BCF;
(2)判断△BEF的形状,并说明理由;
(3)设△BEF的面积为S,求S的取值范围.
您最近一年使用:0次
8 . 如图,在菱形
中,
,
,点
为边
上一个动点,延长
到点
,使
,且
、
相交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/224984a3-22af-4e9d-b1fb-b3fcee697cd0.png?resizew=562)
(1)当点
运动到
中点时,证明:四边形
是平行四边形;
(2)当
时,求
的长;
(3)当点
从点
开始向左运动到点
时,求点
运动路径的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac3d3b55561ec5d4acc242ecd1c7f41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/224984a3-22af-4e9d-b1fb-b3fcee697cd0.png?resizew=562)
(1)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c78b5b3732d43103e575dbb3e1b95d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6f6c04bc017ced739230d14ba31948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(3)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
名校
9 . 如图,正方体
的棱长为1,线段
上有两个不同的动点
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/10bf0881-c35e-4fa0-971a-7799059f02ab.png?resizew=269)
(1)求证:
平面
;
(2)求证:
;
(3)二面角
的大小是否为定值,若是,求出其余弦值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/10bf0881-c35e-4fa0-971a-7799059f02ab.png?resizew=269)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
(3)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770d42343599d3f26f0e0de8d5849f52.png)
您最近一年使用:0次
2022-06-13更新
|
1507次组卷
|
2卷引用:四川省成都市天府新区2020-2021学年高一下学期期末学业水平监测数学(理)试题
名校
10 . 函数
对任意的实数
恒有
,且当
时,
.
(1)求证:
是R上的减函数;
(2)若
,解关于
的不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f640d4c6ea2591d85488d00d13da92d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd384d86840b7b158af41f56fe29c7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d104250033a2039fa591c8d99c912ad.png)
您最近一年使用:0次