名校
解题方法
1 . 数列
满足
则称数列
为下凸数列.
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
,其中
,
分别是公比为
,
的两个正项等比数列,且
,证明:
是下凸数列且不是等比数列;
(3)若正项下凸数列的前
项和为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0bee75d4d83c0b76421fd87113e4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f67fc95a626251da11649acb5e1706f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c340d7d093dd4a275ffea4b87cd26827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c171ff5c2728e7cf00a88f88de14f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755d7aa870e2f199d6c12264fc9be86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若正项下凸数列的前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0002f427eded1721f43d60dd0fd3ffe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd419dc0a6580ab97777b2cb8fd7cded.png)
您最近一年使用:0次
7日内更新
|
1116次组卷
|
5卷引用:2024届湖北省高三普通高中5月联合质量测评数学试卷
名校
解题方法
2 . 已知函数
恰有两个零点
,
和一个极大值点
,且
,
,
成等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b029ff1ec707abd0d2a14b9a3d4c2082.png)
__________ ;若
的解集为
,则
的极大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b269dce1ae3396d2afc82a91dc6f97ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90aa505e4e41dd4becc7e55d2e938f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b029ff1ec707abd0d2a14b9a3d4c2082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85db4f72795b4a150a734d835ffbd913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c253ea436c94f88bd5a3ddb799ef30ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2022-10-11更新
|
1105次组卷
|
5卷引用:2023年普通高等学校招生星云线上统一模拟考试Ⅰ数学试卷
3 . 已知函数
,其中
.
(1)当
时,
,求
的取值范围.
(2)若
,证明:
有三个零点
,
,
(
),且
,
,
成等比数列.
(3)证明:
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f1fbd89d2a6c03f0afb467ad2afce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301605e86e5a5e61a65c91cd3dd8b77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8a263f0dff43a4febb0b511b41c0db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
您最近一年使用:0次
解题方法
4 . 已知三条直线
(
)分别与抛物线
交于点
、
,
为
轴上一定点,且
,记点
到直线
的距离为
,△
的面积为
.
(1)若直线
的倾斜角为
,且过抛物线
的焦点
,求直线
的方程;
(2)若
,且
,证明:直线
过定点;
(3)当
时,是否存在点
,使得
,
,
成等比数列,
,
,
也成等比数列?若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88036e3c1badc0d0b3f9145cd52d1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79059a3366ed1b339ba1317ce8a1e7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146294fdb064581da7987fdca20ee912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc5c895153932c3e827a464664cef90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439e95540157803d4ac3cf61a49f50a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f1254f1ff64e7fc1918b84e75dceaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468edcfef1bcd7e74491a57a70c1bcb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50a4b1e4f8b1d044300df7ef8205c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb4be53c952d1edc5ecba3125c1111a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9bb415ebf91617fe843b83d0a140ea.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a251fb581ee87c54da42d43dc0f8fb68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7803037f78d54221e0bd45a2bff37c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d0252c1b2f7d2a84b5c985d19d547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
名校
5 . 已知
是函数
的零点,
是函数
的零点,且
下列说法正确的是( )(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f33a8d30ebf2afda1cbdc420e3c0479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df79854c0ad67f1b29ba550474ed7c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a04aa96c36522fc60bbbd61b15746ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c26fb0014f56cad9395c215f2a06cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c38f960830a5a901f88acbdb38d936.png)
A.![]() |
B.若![]() ![]() |
C.存在实数![]() ![]() ![]() |
D.存在实数![]() ![]() |
您最近一年使用:0次
6 . 将一个数列中部分项按原来的先后次序排列所成的一个新数列称为原数列的一个子数列,如果数列存在成等比数列的子数列,那么称该数列为“弱等比数列”.已知
,设区间
内的三个正整数
,
,
满足:数列
,
,
,
为“弱等比数列”,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72e056edc8ce492ccbaaacaeaa7cb1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cc0b4997cae4d8aec791a1d3923314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bd3ea56596730917cd797c963072a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51d60c9e444ef2d7705c3c6bee3efe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e1fbe0fb49725cf6d1e689ee8986d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb59638769faa7d399f622c03ee3674f.png)
您最近一年使用:0次
2020-02-14更新
|
967次组卷
|
2卷引用:上海市宝山区2015-2016学年高二上学期期末教学质量监测数学试题
解题方法
7 . 混沌现象普遍存在于自然界和数学模型中,比如天气预测、种群数量变化和天体运动等等,其中一维线段上的抛物线映射是混沌动力学中最基础应用最广泛的模型之一,假设在一个混沌系统中,用
来表示系统在第
个时刻的状态值,且该系统下一时刻的状态
满足
,
,其中
.
(1)当
时,若满足对
,有
,求
的通项公式;
(2)证明:当
时,
中不存在连续的三项构成等比数列;
(3)若
,
,记
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034983375860d2b404f6fbd7d40a44b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85a01f2a5b003d545aabd58658f430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d5b159da139b50cde0d087f462aa4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cb047913c41b42b47ac00bf91f2e45.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3d565c588f31510c613f32122778ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195fc747e2fc50cb6df2c844d51e4d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fbbb97adee9c7cb6af553e1c8e2b047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c7636532d8414f52061bba28a1b9a3.png)
您最近一年使用:0次
8 . 已知正项等比数列{an}的前n项和为Sn(n∈N*),且a3=a2+2,a2•a4=16.数列{bn}的前n项和为Tn,且
,
.
(1)求数列{an}的通项公式及其前n项和Sn;
(2)证明数列{bn}为等差数列,并求出{bn}的通项公式;
(3)设数列
,问是否存在正整数m,n,l(m<n<l),使得cm,cn,cl成等差数列,若存在,求出所有满足要求的m,n,l;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8acac935181771fc709ebfa793e726dc.png)
(1)求数列{an}的通项公式及其前n项和Sn;
(2)证明数列{bn}为等差数列,并求出{bn}的通项公式;
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1559d07f9c9aa7bc3f5c335d8d2b8804.png)
您最近一年使用:0次
2020-09-22更新
|
755次组卷
|
5卷引用:【市级联考】江苏省南通市2019届高三阶段性学情联合调研数学试题
【市级联考】江苏省南通市2019届高三阶段性学情联合调研数学试题(已下线)期中测试卷(基础卷)-2020-2021学年高二数学十分钟同步课堂专练(苏教版必修5)(已下线)专题3.5+不等式(基础卷)-2020-2021学年高二数学十分钟同步课堂专练(苏教版必修5)(已下线)第四章++数列2(能力提升)-2020-2021学年高二数学单元测试定心卷(人教A版2019选择性必修第二册)(已下线)本册内容测试(能力提升)-2020-2021学年高二数学单元测试定心卷(人教A版2019选择性必修第二册)
9 . Fibonacci数列又称黄金分割数列,因为当n趋向于无穷大时,其相邻两项中的前项与后项的比值越来越接近黄金分割数
.已知Fibonacci数列的递推关系式为
.
(1)证明:Fibonacci数列中任意相邻三项不可能成等比数列;
(2)Fibonacci数列{an}的偶数项依次构成一个新数列,记为{bn},证明:{bn+1-H2·bn}为等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d956c1c07d2b622af28908b25843f2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8ab68a92a52246865da222064b34cf.png)
(1)证明:Fibonacci数列中任意相邻三项不可能成等比数列;
(2)Fibonacci数列{an}的偶数项依次构成一个新数列,记为{bn},证明:{bn+1-H2·bn}为等比数列.
您最近一年使用:0次
10 . 已知函数
满足
,当
时,
.
(1)当
时,求函数
的图像与x轴所围成的图形面积;
(2)当
时,求函数
的最大值;
(3)当
时,函数
与
的图像有交点,将从左向右的交点的横坐标依次记为
、
、
、…,数列
是否可能为等比数列,若可能,请求出对应的m值,若不可能请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a940e5f45501eba9b07b73b2248bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356d300456f7f1c5fd6c90005aadeedb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb13318f27e55da0b1235027cff5f9f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028fc8d6c0d37e57d5ceb33b707a59f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536e30616558446d4a6db6917296128e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4318a47d7e83d587e74bab4d3d1f6883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d4d0b32b13857630f986eabb11bc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
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