解题方法
1 . 已知函数
,令
,
,则下列正确的选项为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de0861a5d6af9ca97bed91516bb07cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195fc747e2fc50cb6df2c844d51e4d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85a01f2a5b003d545aabd58658f430.png)
A.数列![]() ![]() ![]() |
B.![]() |
C.若数列![]() ![]() ![]() |
D.![]() |
您最近一年使用:0次
2 . 已知函数
的定义域均为R,且满足
则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf6aefea0eaf6a1b4a9803c91dd72ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7495bba454dd9d5e40347caa423c6e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0019846161d8a553045e5809c5cf6419.png)
A.![]() | B.795 | C.1590 | D.![]() |
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2022-10-12更新
|
2096次组卷
|
7卷引用:江西省重点校2023届高三上学期10月统一调研测试数学(理)试题
江西省重点校2023届高三上学期10月统一调研测试数学(理)试题四川省广安市邻水县九龙中学2022-2023学年高三上学期10月月考理科数学试题 重庆市巴蜀中学校2023届高三下学期4月月考数学试题(已下线)专题6-1 数列函数性质与不等式放缩(讲+练)-1(已下线)专题2-1 函数性质(单调性、奇偶性、中心对称、轴对称、周期性)-2(已下线)专题4 抽象函数问题(过关集训)(压轴题大全)(已下线)第16题 抽象函数与数列结合(一题多变)
22-23高三上·江苏盐城·阶段练习
名校
解题方法
3 . 为了研究某单链RNA病毒,科学家先对该病毒的RNA进行分析,得知其中碱基
约占
,碱基
约占
,碱基
约占
,碱基
约占
.现科学家欲人工模拟合成一条RNA,采用的原料按照原病毒RNA各碱基之比混合而成,原料中每个碱基片段连接到合成RNA上的概率相等,合成的RNA上连续出现两个
时即停止合成.
(1)计算合成RNA仅有4个碱基的概率,并计算27次重复实验下,仅有4个碱基的数学期望
(2)求合成RNA的碱基数量的数学期望.
(提示:当
充分大时,对于某一绝对值小于
的常数
,认为有
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1dd362f843e640ce551ad1787c9873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af46237d7279ffb682d57e4e7b57a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b624e6d456c5aa077dfd00ada3a311d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af46237d7279ffb682d57e4e7b57a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)计算合成RNA仅有4个碱基的概率,并计算27次重复实验下,仅有4个碱基的数学期望
(2)求合成RNA的碱基数量的数学期望.
(提示:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9526c32a3859acb8b0ec57f72ef2afec.png)
您最近一年使用:0次
名校
解题方法
4 . 已知数列
满足
,
,
为数列
的前n项和,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1381f0937c6052ce088e0eaee7df4880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3fb2dbaed5873d28ad2e9e1bbf693d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
A.![]() | B.![]() |
C.![]() | D.若![]() ![]() |
您最近一年使用:0次
2022-09-12更新
|
1015次组卷
|
2卷引用:福建省福州第一中学2023届高三上学期开学质检考试数学试题
5 . 在
中,
,
,O是
的外心,若
的最大值是m,数列
中,
,
,则
的通项公式为
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226741a02640e1710d93b2e39ec61440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdeeaefd7eca104aca3b6f6f3a5131a4.png)
![](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/3d578da4527f71cfc653240bf44a2729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
6 . 给定正整数m,数列
,且
.对数列A进行T操作,得到数列
.
(1)若
,
,
,
,求数列
;
(2)若m为偶数,
,且
,求数列
各项和的最大值;
(3)若m为奇数,探索“数列
为常数列”的充要条件,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee00267997ecd957562fe62214153ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e972bd6405268bcb111d97039df7c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8743cb652671f7a19a5c9aca1c65a43.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced4e381e8c3336848b8c436dbc584f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
(2)若m为偶数,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d14ae78ff7bc3ecb1735171cdeda7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21548fbce5a8c4385975335a66401bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
(3)若m为奇数,探索“数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
您最近一年使用:0次
2022-06-02更新
|
1227次组卷
|
8卷引用:北京市大兴区兴华中学2022届高三三模数学试题
北京市大兴区兴华中学2022届高三三模数学试题北京市第十二中学2022届高三第三次模拟练习数学试题 (已下线)2022年新高考北京数学高考真题变式题13-15题北京市第十二中学2022届高三下学期第三次模拟练习数学试题(已下线)2022年新高考北京数学高考真题变式题19-21题北京市对外经济贸易大学附属中学2023届高三上学期12月月考期末综合测试(一)数学试题北京市日坛中学2023届高三上学期12月月考数学试题(已下线)模块九 数列-2
7 . 在数列
中,
,且对任意的
,都有
.
(1)求数列
的通项公式;
(2)若
,定义集合A的长度为
.已知数列
的通项公式为
,若关于x不等式
的解集A,求集合A的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cefeddf71dca8ae824328df3f0e5e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c548da8d22f8f7e63361f174e788250b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024c7c66f8103c5950e4dd45e1512dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c613e16b95b1fb880d1ba401dfb21c27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5771ab3b1121633361e93cb3e73c8013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949c693a0554c9834b910cb131b77352.png)
您最近一年使用:0次
8 . 在数学中,双曲函数是与三角函数类似的函数,最基本的双曲函数是双曲正弦函数与双曲余弦函数,其中双曲正弦:
,双曲余弦函数:
,(e是自然对数的底数)
(1)解方程:
;
(2)写出双曲正弦与两角和的正弦公式类似的展开式:
_________,并证明;
(3)无穷数列
,是否存在实数a,使得
?若存在,求出a的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/444eaaaf560b7ed9b225e9ba34c5dbbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f980c011d926a51ef8201dc79e88002.png)
(1)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01958f2959a7fa4a86d8b25058ccb1ba.png)
(2)写出双曲正弦与两角和的正弦公式类似的展开式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13b62168f8e90860410fde112257aec.png)
(3)无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d04f8e5504b64a6eada18e2dc997b55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd167bb422b4b23cfc8fe76c9a6c5a41.png)
您最近一年使用:0次
名校
9 . 设复数
为虚数单位,
.
(1)若
,且
,试确定虚数q的值,使得
,并计算
的值;
(2)若数列
是各项均为正数的等比数列,
,
,
,求
的值;
(3)若
,且
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a036e9ee70ced65188b33599f9c5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22214f48085c06e62521bf96c27191b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a58dcdbc4ba66c058b9c2ea0b66c78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cf89ab7d054f735048e3f2de3790952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e958699ed7f4ec14624af584b08869c.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a19c1b64ab0b0ddcf2392cdc57b3772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0dd3fb6af23def773e1b0032a4f3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d308b3a2305c0a30cd95d08e6b039986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621c88d8efebb14c021243cf153046bb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4638a75e65012bebf3684a34212a2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93fb330f2c2ee620c57204e75f439e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900298ea19e2fd2d1c99e9744484b0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4914cce8e01442532dbcee3564708e85.png)
您最近一年使用:0次
10 . 如图,已知正方体
顶点处有一质点Q,点Q每次会随机地沿一条棱向相邻的某个顶点移动,且向每个顶点移动的概率相同.从一个顶点沿一条棱移动到相邻顶点称为移动一次.若质点Q的初始位置位于点A处,记点Q移动n次后仍在底面ABCD上的概率为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
A.![]() |
B.![]() |
C.点Q移动4次后恰好位于点![]() |
D.点Q移动10次后仍在底面ABCD上的概率为![]() |
您最近一年使用:0次
2022-05-21更新
|
2716次组卷
|
7卷引用:2022届山东省济南市高三下学期5月高考模拟考试(三模)数学试题