名校
解题方法
1 . 已知函数
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b647867d91de52884cea8c492fb0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b29e5cc1e369f351eb1b505919f6ab.png)
A.函数![]() ![]() ![]() |
B.令![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() |
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|
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|
2卷引用:辽宁省七校协作体2023-2024学年高二下学期6月月考数学试题
2 . 已知函数
是定义在
上的奇函数,且当
时,
,对于数列
,若
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a28068770a85b88b42321cd71ecd3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5a05989a8c0f72fa134a31e9dbb1cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d27e9d6651c189516650fb11301b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aae580ebcfce670585ba54023be02ed.png)
A.存在![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.若存在等差数列![]() ![]() ![]() ![]() ![]() |
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3 . 定义:对于数列
,若从第2项起,每一项与它的前一项之差都大于或等于同一个常数
,且小于或等于另一个常数
,则
叫作类等差数列(若
,则
是等差数列).
(1)若类等差数列
满足
,
,
,
均为已知数,请类比等差数列的通项公式,求出数列
的通项不等式(即第
项
与首项
及
的不等式关系,要求写出推导过程);
(2)若数列
中,
,
.判断数列
是否为类等差数列,若是,请证明;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d48141571f43bdb1211a62edf02a011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(1)若类等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57b3ca3af4f43d8ea2699f05cc8014e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecf9a2cfa6d5cba8c0b6c61dbf1235c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2f1c1409a06278e847e6b573cef254.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddda8e6c1ea80647c96a6b89ee544e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
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解题方法
4 . 已知函数
,其极大值点和极小值点分别为
,记点
,直线
交曲线
于点
,若存在常数
,使得
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef3e79110067a46276f0869bea25af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2790aecde6df3b05f195ab8daddb56be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e11699fa0813a5e9d6baf694f5bf4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357924c44549675683398a0b7c9bcb26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
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5 . 下列说法正确的是( )
A.![]() ![]() ![]() ![]() |
B.在![]() ![]() ![]() |
C.15人围坐在圆桌旁,从中任取4人,他们两两互不相邻的概率是![]() |
D.已知函数![]() ![]() ![]() ![]() ![]() |
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6 . 差分法的定义:若数列
的前
项和为
,且
,则
时,
.例如:已知数列
的通项公式是
,前
项和为
,因为
,所以
.
(1)若数列
的通项公式是
,求
的前
项和
;
(2)若
,且数列
的前
项和分别为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](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/314fa1f4da470780673cc7246974180c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9361afc7cc02253140585eedc39a695d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e46ecd051c92489c0d1d458932f37.png)
![](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/e3bd2e55bb083a90ecba8cc98fac9536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237ce153a42d4e2378d5435051734cb3.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd845d1bfac72200926447db04563fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77af844c4444e536adae9bc0b1cff614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04f062dc12653209868713f2142fe06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee1c51f15c934050099b460b19a04f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/038e3af7c9f2fb642b9209415662aeff.png)
您最近一年使用:0次
2024-05-30更新
|
166次组卷
|
2卷引用:辽宁省朝阳市建平县高级中学2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
7 . 若函数
在
上有定义,且对于任意不同的
,都有
,则称
为
上的“
类函数”.
(1)若
,判断
是否为
上的“2类函数”;
(2)若
,为
上的“2类函数”,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f0e1ac411fd3a260a5c71df178bd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62f64bce0222f01a519ab1b26236bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4613910bb8aa030db2fc5d2768e533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f248318141e0016d38f9f5a692797f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3616e4a7268ef41b750fe22afbcd74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f248318141e0016d38f9f5a692797f.png)
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2024-05-08更新
|
250次组卷
|
3卷引用:辽宁省沈阳市东北育才学校2023-2024学年高二实验部下学期阶段检测二(6月)数学试题
名校
8 . 已知函数
,关于
的不等式
的解集为
,其中
,
为常数.给出下列四个结论:
①直线
是曲线
的一条切线;
②
;
③当
时,
的取值范围是
;
④要使
取唯一的值,仅当
.
其中,所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe819909452c1edb8e1f0e3f1adc562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce84901e2f29f740265e278be8e34de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea69fb59dc615852a0d248675788d82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a27c31d57a84a5928898de139cb40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b5b0840d90d0654e9bcb0f866ff10d.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51969fc1a8030cef11cab59267689e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50188f84f379b3d0418c54cbade7d7.png)
④要使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdc6e6a0e6584bea7deb91b0841fa28.png)
其中,所有正确结论的序号是
您最近一年使用:0次
名校
9 . 马尔科夫链是概率统计中的一个重要模型,也是机器学习和人工智能的基石,在强化学习、自然语言处理、金融领域、天气预测等方面都有着极其广泛的应用.其数学定义为:假设我们的序列状态是……
,…,那么
时刻的状态的条件概率仅依赖前一状态
,即
.
现实生活中也存在着许多马尔科夫链,例如著名的赌徒模型.
假如一名赌徒进入赌场参与一个赌博游戏,每一局赌徒赌赢的概率为
,且每局赌赢可以赢得1元,每一局赌徒赌输的概率为
,且赌输就要输掉1元.赌徒会一直玩下去,直到遇到如下两种情况才会结束赌博游戏:记赌徒的本金为
一种是赌金达到预期的B元,赌徒停止赌博;另一种是赌徒输光本金后,赌徒可以向赌场借钱,最多借A元,再次输光后赌场不再借钱给赌徒.赌博过程如图的数轴所示.
时,最终欠债 A元(可以记为该赌徒手中有 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c590e4795751a8b932c63e0ad3bc49dd.png)
元)概率为
,请回答下列问题:
(1)请直接写出
与
的数值.
(2)证明
是一个等差数列,并写出公差d.
(3)当
时,分别计算
时,
的数值,论述当B持续增大时,
的统计含义.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e54fb0a18558ef56d8100f58564c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b49fdb5924134bfc54266f0fee35ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb150b73ea7c87972a0b57510a99472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a27e7e2acb3aef8c7c9b504e8a5ab2.png)
现实生活中也存在着许多马尔科夫链,例如著名的赌徒模型.
假如一名赌徒进入赌场参与一个赌博游戏,每一局赌徒赌赢的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1065ae0947705c7d16a5a86c78f07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1065ae0947705c7d16a5a86c78f07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9063713e024a66e6daca3ec781a639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91c4c2fe859ad0805dcc2fc26d6dc537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c590e4795751a8b932c63e0ad3bc49dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532084481ae3a67c8208b7783bf22e8e.png)
(1)请直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabb71334b127f1719f2a5e728d5fae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b459aa38bd06fa9b5b0412c51121dd48.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaef76a1500c26dc42bd88f89c15dd27.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf47b8e265017c3a85fe62885cfe326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2761b0fdb9640f2def02525128c74a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391c6e33329f5f4ad0c5107520d9a5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391c6e33329f5f4ad0c5107520d9a5cf.png)
您最近一年使用:0次
2024-04-17更新
|
1217次组卷
|
3卷引用:辽宁省实验中学2023-2024学年高二下学期3月月考数学试题
辽宁省实验中学2023-2024学年高二下学期3月月考数学试题(已下线)专题03 第七章 随机变量及其分布列--高二期末考点大串讲(人教A版2019)江西省南昌市第十九中学2024届高三下学期第四次模拟考试数学试卷
10 . 若数列
满足:存在等差数列
,使得集合
元素的个数为不大于
,则称数列
具有
性质.
(1)已知数列
满足
,
.求证:数列
是等差数列,且数列
有
性质;
(2)若数列
有
性质,数列
有
性质,证明:数列
有
性质;
(3)记
为数列
的前n项和,若数列
具有
性质,是否存在
,使得数列
具有
性质?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48dfe427f8841f24337b83a767750352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5b653a209622a9136a15c3b11b0a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87e0860e3f142e7ddd7b45c16b211fa.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24ba3195cbf220d03a1ef5bfe954f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde3c47074b6f1b16af81c3684d04419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e196cf353f8f832f24be4951a9fefab8.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d16238329f13aeeb2d13aaf025ba07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662422cae5190af5fa05475a1e16f2d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b211310c6b436c4b7c4f38ce483d9b13.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2024-04-10更新
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3卷引用:辽宁省大连市第八中学2023-2024学年高二下学期期中考试数学试题