名校
解题方法
1 . 已知数列
满足:对任意
,都有
,
, 设数列
的前
项和为
,若
,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c52c908859e988302ac7f411a46452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b66796ca5b684d1a1e158654033d07.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addee6ce5163a2580888ce2da22714af.png)
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2 . 根据三角不等式我们可以证明:
,当且仅当
,
,
时等号成立.若等式
对任意x,y,
都成立,则符合要求的有序数组
数量为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63a54f1a49e7d84cb064ac80e13dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eacd0a48a993d1cd82054d55d80b4b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8d7c76b84ff78f9333046f71761b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba383b25120365f4778dc858489199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafeb20c434b2a9002a1f9700b5bee25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a89495c19be4f58ee3f60940f9765f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a57d1215099fab4a97db12b2fa8f14.png)
A.有且仅有6组 | B.有且仅有12组 |
C.大于12组,但为有限多组 | D.无穷多组 |
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3 . 若从无穷数列
中任取若干项
(其中
)都依次为数列
中的连续
项,则称
是
的“衍生数列".给出以下两个命题:
(1)数列
是某个数列的“衍生数列”;
(2)若
各项均为0或1,且是自身的“衍生数列”,则
从某一项起为常数列.下列判断正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d255743a932f013f8cd3c90942aea1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bacaf758c8b5c2f52624f80debc02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4429ffb4a826e1c7c474eea9c539391d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.(1)(2)均为真命题 |
B.(1)(2)均为假命题 |
C.(1)为真命题,(2)为假命题 |
D.(1)为假命题,(2)为真命题 |
您最近一年使用:0次
4 . 若数列
满足
(n为正整数,p为常数),则称数列
为等方差数列,p为公方差.
(1)已知数列
的通项公式分别为
判断上述两个数列是否为等方差数列,并说明理由;
(2)若数列
是首项为1,公方差为2的等方差数列,数列
满足
,且
,求正整数m的值;
(3)在(1)、(2)的条件下,若在
与
之间依次插入数列
中的
项构成新数列
,
,求数列
中前50项的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595955aa3a2670abcd60c78a5086f2fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56c975b8b3195cea6ef4b9949e5d0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9764763cde4a065aa276c7dbe91773.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d4d1ac46eb6cf5f711cdfa8662dd6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a647029ac8d38aba9dda5b94588dcbd4.png)
(3)在(1)、(2)的条件下,若在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4741eb4c177d75ca74fe2d36e52ecbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cf52946ef832dd2fa7a82dcd6d1bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41806cbde05bd95cc402c702485bd84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50ee5f150f0dbd416e0f8fe9c80ce9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc1e7a87da7751da31f851ae6d46aff.png)
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2023-06-07更新
|
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3卷引用:上海市进才中学2024届高三上学期开学考试数学试题
名校
5 . 定义有序实数对(a,b)的“跟随函数”为
.
(1)记有序数对(1,-1)的“跟随函数”为f(x),若
,求满足要求的所有x的集合;
(2)记有序数对(0,1)的“跟随函数”为f(x),若函数
与直线
有且仅有四个不同的交点,求实数k的取值范围;
(3)已知
,若有序数对(a,b)的“跟随函数”
在
处取得最大值,当b在区间(0,
]变化时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2cc652bd9ca23554830dd042dd77de7.png)
(1)记有序数对(1,-1)的“跟随函数”为f(x),若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2701e8073d8862b4c2bc0a34e57283.png)
(2)记有序数对(0,1)的“跟随函数”为f(x),若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c735cc0c181bf7ec7c36654aba02a90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead6a3dbd03539ef5e0807be57bb1e17.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e0e24323fe73e5d9fc6136219306da.png)
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名校
解题方法
6 . 意大利著名数学家斐波那契在研究兔子繁殖问题时,发现有这样一列数:
.该数列的特点为前两个数都是1,从第三个数起,每一个数都等于它的前面两个数的和,即
,人们把这样的一列数组成的数列
称为“斐波那契数列”,则
( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a238c89ab1b54d5fde6b18770629b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5e89456955d7070ab95f5b760ad9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0232b5ad565ba5c45e2c34a130055bf.png)
A.-2024 | B.2024 | C.-1 | D.1 |
您最近一年使用:0次
2023-04-28更新
|
867次组卷
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3卷引用:上海市建平中学2022-2023学年高一下学期6月月考数学试题
7 . 若数列
、
均为严格增数列,且对任意正整数n,都存在正整数m,使得
,则称数列
为数列
的“M数列”.已知数列
的前n项和为
,则下列选项中为假命题的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102db69b759f7bea82298ac24dee642b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.存在等差数列![]() ![]() ![]() |
B.存在等比数列![]() ![]() ![]() |
C.存在等差数列![]() ![]() ![]() |
D.存在等比数列![]() ![]() ![]() |
您最近一年使用:0次
2023-04-14更新
|
1353次组卷
|
8卷引用:上海市建平中学2022-2023学年高一下学期期末数学试题
上海市建平中学2022-2023学年高一下学期期末数学试题上海市闵行区2023届高三二模数学试题(已下线)专题06 数列及其应用(已下线)专题17 数列探索型、存在型问题的解法 微点3 数列探索型、存在型问题综合训练上海市华东政法大学附属松江高级中学2023-2024学年高二上学期期中考试数学试卷(已下线)专题06 数列在高考中的考法(难点,十一大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)上海市川沙中学2023-2024学年高一下学期数学5月月考数学试卷
名校
8 . 欧拉(1707-1783),他是数学史上最多产的数学家之一,他发现并证明了欧拉公式
,从而建立了三角函数和指数函数的关系,若将其中的
取作
就得到了欧拉恒等式
,它是令人着迷的一个公式,它将数学里最重要的几个量联系起来,两个超越数——自然对数的底数e,圆周率
,两个单位——虚数单位i和自然数单位1,以及被称为人类伟大发现之一的0,数学家评价它是“上帝创造的公式”,请你根据欧拉公式:
,解决以下问题:
(1)将复数
表示成
(
,i为虚数单位)的形式;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5aa584db159b0f9bfae801d0134393b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a462b902989401ed07851ba4dd6dd137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5aa584db159b0f9bfae801d0134393b.png)
(1)将复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696ed4fd06f9aaa7a01d3be6ced5af1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceb6e0153b07bf81c3b169c7c8a1c5f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91413c558d7a35bab90e33241c0d9885.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba602453a82da3e502958a560ce5e9b.png)
您最近一年使用:0次
2023-04-12更新
|
726次组卷
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7卷引用:上海市建平中学2022-2023学年高一下学期期末数学试题
上海市建平中学2022-2023学年高一下学期期末数学试题重庆市西南大学附属中学校2022-2023学年高一下学期期中考试数学试题陕西省延安中学2022-2023学年高一下学期期中数学试题黑龙江省佳木斯市第八中学2022-2023学年高一下学期5月期中数学试题(已下线)7.2.1?复数的加、?减运算及其几何意义——课后作业(基础版)(已下线)5.2.1复数的加法与减法-【帮课堂】(北师大版2019必修第二册)(已下线)专题03 第七章 复数-期末考点大串讲(人教A版2019必修第二册)
名校
解题方法
9 . 下列命题正确的有( )个
(1)若数列
为等比数列,
为其前n项和,则
,
,
也成等比数列;
(2)数列
的通项公式为
,则对任意的
,存在
,使得
;
(3)设
为不超过实数x的最大整数,例如:
,
,
.设a为正整数,数列
满足
,
,记
,则M为有限集.
(1)若数列
![](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/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b0ed9533c1ea30a87249539a005e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48e167c9bcef9eb89d7a456d8ca21b7.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7476db4d8d32edf309372a3ef067b839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4004a42ff7dc0afb6d53c73859e7c49b.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3420606c96b68fb884c839923fd20a25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5971b06a0758bb830c4e09a25bb665a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fb370b8bd5422314299f1dd4f1ec25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c4cdcb32e3a0ce527c13978c022a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4b0cd80d95662729de6af4fa5add73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3440756e96122c23a882a4592b45b4f2.png)
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
名校
10 . 已知曲线
对坐标平面上任意一点
,定义
.若两点
满足
,称点
在曲线
两侧.记到点
与到
轴距离和为5的点的轨迹为曲线
,曲线
,若曲线
上总存在两点
在曲线
两侧,则实数
的取值范围是_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735ba4f3bb4ce2114682daa3ecf19fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174861299cb1b64e5304c25c70eb216f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba794d5df10924e9e0672e70834e3966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ad58997b9dc0b341c9af08f0cd1fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb816267961a90cfe0ffc18907426fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ad58997b9dc0b341c9af08f0cd1fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06d31c9a2298b02664a86ddd91b1121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/312ff07bdf7332953dff59b246a99655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-03-23更新
|
50次组卷
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4卷引用:上海市实验学校2021-2022学年高二下学期期中数学试题
上海市实验学校2021-2022学年高二下学期期中数学试题上海市南洋模范中学2020-2021学年高二上学期期末数学试题(已下线)核心考点04抛物线、曲线与方程(1)(已下线)高三数学开学摸底考02(上海专用)