名校
解题方法
1 . 数列
有
项,
,对任意
,存在
,若
与前
项中某一项相等,则称
具有性质
.
(1)若
,求
可能的值;
(2)若
不为等差数列,求证:
中存在满足性质
;
(3)若
中恰有三项具有性质
,这三项和为
,使用
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccf7e4dc2f2528b70a7b6920a0360de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c439f52fd3e4c4f6c9872041044d7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a45cd3046323db116ec970be533d2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/470a3b303d8e0a78a68dde895a46bb88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b07d62c4025696b4c648db0c3dd67bf.png)
您最近一年使用:0次
名校
解题方法
2 . 约数,又称因数.它的定义如下:若整数
除以整数
得到的商正好是整数而没有余数,我们就称
为
的倍数,称
为
的约数.设正整数
共有
个正约数,即为
,
,
,
,
.
(1)当
时,若正整数
的
个正约数构成等比数列,请写出一个
的值;
(2)当
时,若
,
,
,
构成等比数列,求正整数
的所有可能值;
(3)记
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87484a879f450ab097f720fb2a0f4a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c0cd13ec90e5697013e59d73d3e82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afeed05dbd9752dd537a06bbcbc867cf.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbd5bb726a08c308b48373afebbb768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeaed9ec21e090defafcfeefe0059c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe164d8a8a4049e01565b576007651de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01416ee1d48b17f889e444b7eda99740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a49832d7c33597639bea9eace7989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57e391b1d575796894fea80cce6329b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04bc6dcaef3c78886e21f1c41e7f2cd6.png)
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2024-05-04更新
|
165次组卷
|
12卷引用:北京市通州区2023届高三上学期期末数学试题
北京市通州区2023届高三上学期期末数学试题北京市第五十五中学2024届高三上学期10月月考数学试题北京市东城区第六十五中学2024届高三上学期12月月考数学试题广东省广州市广东实验中学2023-2024学年高三下学期教学情况测试(二)数学试卷A湖南省长沙市雅礼中学2024届高三一模数学试卷(已下线)高考数学冲刺押题卷02(2024新题型)(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编(已下线)专题06 数列(已下线)第四套 艺体生新高考全真模拟 (一模重组卷)北京市西城区北京师范大学第二附属中学2023-2024学年高二下学期期中考试数学试题湖南省常德市第一中学2023-2024学年高二下学期第一次月考数学试题(已下线)高二下学期第三次月考模拟卷(新题型)(范围:导数+选择性必修第三册)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第三册)
名校
3 . 已知函数
,
.
(1)证明:
;
(2)求函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc873fc03e6e4d3c4ba02f8b1147b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8fb90b625d42b51fabcc66a35b9ebf7.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502416314c8c26f8442e639ea6a5db13.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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解题方法
4 . 已知椭圆
,其离心率
,长轴长为
.
(1)求椭圆
的标准方程;
(2)椭圆
的上、下顶点分别为
、
,右顶点为
,过点
的直线
与椭圆
的另一个交点为
,点
与点
关于
轴对称,直线
交
于
,直线
交
于点
,点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50bbe873760a74d9aedaafc98fe7e83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)椭圆
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a23ec4dbeacef576720699db1f8ad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800f03011e616124865745524656e827.png)
您最近一年使用:0次
2023-09-09更新
|
746次组卷
|
3卷引用:北京市清华附中2024届高三开学摸底考数学试题
5 . 已知函数
在
上恰有4个不同的零点,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0d6aa12f9c4c6edc7c56fb71caad55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-09-04更新
|
1638次组卷
|
6卷引用:北京市清华附中2024届高三开学摸底考数学试题
北京市清华附中2024届高三开学摸底考数学试题北京市广渠门中学2024届高三上学期10月考数学试题北京市清华大学附属中学2024届高三上学期开学考试数学试题湖北省武汉市第二中学2023-2024学年高三上学期10月月考数学试题(已下线)第四章 三角函数与解三角形 专题7 三角函数中w取值范围问题(已下线)专题08 活用三角函数的图象与性质(6大核心考点)(讲义)
名校
6 . 空旷的田野上两根电线杆之间的电线有相似的曲线形态.这些曲线在数学上称为悬链线.悬链线在工程上有广泛的应用.在恰当的坐标系中,这些曲线对应的函数表达式可以为
(其中a,b为非零常数),则对于函数
以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7de2689549fbbe15489912408ab8d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-01-24更新
|
347次组卷
|
10卷引用:北京市第八十中学2023-2024学年高三上学期10月月考数学试卷
北京市第八十中学2023-2024学年高三上学期10月月考数学试卷湖北省黄冈市2022-2023学年高一上学期元月期末数学试题湖北省荆门市龙泉中学2022-2023学年高一上学期期末数学试题辽宁省沈阳市第二中学2023-2024学年高一上学期12月月考数学试卷(已下线)江西省南昌市第二中学2023-2024学年高一上学期第二次月考数学试题江西省南昌市第二中学2023-2024学年高一上学期12月月考数学试题(已下线)高一(上)期末模拟考试(B 能力提升)-【冲刺满分】山东省临沂第十八中学2023-2024学年高一上学期1月阶段性测试数学试题广东省广州市广雅中学2023-2024学年高一上学期期末数学试题四川省绵阳南山中学2023-2024学年高一下学期入学考试数学试题
名校
7 . 已知正方体
的棱长为
,
是正方体表面上一动点,且
,记点
形成的轨迹为
,给出下列四个命题:
①
、
,
;
②
、
,
;
③
的长度是
;
④
的长度是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b04d26b859f3011566c4d4955dfa993.png)
其中真命题的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc04804a43974bdfdd61f5c6fe440f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b442343554ab0dc737a0dce2090f6f04.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b08e6d6e22713631a74cc6c906b085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90d77e81a18c23eb0ef684f6398d1a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d29eb6a833e455b9af821d7598e4e42.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e29dabc664557611726b0d36e938c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d11ea5a517593620af5ec92e117295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f21fde1ee999ce13afaca22345cf34.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70f280d062923a39c0c881aad5d429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3113c748ec660388c3ae764f40a309f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b04d26b859f3011566c4d4955dfa993.png)
其中真命题的个数是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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8 . 设函数
.
(1)若
,求曲线
在点
处的切线方程;
(2)若
,当
时,求证:
.
(3)若函数
在区间
上存在唯一零点,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ef7de45c7c920dff0762e81aaf70cf.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb9374a0245ffdcb4b23bd8bd5b662a.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
您最近一年使用:0次
9 . 已知点
在函数
的图象上,点
在函数
的图象上,且
,
,
,给出下列说法:
①当
时,
;
②存在点
在直线
上;
③
,
,使点
和点
为两个函数图象的公共点;
④若点
在函数
的图象上,则函数
的周期是
,
两点间距离的整数倍;
⑤定义满足长度
取最小值时的区间
为最小区间.若
,区间
是满足
的最大区间,则函数
的周期为
.
其中,说法正确的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369e2cc0b7c553969627461819e80229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04129b7390acd7d936fbd204cc111dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6db7130ea4b0ea4da3d316b3070f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7602e4015d02cb188ffb82092ee980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b59c92a868cc6f448e5d92d257401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96d62cdf358f79c7831dd009c26430c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b519531dbeee800a08ba5ce55ff7e51.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d387a4f4ed6f48afd7fc75ff68ae026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75ff0c325ddcac48cf1c233f033c2c7.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67de794bd1d73ebe1e7fca6622579587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677ad4c4ea0722f0ee064f44624c585f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96d62cdf358f79c7831dd009c26430c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369e2cc0b7c553969627461819e80229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6db7130ea4b0ea4da3d316b3070f46.png)
④若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6db7130ea4b0ea4da3d316b3070f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e59bc063c88b1add34184da82283251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e59bc063c88b1add34184da82283251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
⑤定义满足长度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31d1c786e88987bb3bc7c54b7b66819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63313f7ac7402fcb5a9a840db64c6f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85cbdee531d4b394d674d90adda132b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b83fe99c90a7bf139a7e6e537820c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00feb80debaf63029240652a21b4b38f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04129b7390acd7d936fbd204cc111dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
其中,说法正确的序号是
您最近一年使用:0次
名校
10 . 已知函数
.
(1)当
时,求函数
在点
处的切线方程;
(2)讨论
的单调性;
(3)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8190ae30e91fb02d4aae347679701a92.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba4f5f03bb09e4afa5b2626251545ea.png)
您最近一年使用:0次