2024高三·全国·专题练习
1 . 已知函数
恰有两个零点
.
(1)求实数
的取值范围;
(2)若函数
,求证:
在
上单调递减;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9041e48fb655996cfc996fceefefa0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc74b04b18f5ed278420b45b53d7fb3.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0622e759d2c32552428b0bbf1411b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5bbb4e91c232d62cb331c02087ef6b.png)
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名校
解题方法
2 . 设实系数一元二次方程
①,有两根
,
则方程可变形为
,展开得
②,
比较①②可以得到![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e360b7ba27dfc3e5d401027d5bd8a5.png)
这表明,任何一个一元二次方程的根与系数的关系为:两个根的和等于一次项系数与二次项系数的比的相反数,两个根的积等于常数项与二次项系数的比.这就是我们熟知的一元二次方程的韦达定理.
事实上,与二次方程类似,一元三次方程也有韦达定理.
设方程
有三个根
,则有
③
(1)证明公式③,即一元三次方程的韦达定理;
(2)已知函数
恰有两个零点.
(i)求证:
的其中一个零点大于0,另一个零点大于
且小于0;
(ii)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3f3db6b7c682450309a6ccba5ac5a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
则方程可变形为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455d33fcfd9a59d6b374e9d25888cd2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e42b42152492cbdfec62c7a02be4055.png)
比较①②可以得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e360b7ba27dfc3e5d401027d5bd8a5.png)
这表明,任何一个一元二次方程的根与系数的关系为:两个根的和等于一次项系数与二次项系数的比的相反数,两个根的积等于常数项与二次项系数的比.这就是我们熟知的一元二次方程的韦达定理.
事实上,与二次方程类似,一元三次方程也有韦达定理.
设方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ddc5e3c2c7c6f4d2d0ab396b65679a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8d75a2417827b2c5b09ba9385fe252.png)
(1)证明公式③,即一元三次方程的韦达定理;
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b5e4746c2bd0afb279630698afd3a0.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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3 . 已知动圆
过定点
且与直线
相切,记圆心
的轨迹为曲线
.
(1)已知
、
两点的坐标分别为
、
,直线
、
的斜率分别为
、
,证明:
;
(2)若点
、
是轨迹
上的两个动点且
,设线段
的中点为
,圆
与动点
的轨迹
交于不同于
的三点
、
、
,求证:
的重心的横坐标为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5421a28dc3675ae20190d6090793246e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)已知
![](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/879a4007beef22e009248112d664f7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf209717d3bde602ab96c53d6a43a811.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb2356a3833defed220ee1fa481aad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.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/acc290b44635265137fdf13146b6a6d9.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaecf08a22124a457128fb04c9c02bb.png)
您最近一年使用:0次
4 .
个有次序的实数
,
,
,
所组成的有序数组
,
,
,
称为一个
维向量,其中
,2,
,
称为该向量的第
个分量.特别地,对一个
维向量
,若
,
,
,称
为
维信号向量.设
,
,则
和
的内积定义为
,且
.
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在6个两两垂直的6维信号向量.
(3)已知
个两两垂直的2024维信号向量
,
,
,
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5b983949f56bc3137d48e72a393b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e3810cf1eca832ef7487d354e474d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811ba47ff724fd153378ffe14c1e0b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/713ac1eb0d8cce55d51e62ef4a2b1634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42b3123092bbc1c62e30b0253edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bd9ca5f1ebecf069be3b25efafd29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6460555341932b6b590af7d74b8f0db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42b3123092bbc1c62e30b0253edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3507f3193277c2f2a5e9d83d25cc9366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b73255f197b518efc343bc9776837e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cfce6ff54e403e1486244d51395bed.png)
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在6个两两垂直的6维信号向量.
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
您最近一年使用:0次
2024-05-03更新
|
430次组卷
|
3卷引用:上海市进才中学2023-2024学年高一下学期期中数学试题
上海市进才中学2023-2024学年高一下学期期中数学试题(已下线)专题03 高一下期末考前必刷卷01(基础卷)-期末考点大串讲(人教A版2019必修第二册)重庆市乌江新高考协作体2023-2024学年高一下学期5月期中数学试题
5 .
个有次序的实数
所组成的有序数组
称为一个
维向量,其中
称为该向量的第
个分量.特别地,对一个
维向量
,若
,
,称
为
维信号向量.设
,
,则
和
的内积定义为
,且
.
(1)直接写出4个两两垂直的4维信号向量;
(2)证明:不存在14个两两垂直的14维信号向量;
(3)已知
个两两垂直的2024维信号向量
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27bb33ccdad573e2b2b0e7facbcca07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d038f2967ee70acc7777c32c8b43c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9925b25d5708cbd87f69cca1b5c66c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143f87bed8eee1f43d3e67be747b7d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcadd9ce3631b6e230fe7b21a0719c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e0d46fb5c7c978e4fe9c23f33ba151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143f87bed8eee1f43d3e67be747b7d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777dac26504cae699de348ec1df9dc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8346ea7024dd0c905cc4c80cb16dc6a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c7c807358869b70becd16ca80e1714.png)
(1)直接写出4个两两垂直的4维信号向量;
(2)证明:不存在14个两两垂直的14维信号向量;
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9cae65660b220cc622b87ed9eea092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
您最近一年使用:0次
2024-02-23更新
|
696次组卷
|
6卷引用:湖北省武汉市华中师大第一附中2023-2024学年高二下学期数学独立作业(一)
湖北省武汉市华中师大第一附中2023-2024学年高二下学期数学独立作业(一)(已下线)模块一 专题3 平面向量的应用(B)(已下线)模块一专题3 《平面向量的应用》B提升卷(苏教版)(已下线)模块三专题4大题分类练(专题3 平面向量数量积)【高一下人教B版】(已下线)高一数学下学期期中模拟卷(新题型)-同步题型分类归纳讲与练(人教A版2019必修第二册)广东韶关实验中学2023-2024学年高一下学期3月月考数学试题
6 . 已知
是由正整数组成的无穷数列,该数列前
项的最大值记为
,即
;前
项的最小值记为
,即
,令
(
),并将数列
称为
的“生成数列”.
(1)若
,求其生成数列
的前
项和;
(2)设数列
的“生成数列”为
,求证:
;
(3)若
是等差数列,证明:存在正整数
,当
时,
,
,
,
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d7fcd7b8817a82478bd872bc61a132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09b082619df0e06d2dcd83a3bc0fb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd9b9869da85bfffac7c01d7c34e35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414f4f53b4ae5085836107278784e3ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7f82f00fe6163833431241820687ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef1643721ad2b804d4ee2ba1a091a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b6a226d310f16ea311db851216e894.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ef2909bf624c3d346474741d226b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c29bfcb2e31e3c21967ede660eaa0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39222f0687c9124bddb35544bcc7798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
您最近一年使用:0次
2024-04-17更新
|
1593次组卷
|
10卷引用:广东省梅州市2024届高三下学期总复习质检(二模)数学试题
广东省梅州市2024届高三下学期总复习质检(二模)数学试题(已下线)模块五 专题4 全真能力模拟4(人教B版高二期中研习)(已下线)模块三 专题2 新定义专练【高二下人教B版】(已下线)5.2 等差数列和等比数列(高考真题素材之十年高考)(已下线)第4套 新高考全真模拟卷(二模重组)(已下线)压轴题05数列压轴题15题型汇总-1(已下线)第六套 艺体生新高考全真模拟 (二模重组卷)湖北省荆州市沙市中学2024届高三下学期高考全真模拟数学试卷广西南宁市第三十六中学2024届高三下学期适应性训练数学试题(已下线)数学(广东专用02,新题型结构)
2024高三·全国·专题练习
解题方法
7 . 设数列
的各项为互不相等的正整数,前
项和为
,称满足条件“对任意的
,
,均有
”的数列
为“好”数列.
(1)试分别判断数列
,
是否为“好”数列,其中
,
,
并给出证明;
(2)已知数列
为“好”数列,其前
项和为
.
①若
,求数列
的通项公式;
②若
,且对任意给定的正整数
,
,有
,
,
成等比数列,求证:
.
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8134cb1772cc78e318280a19fe4124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)试分别判断数列
![](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/677e46ecd051c92489c0d1d458932f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7bb72b3ebbca741b3eda49cd617c058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
(2)已知数列
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a90323142c0d14429c5124541a295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff2eb0fb845a82db057a3bbaf314c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb4a3b2465a8dcc8a677882c8d6862d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d4ad9afdd266c6d38421bdfccd45e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b924cf3c2252a73ec6809ca262643f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbdd68463267382ef3d410eb5417a23.png)
您最近一年使用:0次
8 . 已知函数
(a为常数).
(1)求函数
的单调区间;
(2)若存在两个不相等的正数
,
满足
,求证:
.
(3)若
有两个零点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa8ea75ca2f775085b1838bef2c641d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若存在两个不相等的正数
![](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/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3da00fe1feafb42d7e2254dd5f8589.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.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/40c67a34394380636fdf4b882ce28d40.png)
您最近一年使用:0次
2023-12-30更新
|
1241次组卷
|
10卷引用:模块三 大招10 对数平均不等式
(已下线)模块三 大招10 对数平均不等式(已下线)模块五 专题6 全真拔高模拟6(已下线)模块2专题7 对数均值不等式 巧妙解决双变量练(已下线)专题6 导数与零点偏移【练】(已下线)专题16 对数平均不等式及其应用【讲】黑龙江省哈尔滨市第六中学校2022-2023学年高三上学期期中数学试题(已下线)5.3 导数在研究函数中的应用(练习)-高二数学同步精品课堂(苏教版2019选择性必修第一册)(已下线)模块三 大招24 对数平均不等式重庆缙云教育联盟2024届高三高考第一次诊断性检测数学试卷福建省宁德市福安市福安一中2023-2024学年高三上学期10月月考数学试题
9 . 已知数列
的前n项和为
,且满足
,
.
(1)判断
是否为等差数列?并证明你的结论;
(2)求
和
;
(3)求证:
.
![](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/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a022b4111eeada0a90412ab74e2ad325.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31066efaa85cde2cedf2cb065bbc162a.png)
您最近一年使用:0次
2024-01-11更新
|
1626次组卷
|
4卷引用:每日一题 第26题 由Sn求an 作差检验(高二)
(已下线)每日一题 第26题 由Sn求an 作差检验(高二)(已下线)模块六 大招4 数列不等式的放缩河南省南阳市第一中学校2023-2024学年高二下学期第一次月考数学试题上海市青浦高级中学2023-2024学年高二上学期期末考试数学试题
解题方法
10 . 已知数列
的首项
,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6931285e9564e0edecab772a79db523.png)
(1)求证:数列
为等比数列;
(2)证明:数列
中的任意三项均不能构成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6545b8eca1c4223ed701a199a85683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6931285e9564e0edecab772a79db523.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
您最近一年使用:0次