名校
解题方法
1 . 已知数列
的首项
,
,
、
、
.
(1)求证:数列
为等比数列;
(2)记
,若
,求最大正整数
;
(3)是否存在互不相等的正整数
、
、
,使
、
、
成等差数列且
、
、
成等比数列,如果存在,请给出证明;如果不存在,请说明理由.
![](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/7643e8b7aa32ebf299048417a94432dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fa34d5a86d929757c2bc3db1a51e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f92693c8b5e2828929376a6fbb8e638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)是否存在互不相等的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb10dd730b827d3ec05aebe8c18c9e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff1721a696504d02a4c4b20e5ba7f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07812c89c11b5cb96c2eb573e681cbd3.png)
您最近一年使用:0次
2020-07-26更新
|
349次组卷
|
10卷引用:福建省永泰一中2021届高三上学期数学月考试题
福建省永泰一中2021届高三上学期数学月考试题江苏省南通市如皋中学2017-2018学年第一学期高三第二次阶段测试12月数学试题湖南省长沙市长郡中学2019-2020学年高三10月月考数学(理)试题广东省茂名市电白区2018-2019学年高一下学期期中数学试题湖南省长沙市长郡中学2019-2020学年高三上学期第二次月考理科数学试题江西省抚州市临川第一中学2019-2020学年高一下学期开学考试数学试题江苏省南通市2019-2020学年高三上学期开学模拟考试数学试题(已下线)专题07 《数列》中的最值问题-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)江西省景德镇一中2021-2022学年高一(19)班下学期期中考试数学试题广东省广州市第十七中学2023-2024学年高二下学期期中考试数学试卷
解题方法
2 . 如图所示的五面体中,
是正方形,
是等腰梯形,且平面
平面
,
为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/5f7325ef-fea7-4210-9ac9-8317e8901ee3.png?resizew=209)
(1)求证:平面
平面
;
(2)
为线段
的中点,
在线段
上,记
,
是线段
上的动点. 当
为何值时,三棱锥
的体积为定值?证明此时二面角
为定值,并求出其余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5747d138808e8ae03858c07dca6f19f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9003d21719232f65698743d8ecf8edd6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/5f7325ef-fea7-4210-9ac9-8317e8901ee3.png?resizew=209)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e92d42e94cb01dabba1db6fc18c66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7e524de0f5d99fbd82f58d28dd4219.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f1d42d8642fcdd53522c07fe7b3db8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cc391036004bfc202e934285ee7fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63884ba9b24c3729315d0bb8a230d66.png)
您最近一年使用:0次
解题方法
3 . 在如图所示的六面体中,四边形ABCD是边长为2的正方形,四边形ABEF是梯形,
,平面
平面ABEF,BE=2AF=2,EF
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/7bdd7d5b-cfe5-4383-a128-6a9558fd4a51.png?resizew=147)
(1)在图中作出平面ABCD与平面DEF的交线,并写出作图步骤,但不要求证明;
(2)求证:
平面DEF;
(3)求平面ABEF与平面ECD所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3e927b7b2383ccded03838ae8b30b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/7bdd7d5b-cfe5-4383-a128-6a9558fd4a51.png?resizew=147)
(1)在图中作出平面ABCD与平面DEF的交线,并写出作图步骤,但不要求证明;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8197bf06d017950c85c3ba6a291c095e.png)
(3)求平面ABEF与平面ECD所成锐二面角的余弦值.
您最近一年使用:0次
名校
解题方法
4 . 各项均为正数的数列
的前
项和为
,
,且
.
(1)求证:数列
不是等差数列;
(2)是否存在整数
,使得
对任意的
都成立?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/c624432439688019ef8fbcaf11cfbfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322924b25caf788076ff0d97ebb27025.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)是否存在整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f3d93ca2745c3813c135b46e582fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
您最近一年使用:0次
5 . 已知直线与抛物线交于两点.
(1)求证:若直线
过抛物线的焦点,则
;
(2)写出(1)的逆命题,判断真假,并证明你的判断.
(1)求证:若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749b17e02ac5325dcfcac745a51b5170.png)
(2)写出(1)的逆命题,判断真假,并证明你的判断.
您最近一年使用:0次
名校
解题方法
6 . 已知函数
(
,
为自然对数的底数),
是
的导数.
(1)当
时,求证:
;
(2)是否存在整数
,使得
对一切
恒成立?若存在,求出
的最大值,并证明你的结论;若不存在,也请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc62bb186214f638ae7eb5600a90b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)是否存在整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91b7c3887ad1e4cc1d71a6c04645806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-03-22更新
|
427次组卷
|
4卷引用:2020届福建省福州第一中学高三下学期教学反馈检测数学(理)试题
2020届福建省福州第一中学高三下学期教学反馈检测数学(理)试题福建省福鼎第一中学2021-2022学年高二下学期第一次月考数学试题(已下线)2020届高三3月第01期(考点03)(理科)-《新题速递·数学》安徽省芜湖市第一中学2020届高三下学期3月第五次线上考试数学试题
名校
解题方法
7 . 已知函数
,
,函数
的图象在点
处的切线平行于
轴.
(Ⅰ)求
的值
(Ⅱ)设
,若
的所有零点中,仅有两个大于
,设为
,
(
)
(1)求证:
,
.
(2)过点
,
的直线的斜率为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc873fc03e6e4d3c4ba02f8b1147b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab76a882449cbc52eed09ed4721ff6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d599059e6b2c918ab15ee22611b6962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863b54185da5a3f1a765e1aa0577e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/0fdad769b543148ae11205120a12fa58.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837aa7c0803b1db2f5bb81b9f64987a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96e97805f0853d6f994f0fad3b5aa05.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc47735cc385a3474bc1dabad322304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c67ecb1d07abe1dc74a78c757c495ce.png)
您最近一年使用:0次
8 . 在如图所示的六面体中,四边形
是边长为
的正方形,四边形
是梯形,
,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/fd1ca737-af71-4dbf-99ea-98a5938bf71b.png?resizew=163)
(1)在图中作出平面
与平面
的交线,并写出作图步骤,但不要求证明;
(2)求证:
平面
;
(3)求平面
与平面
所成角的余弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c766942d554e7f15ffec6eaacbe0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49282ee0fe94e4c25ffaabf419ea83b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68004768b879c6a052f45a2c45217cd6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/fd1ca737-af71-4dbf-99ea-98a5938bf71b.png?resizew=163)
(1)在图中作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81fa367ec317fe2a30142e1c30cce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2977ae4bfa32de8c6f0fb136205c4fe7.png)
您最近一年使用:0次
真题
名校
9 . 已知函数
,
.
(1)求证:
是奇函数并求
的单调区间;
(2)分别计算
合
的值,由此概括出涉及函数
和
的对所有不等于零的实数
都成立的一个式,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2981ce7dfb246ad72da74f9940dda1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f3b8eab5443cfc8616b88954d3536b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)分别计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d29c2735f1dd5f251284bfad833250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5220ac57e8ca9f4f78dc5f8d1eeaf0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2019-10-30更新
|
396次组卷
|
3卷引用:福建省仙游第一中学2020-2021学年高一上学期期中考试热身模拟考数学试题
10 . 如图所示,已知点P是
所在平面外一点,M,N,K分别AB,PC,PA的中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/8ecfde2c-2600-474a-93c3-a713ecedbff4.png?resizew=171)
(1)求证:
平面PAD;
(2)直线PB上是否存在点H,使得平面
平面ABCD,并加以证明;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a09d03d26008b17d89e98125eff110c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d19526cadbce0e984c2edc3f31d591.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/8ecfde2c-2600-474a-93c3-a713ecedbff4.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02438f0423acd0ff2dfa5ffb6abf143f.png)
(2)直线PB上是否存在点H,使得平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f37ad65abc2d37d457f6b91088f187.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350799f6c6e340d5176c91805f0ef02d.png)
您最近一年使用:0次
2020-02-20更新
|
535次组卷
|
2卷引用:福建省莆田锦江中学2020-2021学年高一下学期期中考试数学试题