解题方法
1 . 定义首项为1,且公比为正数的等比数列为"M—数列”
(Ⅰ)已知数列
是单调递增的等差数列,满足
,求数列
的通项公式;
(Ⅱ)已知数列
的前n项和为
,若
是
和1的等差中项,证明:数列
是"M-数列";
(Ⅲ)在(Ⅰ)的条件下,若存在"M—数列”
,对于任意正整数k,都有
成立.求此时数列
公比q的最小值.
(Ⅰ)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b507923114ca32ef53982240bdd33852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(Ⅱ)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(Ⅲ)在(Ⅰ)的条件下,若存在"M—数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c9062bc228495507c8576177fd2789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
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2 . 数列
中
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6a2f1bfdc4c1f262d7775ad7f6ce4e.png)
(1)
时,求
;
(2)证明:若存在
,其中
,设
的取值范围设为
,
;
(3)若
,求
的取值个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e076d53e0fab96afda46ff7ac1689dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6a2f1bfdc4c1f262d7775ad7f6ce4e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3129ddd2ea97fd010b9e0b644225da8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6fe44bc49b478979589face327799.png)
(2)证明:若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd42f8e3f220a7b1c6f6945e73bc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153fb853cd99beec9e600a4eaf73fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5b5f7e398a382c96b3bdcb0b4b2a6f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc473418716524061f271116d3f0b065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
3 . 如图,已知四边形
为菱形,且
,取
中点为
.现将四边形
沿
折起至
,使得
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/eea842dd-27de-403d-ba06-8523cc7fd8cc.png?resizew=282)
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的余弦值;
(Ⅲ)若点
满足
,当
平面
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a6f36741b86f464be362b12bac13d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e1e4ea140260a790885868bc7a94f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b29f99026a0ea8890fcd5ad58aebfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b5be85715f868fe603eba37ca0fd94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/eea842dd-27de-403d-ba06-8523cc7fd8cc.png?resizew=282)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b29f99026a0ea8890fcd5ad58aebfb.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be00ab92da5293c11886eb75fc963733.png)
(Ⅲ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4025ed22666217a6881e5cee62986b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4add4f2d0dc3b8832581436af6aad41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
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解题方法
4 . 如图,在菱形
中,
,
是
的中点,
平面
,且在矩形
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/f3e25ba0-431a-4099-bdea-44e22f95004c.png?resizew=201)
(1)求证:
;
(2)求证:
平面
;
(3)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3f4f259d60ade01bd9bf6632238e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39967d6f3aed6ce7b6643787795d451d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ab4fdfc612c9fa2dd8ae24904192d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1863a65cf1f24adc10ddbfcc9d46e1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/f3e25ba0-431a-4099-bdea-44e22f95004c.png?resizew=201)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf21399dcf3682bf5d3f9cbd5eed86c.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/250833a6c405ffd724b673b478c22919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711da913d92fc989e581bcfdfe092a18.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90985b4cec465c6c3710ffe7e0ed9fae.png)
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名校
5 . 如图,在多面体ABCDEF中,四边形ABCD为平行四边形,平面ADE⊥平面CDEF,∠ADE=60°,DE∥CF,CD⊥DE,AD=2,DE=DC=3,CF=4,点G是棱CF上的动点.
(Ⅰ)当CG=3时,求证EG∥平面ABF;
(Ⅱ)求直线BE与平面ABCD所成角的正弦值;
(Ⅲ)若二面角G﹣AE﹣D所成角的余弦值为
,求线段CG的长.
(Ⅰ)当CG=3时,求证EG∥平面ABF;
(Ⅱ)求直线BE与平面ABCD所成角的正弦值;
(Ⅲ)若二面角G﹣AE﹣D所成角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3dc0a411f385c4df07613b4b54b0c6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/e70f24b9-d55c-4393-bdab-15b5787cdbec.png?resizew=168)
您最近一年使用:0次
2020-03-08更新
|
522次组卷
|
8卷引用:北京一零一中学2019-2020学年度第二学期高三数学统练(二)
北京一零一中学2019-2020学年度第二学期高三数学统练(二)(已下线)专题02 必拿分题目强化卷(第一篇)-备战2021年新高考数学分层强化训练(北京专版)【校级联考】天津市十二重点中学2019届高三下学期毕业班联考(二)数学(理)试题天津市西青区2019-2020学年高三第一学期期末考试数学试题(已下线)强化卷05(3月)-冲刺2020高考数学之必拿分题目强化卷(山东专版)天津市(芦台一中、静海一中、蓟州一中等)六校2020-2021学年高二上学期期中联考数学试题(已下线)专练30 期中综合检测卷(B卷)-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)天津市汇文中学2022-2023学年高二上学期第二次阶段性测试数学试题
名校
6 . 设函数
,其中
是非空数集.
记
.
(1)若
,求
;
(2)若
,且
是定义在
上的增函数,写出满足条件的集合P,M,并说明理由;
(3)判断命题“若
,则
”的真假,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99289fce2266ea828b2f7b6223ba3f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffbc423070f5d7ce2c72229066ee1cf.png)
记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0235ba2fa615d46fbd387dc2ee68e227.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b089d7a8c405ef53df555e96af2de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b7cc58950ca8dd127b0531dc7c7be4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5eb03e97d9498bff9c3dfac271dad01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)判断命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6eaccad72758bde85c35bc6c66e715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122140098fd20de9a0273defac528f48.png)
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7 . 已知集合
,且
中的元素个数
大于等于5.若集合
中存在四个不同的元素
,使得
,则称集合
是“关联的”,并称集合
是集合
的“关联子集”;若集合
不存在“关联子集”,则称集合
是“独立的”.
分别判断集合
和集合
是“关联的”还是“独立的”?若是“关联的”,写出其所有 的关联子集;
已知集合
是“关联的”,且任取集合
,总存在
的关联子集
,使得
.若
,求证:
是等差数列;
集合
是“独立的”,求证:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cdcb0e77b3ae3e701c6b51e15e2346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eeda5cef4846ef829069fe27f64e34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bf4032eb5a9ba68131b15182aa3491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9859aa908844a32c0e1e069a046727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918f1c94368c3a41177ff42cfedc0eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e0ad51c5541ec3dcca4a9845f8b7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498f92bf2e605cdbc91973e29b047566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4d89801d24aa43f47d6a366aad0571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1ccce8225324817b0577551956464f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874781ab5711bff6ee8c9cbad5b3b3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62295c36d2e2174908c2bec0eb5b30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8021f4f4c253a00360bf8f9425610e1.png)
您最近一年使用:0次
2020-02-09更新
|
1560次组卷
|
10卷引用:2020届北京市海淀区高三上学期期中数学试题
2020届北京市海淀区高三上学期期中数学试题(已下线)专题02 拿高分题目强化卷(第三篇)-备战2021年新高考数学分层强化训练(北京专版)北京市海淀区2021届高三模拟试题(一)北京市清华大学附属中学朝阳学校2021-2022学年高二5月月考数学试题北京市第五十七中学2021-2022学年高二下学期期末考试数学试题北京市第八中学2023届高三上学期12月测试数学试题北京市朝阳区中国人民大学朝阳分校2021-2022学年高三上学期开学考数学试题北京市日坛中学2023-2024学年高二下学期第三次月考(6月)数学试卷(已下线)考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮上海市上海中学2022届高三下学期高考模拟3数学试题
解题方法
8 . 抛物线
,
为直线
上的动点,过点
作抛物线
的两条切线,切点分别为
,
.
(1)证明:直线
过定点;
(2)若以
为圆心的圆与直线
相切,且切点为线段
的中点,求该圆的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423f5e7781b94f96ff4aac23cba2964d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(2)若以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28765621f3cbcd300a7c8094669a36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
9 . 如图,在四棱锥P﹣ABCD中,底面ABCD是正方形,PA⊥AB,PA⊥AD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/4cb9e1ae-0db2-448c-b27f-c3c442469df2.png?resizew=204)
(Ⅰ)求证:PA⊥平面ABCD;
(Ⅱ)已知PA=AD,点E在PD上,且PE:ED=2:1.
(ⅰ)若点F在棱PA上,且PF:FA=2:1,求证:EF∥平面ABCD;
(ⅱ)求二面角D﹣AC﹣E的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/4cb9e1ae-0db2-448c-b27f-c3c442469df2.png?resizew=204)
(Ⅰ)求证:PA⊥平面ABCD;
(Ⅱ)已知PA=AD,点E在PD上,且PE:ED=2:1.
(ⅰ)若点F在棱PA上,且PF:FA=2:1,求证:EF∥平面ABCD;
(ⅱ)求二面角D﹣AC﹣E的余弦值.
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10 . 平行四边形
所在的平面与直角梯形
所在的平面垂直,
,
,且
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/2/13/2398365531430912/2399327227461632/STEM/3e246c0f-794d-43c9-9c40-1bde26c85f5e.png)
(1)求证:
平面
;
(2)求证:
;
(3)若直线
上存在点
,使得
,
所成角的余弦值为
,求
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70a7cdc478a7ba3915bc1d7cd478400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2cd928cc17dec710a5d38928eb9493d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eed15d0ed75bf936f224f931da5d950.png)
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(1)求证:
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(2)求证:
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(3)若直线
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2020-02-15更新
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7卷引用:2019届北京市中国人民大学附属中学高三考前热身练习数学(理)试题
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