解题方法
1 . 如图所示,已知点
是平行四边形
所在平面外一点,
分别为
的中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/6a24d469-4f8b-4698-86e5-c976d6d83d41.png?resizew=160)
(1)求证:
;
(2)直线
上是否存在点
,使得平面
平面
,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845c5b950acdcce49fc3e75c6b1d1556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61de6d673ecbbbd9458991558e7dc90.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/2022/12/26/6a24d469-4f8b-4698-86e5-c976d6d83d41.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbf6462666c8015e7de28e344af30b2.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c77a2c384acd6e7fb0b8ff29cdb82ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
解题方法
2 . 已知数列
满足
,
,
,
.
(1)证明:数列
为等差数列,并求数列
的通项公式;
(2)若
,记数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f4e1236d7dc0366d9523d0cbb426be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b039543372ce127c7b85782a118f0f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452441c97433c6dee7d6a8dd4aaa7133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21051c2cb82f0cf87d005dc258ec9847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55e9df52276e2d89c646a0714bbee8f.png)
您最近一年使用:0次
2021-02-02更新
|
1515次组卷
|
7卷引用:浙江省嘉兴市2020-2021学年高三上学期期末数学试题
浙江省嘉兴市2020-2021学年高三上学期期末数学试题(已下线)【新东方】绍兴高中数学00034江苏省苏州中学2020-2021学年高二下学期期初质量评估数学试题(已下线)专题24 数列(解答题)-2021年高考数学(理)二轮复习热点题型精选精练(已下线)专题22 数列(解答题)-2021年高考数学(文)二轮复习热点题型精选精练(已下线)专题23 数列(解答题)-2021年高考数学二轮复习热点题型精选精练(新高考地区专用)(已下线)【新东方】绍兴高中数学00038
名校
3 . 已知数列{an}满足a1=2,
(n∈N*).
(1)求证:数列
是等比数列;
(2)比较
与
的大小,并用数学归纳法证明;
(3)设
,数列{bn}的前n项和为Tn,若Tn<m对任意n∈N*恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04e45f0f7233e1766ba93f36fafb0f3.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0210bf1fb13af42d057c1cf7ccdf7e92.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245460a7f2be54fa45095316e71014a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0763ff5f577b56744a5969dd1ab8f86.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe115795f19a35c719a10c729edd9885.png)
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2020-10-27更新
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11卷引用:【校级联考】浙江省嘉兴市第一中学、湖州中学2018-2019学年高一下学期期中考试数学试题
【校级联考】浙江省嘉兴市第一中学、湖州中学2018-2019学年高一下学期期中考试数学试题【校级联考】浙江省浙北G2期中联考2018学年高一第二学期数学试题浙江省浙北G2联考2018-2019学年高一第二学期期中考试数学试题(已下线)专题6.6 数学归纳法(讲)- 浙江版《2020年高考一轮复习讲练测》(已下线)第四章++数列2(能力提升)-2020-2021学年高二数学单元测试定心卷(人教A版2019选择性必修第二册)(已下线)第四章++数列1(能力提升)-2020-2021学年高二数学单元测试定心卷(人教A版2019选择性必修第二册)(已下线)专题7.6 数学归纳法(讲)-2021年新高考数学一轮复习讲练测(已下线)专题08 数列的通项、求和及综合应用 第一篇 热点、难点突破篇(练)-2021年高考数学二轮复习讲练测(浙江专用))(已下线)第04讲 数学归纳法-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第一册)(已下线)专题28 证明不等式的常见技巧-学会解题之高三数学万能解题模板【2022版】(已下线)第04讲 数学归纳法(核心考点讲与练)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)
4 . 如图所示,在四棱锥
中,四边形
是正方形,点
分别是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/684f0061-f471-44fa-b0ef-91fd3df2774a.png?resizew=140)
(1)求证:
;
(2)线段
上是否存在一点
,使得面
面
,若存在,请找出点
并证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1e038b4e76b3a368731d3331522b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a003de8409231a347edebc8284be186c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85de410d85be189dfa5aabb33410b896.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/684f0061-f471-44fa-b0ef-91fd3df2774a.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da4cd5cd0de37a81455262f96acaca01.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f32299ca54d8b38967931d69a218c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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2019-01-26更新
|
2605次组卷
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18卷引用:浙江省嘉兴八校联盟2020-2021学年高一下学期期中联考数学试题
浙江省嘉兴八校联盟2020-2021学年高一下学期期中联考数学试题【全国百强校】重庆市江津中学、合川中学等七校2018-2019学年高二上学期期末考试数学(理科)试题【校级联考】重庆市江津中学、合川中学等七校2018-2019学年高二上学期期末考试数学(文科)试题安徽省皖北名校2020-2021学年高二上学期第一次联考数学试题安徽省合肥市肥东县第二中学2020-2021学年高二上学期第一次月考数学(理)试题(已下线)2.2.4 平面与平面平行的性质-2020-2021学年高一数学课时同步练(人教A版必修2)福建省厦门一中2020-2021学年高一下学期期中考数学试题湖南省郴州市嘉禾县第一中学2020-2021学年高一下学期第二次月考数学试题湖北省鄂东南三校联考2021-2022学年高一下学期阶段考试(二)数学试题四川省峨眉第二中学校2022-2023学年高二上学期10月月考文科数学试题四川省眉山市2022-2023学年高二上学期期末教学质量检测数学(文)试题四川省眉山市2022-2023学年高二上学期期末教学质量检测理科数学试题安徽省芜湖市华星学校2021-2022学年高一下学期期中数学试题四川省眉山市2022-2023学年高二上学期期末数学(理)试题陕西省西安市鄠邑区2022-2023学年高一下学期期中数学试题陕西省渭南市韩城市新蕾中学2020-2021学年高一上学期第三次月考数学试题云南省红河州开远市第一中学校2022-2023学年高一下学期4月月考数学试题(已下线)核心考点07空间直线、平面的平行-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)
名校
解题方法
5 . 如图,在菱形
中,
⊥平面
,且四边形
是平行四边形.
![](https://img.xkw.com/dksih/QBM/2017/10/11/1793058665390080/1795120232783872/STEM/af55a97e45d5478abe96891c2a29a524.png?resizew=212)
(1)求证:
;
(2)当点
在
的什么位置时,使得
∥平面
,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ab4fdfc612c9fa2dd8ae24904192d8.png)
![](https://img.xkw.com/dksih/QBM/2017/10/11/1793058665390080/1795120232783872/STEM/af55a97e45d5478abe96891c2a29a524.png?resizew=212)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf21399dcf3682bf5d3f9cbd5eed86c.png)
(2)当点
![](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/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711da913d92fc989e581bcfdfe092a18.png)
您最近一年使用:0次
2017-10-14更新
|
686次组卷
|
3卷引用:浙江省嘉兴市第一中学2017-2018学年高二10月月考数学试题
6 . 在数列
中,
,![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/8cdce57f0dab4762aed7f51775c4de84.png)
(Ⅰ)求
,判断数列
的单调性并证明;
(Ⅱ)求证:
;
(Ⅲ)是否存在常数
,对任意
,有
?若存在,求出
的值;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/05d543e2a8384967a8d344903da637bc.png)
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/7cead9914c774d2fbb9e1cf41b952e71.png)
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/8cdce57f0dab4762aed7f51775c4de84.png)
(Ⅰ)求
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/76e22fe66fd44db78023bd35e05a1d61.png)
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/05d543e2a8384967a8d344903da637bc.png)
(Ⅱ)求证:
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/3224578f42c24265a67da249e3fafefc.png)
(Ⅲ)是否存在常数
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/ae69243d1e8a4445b4bd917cc480edce.png)
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/552a04b7c6bb428cbfa5168601a82f15.png)
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/c9d22aabd3d5467cb3bb4a0fa16c0014.png)
![](https://img.xkw.com/dksih/QBM/2015/6/26/1572149928591360/1572149934268416/STEM/ae69243d1e8a4445b4bd917cc480edce.png)
您最近一年使用:0次
2016-12-03更新
|
552次组卷
|
2卷引用:2015届浙江省嘉兴市高三下学期教学测试一理科数学试卷
7 . 已知数列
的首项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66d7c5dae4d357a278bfd224144ee1f.png)
的前
项和为
.
(1)求证:数列
是等比数列,并求数列
的通项公式;
(2)证明:对任意的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23aacab3c20b215a9616bc3434cc4e28.png)
(3)证明:
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572207888957440/1572207895076864/STEM/d0da94816c534be4a101db4c0e7e0bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66d7c5dae4d357a278bfd224144ee1f.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572207888957440/1572207895076864/STEM/d0da94816c534be4a101db4c0e7e0bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e06816992e1b854b5d4dae9a957b5e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23aacab3c20b215a9616bc3434cc4e28.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e37c8ff63c08973e2a5bb9fdc2a1cd7.png)
您最近一年使用:0次
2012高二下·浙江嘉兴·学业考试
名校
解题方法
8 . 已知函数
.
(1)求函数
的极值;
(2)对于曲线上的不同两点
,如果存在曲线上的点
,且
使得曲线在点
处的切线
,则称
为弦
的伴随直线,特别地,当
时,又称
为
的
—伴随直线.
①求证:曲线
的任意一条弦均有伴随直线,并且伴随直线是唯一的;
②是否存在曲线
,使得曲线
的任意一条弦均有
—伴随直线?若存在,给出一条这样的曲线,并证明你的结论;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aca3bb4e25eaef56fb7ba9c79da0944.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对于曲线上的不同两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a00dc6f0af494437c9f98223f3e861f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2752e086b85f9fbb95010bf771072af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69264c1535cf0ccdac2d186da669df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1635f56ef7fb304920f253f30fbba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0429adcf685c47f2d97d567387385461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
①求证:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
②是否存在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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2016-12-01更新
|
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|
4卷引用:2011-2012学年浙江省嘉兴一中高二下学期摸底考试理科数学试卷
(已下线)2011-2012学年浙江省嘉兴一中高二下学期摸底考试理科数学试卷2016-2017学年湖南省长沙市第一中学高二下学期第一次月考数学(理)试卷2020届辽宁省大连市高三上学期第二次模拟考试数学(理)试卷(已下线)江苏省苏锡常镇四市2023届高三下学期3月教学情况调研(一)数学试题变式题17-22
9 . 在如图所示的几何体中,四边形
为平行四边形,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62c231d968cfce1e46f5b9c14836592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,
.
平面
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62c231d968cfce1e46f5b9c14836592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c118858379800688c993a8b61270b356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99abeecaf21825d9f1d6f8366699f50a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ca58b14f9bbdbc3204f6f330525943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4613db540c9cb6a9d7e963bf89c2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9111c8e64fc183a777dbe0e82c9202cd.png)
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解题方法
10 . 海宁一中物理兴趣小组在课外研究三力平衡问题:即三个力的合力为零.已知
,
,
三力平衡,且夹角如图所示.
,
,
,求
的大小;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e96a806570b8c7ce222d8cfc5d1cd24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d0e377444641ce911ba508fda90e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0184b108024de2ded248e9bb382e3df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d03f73bec20b60bc7608972607f5a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85244b0de5bbb50dbd9a56e409f0886d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192b9dab0f68ca2cd2386825f89984a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e121e3e342c58341ef89ce272a2ec4.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f55b6bfaf7f396b3a9caeba37fb18ce.png)
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