名校
1 . 已知数列
前
项和为
,满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e375b8b3791ee98dab11cd97b6379f.png)
(1)证明:数列
是等差数列,并求
;
(2)设
,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/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e375b8b3791ee98dab11cd97b6379f.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f543f3aafa4740bd65aefc8d8de4b6f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ac75838b14085b34c59a0eb385ac4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b340e6cfa6ab9b97da7409f2db62c00.png)
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2016-12-03更新
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865次组卷
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5卷引用:【全国百强校】黑龙江省哈尔滨市第六中学2018-2019学年高一下学期期中考试数学试题
2 . 已知函数
.
(1)求证:
是偶函数;
(2)判断函数
在
和
上的单调性并用定义法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37ddf6c3e54ad634cf03a1be036242e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a8fc8767a57e739249aab76a79c896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65adaad9d9e240e0054e73a882a973e.png)
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3 . 数列
的前
项和为
,且满足
,
.
(1)证明:
是等比数列,并求数列
的通项公式
;
(2)设
,求证:
![](https://img.xkw.com/dksih/QBM/2015/12/1/1572332926500864/1572332932685824/STEM/ea0375ccaa1d4de0a022bbc0d0309885.png)
![](https://img.xkw.com/dksih/QBM/2015/12/1/1572332926500864/1572332932685824/STEM/a504e9a3939a4eceb7ec1aa95adb7c8f.png)
![](https://img.xkw.com/dksih/QBM/2015/12/1/1572332926500864/1572332932685824/STEM/b824ba9702d244c2803019f9dbda82c7.png)
![](https://img.xkw.com/dksih/QBM/2015/12/1/1572332926500864/1572332932685824/STEM/73b53480674b452799b70420282e978f.png)
![](https://img.xkw.com/dksih/QBM/2015/12/1/1572332926500864/1572332932685824/STEM/a323c858ed524313a381e60b4c527394.png)
(1)证明:
![](https://img.xkw.com/dksih/QBM/2015/12/1/1572332926500864/1572332932685824/STEM/e4b087503a214065b0ce0a9e5590204b.png)
![](https://img.xkw.com/dksih/QBM/2015/12/1/1572332926500864/1572332932685824/STEM/ea0375ccaa1d4de0a022bbc0d0309885.png)
![](https://img.xkw.com/dksih/QBM/2015/12/1/1572332926500864/1572332932685824/STEM/7a8239ff87864889891e2b4afefad383.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/517c3094abd005bef02304ad54152e3c.png)
![](https://img.xkw.com/dksih/QBM/2015/12/1/1572332926500864/1572332932685824/STEM/7eca38a5360f48848a0efee467cdc546.png)
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10-11高三上·江西·期中
4 . 一个多面体的直观图和三视图如图所示,其中M、N分别是AB、AC的中点,G是DF上的一动点.
(1)求证:![](https://img.xkw.com/dksih/QBM/2010/11/18/1569907439484928/1569907444736000/STEM/7573863f138947e7b20aa16d1c641dbf.png)
(2)当FG=GD时,在棱AD上确定一点P,使得GP//平面FMC,并给出证明.
(1)求证:
![](https://img.xkw.com/dksih/QBM/2010/11/18/1569907439484928/1569907444736000/STEM/7573863f138947e7b20aa16d1c641dbf.png)
(2)当FG=GD时,在棱AD上确定一点P,使得GP//平面FMC,并给出证明.
![](https://img.xkw.com/dksih/QBM/2010/11/18/1569907439484928/1569907444736000/STEM/3cd5d5cdf7a24d5782167ad77533dc0a.png)
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2016-12-01更新
|
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5卷引用:黑龙江省齐齐哈尔市克东县克东一中、克山一中等五校联考2019-2020学年高二上学期期中数学(文)试题
黑龙江省齐齐哈尔市克东县克东一中、克山一中等五校联考2019-2020学年高二上学期期中数学(文)试题黑龙江省齐齐哈尔市克东县克东一中、克山一中等五校联考2019-2020学年高二上学期期中数学(理)试题(已下线)2011届江西省师大附中高三上学期期中考试数学文卷(已下线)2012届江西省师大附中高三下学期开学考试文科数学(已下线)2011-2012学年江西省白鹭洲中学高二下学期第二次月考文科数学试卷
5 . 数列
.
(1)求证:
是等比数列,并求数列
的通项公式;
(2)设
,求和
,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4d0dcca61d261df330d87e26600353.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a080c94bf1ffea8d5af10f9688978fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c40fe25c4e3fbeadf90539072513b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac96b09d3eccdb9a4c17ecbdec9ecebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83fff70ec803e87beff4fae74df040c8.png)
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|
1032次组卷
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3卷引用:黑龙江省齐齐哈尔地区八校2018届高三期中联考文数试题
6 . 已知数列
中
,函数
.
(1)若正项数列
满足
,试求出
,
,
,由此归纳出通项
,并加以证明;
(2)若正项数列
满足
(n∈N*),数列
的前项和为Tn,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f540ed88caf03ebe453553969e43944.png)
(1)若正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6aa8089b5d9b722aff679af3c4d289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)若正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf9e123fb1b7cf9edb5d53f82a42def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cf906aaaf67f8ff2d23af499c37f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e06b0fda8954c395f1a3ccfbc88698.png)
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|
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|
3卷引用:黑龙江省齐市地区普高联谊校2018-2019学年高二下学期期中考试数学(文)试题
7 . 求证:
.
证明:因为
和
都是正数,
所以为了证明
,
只需证明
,
展开得
,即
,显然成立,
所以不等式
.上述证明过程应用了( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982787c165f45dc0af0c166da31c7b4.png)
证明:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650ef902d427468119ea4f00fc2717ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
所以为了证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982787c165f45dc0af0c166da31c7b4.png)
只需证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe58bdfab519bbc0ba1c1290741da65e.png)
展开得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d7b886ac3f3507463c7313f681b7a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa71cf12282f0c34a439b7b66c121006.png)
所以不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982787c165f45dc0af0c166da31c7b4.png)
A.综合法 |
B.分析法 |
C.综合法、分析法混合 |
D.间接证法 |
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2011·北京朝阳·一模
名校
8 . 如图,在四棱锥
中,底面
为直角梯形,且
,
,侧面
底面
. 若
.
(1)求证:
平面
;
(2)侧棱
上是否存在点
,使得
平面
?若存在,指出点
的位置并证明,若不存在,请说明理由;
(3)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efa6508d6820f972de28c360aea7504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460516ee9c61f1bdd231759be0033e80.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e867e5c7ef4da37d8985ce82022060e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/2e2a8b06-0a67-4422-b704-0ce085dc1db7.png?resizew=200)
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|
847次组卷
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8卷引用:2013-2014学年黑龙江省哈尔滨四中高二下学期期末考试理科数学试卷
(已下线)2013-2014学年黑龙江省哈尔滨四中高二下学期期末考试理科数学试卷(已下线)2011届北京市朝阳区高三第一次综合练习数学理卷(已下线)2012-2013学年广东省广州六中高二上学期期末考试理科数学试卷(已下线)2013届中国人民大学附属中学高考冲刺二理科数学试卷北京市人大附中2018届高三高考数学(理科)零模试题湖南省衡阳市第一中学2020-2021学年高三上学期第五次月考数学试题(已下线)江苏省苏州市吴江区2019-2020学年高二下学期期中联考数学试题天津市蓟州区第一中学2021届高三下学期模拟检测二数学试题
10-11高二下·内蒙古赤峰·阶段练习
名校
9 . 已知三角形ABC的三边长为a、b、c,且其中任意两边长均不相等.若
成等差数列.(1)比较
与
的大小,并证明你的结论;(2)求证B不可能是钝角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f81b8a02e231884bc36fdc4870830cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fe34b1cc3a3cfcfad66fb03b9e22c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c147d6cbd7cbaeb8ec08a0ba69cd59dd.png)
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2016-12-01更新
|
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8卷引用:黑龙江省海林市朝鲜族中学人教版高中数学选修1-2同步练习:模块终结测评(二)
黑龙江省海林市朝鲜族中学人教版高中数学选修1-2同步练习:模块终结测评(二)(已下线)2010-2011年内蒙古赤峰市田家炳中学高二下学期4月月考考试数学文卷(已下线)2011-2012学年河南省周口市高二下学期四校第一次联考文科数学试卷河南南阳一中2015-2016学年高二下第二次月考文科数学试题内蒙古巴彦淖尔市杭锦后旗奋斗中学2017-2018学年高二下学期第一次月考数学(文)试题2018-2019学年人教版高中数学选修1-2 模块综合评价(一)河南省郑州市巩义中学2019-2020学年高二下学期期中考试数学(文)试题辽宁省铁岭市六校协作体2022-2023学年高三质量检测数学试题
10-11高二下·黑龙江牡丹江·期中
解题方法
10 . 证明下列不等式:(1)求证
;
(2)如果
,
,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c19d94ff48082c1cd213c82c99abf0.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd70f831f301205134280f6432c8f84d.png)
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