解题方法
1 . (1)已知
,设
,
,比较
与
的大小;
(2)证明:已知
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec532f119aff0491334d43cf6b1adf70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1166d36cb26ddb11b666ad0faf6a8b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)证明:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a0aa068c979c53361d049ce49987a8.png)
您最近一年使用:0次
2 . 已知函数
.
(1)求证:
是奇函数;
(2)用单调性的定义证明:
在R上是增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362bfce584209628bc4ad3f23e3d7b11.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用单调性的定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2023-08-28更新
|
438次组卷
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3卷引用:6.2 指数函数(2)-【帮课堂】(苏教版2019必修第一册)
(已下线)6.2 指数函数(2)-【帮课堂】(苏教版2019必修第一册)人教A版(2019) 必修第一册 数学奇书 第四章 指数函数与对数函数 4.2 指数函数 第2课时 指数函数的图象和性质的应用新疆喀什地区泽普县第二中学2024届高三上学期第一次月考数学试题
解题方法
3 . (1)证明:若
,求证:
;
(2)已知
,
均为锐角,且满足
,
,求
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d677e6f94d57c506bd007617c50a19e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99db5e19a19614908bee34c4ae100286.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2c1ac87d07d6c7a1a62eb333d112d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8628325b9e41358aec8f97a50da7f27a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfea1e888676a13ad69c72fba0405ea.png)
您最近一年使用:0次
解题方法
4 . 如图,在三棱柱
中,若G,H分别是线段
,
的中点.
![](https://img.xkw.com/dksih/QBM/2023/7/7/3275930420338688/3277428222746624/STEM/014c9cac2e2c428193f7c5750edce478.png?resizew=205)
(1)求证:
//面
.
(2)在线段
上是否存在一点
,使得平面
//平面
,若存在,指出
的具体位置并证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0147945bdf3db4bf5e40be746ef2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://img.xkw.com/dksih/QBM/2023/7/7/3275930420338688/3277428222746624/STEM/014c9cac2e2c428193f7c5750edce478.png?resizew=205)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f1d7219cd40346442b33dba84deb5c.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2c1789c5361169483df2924acd7321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解题方法
5 . 如图,在四棱锥
中,底面ABCD为正方形,
平面ABCD,
,E为PB中点,M为AD中点,F为线段BC上动点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
平面AEF;
(2)证明:平面
平面PBC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a4950a6e4202efd609507964af238b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
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2023-07-07更新
|
403次组卷
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2卷引用:【人教A版(2019)】专题14立体几何与空间向量(第三部分)-高一下学期名校期末好题汇编
名校
6 . 设
,函数
.
(1)若
,求证:函数
是奇函数;
(2)若
,请判断函数
的单调性,并用定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e59926e0de6c10c6b791cb14cf61268.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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2023-09-28更新
|
880次组卷
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7卷引用:模块二 专题4《幂函数、指数与指数函数》单元检测篇 B提升卷(人教A)
(已下线)模块二 专题4《幂函数、指数与指数函数》单元检测篇 B提升卷(人教A)(已下线)期末真题必刷常考60题(22个考点专练)-【满分全攻略】(沪教版2020必修第一册)(已下线)第6章 幂函数、指数函数和对数函数章末题型归纳总结 (1)-【帮课堂】(苏教版2019必修第一册)(已下线)第5章 函数的概念、性质及应用单元复习+热考题型-同步精品课堂(沪教版2020必修第一册)上海市松江区华东政法大学附属松江高级中学2022-2023学年高一上学期期末数学试题(已下线)第06讲:指数运算和指数函数-《考点·题型·难点》期末高效复习 广东省佛山市三水区三水中学2023-2024学年高一上学期第二次统测数学试题
7 . 在底面ABCD为梯形的多面体中.
,BC⊥CD,
,∠CBD=45°,BC=AE=DE,且四边形BDEN为矩形.
(1)求证:BD⊥AE;
(2)线段EN上是否存在点Q,使得直线BE与平面QAD所成的角为60°?若不存在,请说明理由.若存在,确定点Q的位置并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c120a0dafabda27b56c7fa9877f2dbff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/24/8aabdfc9-74d0-4e00-9cbe-625dc6252246.png?resizew=165)
(1)求证:BD⊥AE;
(2)线段EN上是否存在点Q,使得直线BE与平面QAD所成的角为60°?若不存在,请说明理由.若存在,确定点Q的位置并加以证明.
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2023-06-22更新
|
1200次组卷
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5卷引用:第一章 空间向量与立体几何 讲核心03
第一章 空间向量与立体几何 讲核心03(已下线)第06讲 1.4.2用空间向量研究距离、夹角问题(2)(已下线)专题1-3 空间向量综合:斜棱柱、不规则几何体建系计算(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)河南省郑州市等3地2022-2023学年高三下学期6月冲刺卷(五)全国卷理科数学试题(已下线)第11讲 用空间向量研究距离、夹角问题11种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)
8 . 在
中,
,
,若D是AB的中点
,则
;若D是AB的一个三等分点
,则
;若D是AB的一个四等分点
,则
.
(1)如图①,若
,用
,
表示
,你能得出什么结论?并加以证明.
(2)如图②,若
,
,AM与BN交于O,过O点的直线l与CA,CB分别交于点P,Q.
①利用(1)的结论,用
,
表示
;
②设
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e923e4cdcbea6a029f5ba188a59229d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb95d089784702a0b6d459f18a4e1e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0997b1534ce4817fdc86c4b6c75db29d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2634228ecbd45ba775dca73eaf1cc63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bdd1229d9e121bc3bdb2339e76f3e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda838437dab97586710b6220ee74dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075e483c30716072375e7db13e84ad07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1030db2fcd7b8f3f0eae7eb063fb7cba.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/28/1e3da6d3-e471-4d60-901e-c428805cbbdb.png?resizew=379)
(1)如图①,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b83647557c93d7f7e9ceee524601a1.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/bc1070a28cb9cb8553c29747d1993b16.png)
(2)如图②,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5388f2e85a72e2414928ff69e0fd13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1cd8790d5f3cc008befd52e46f42001.png)
①利用(1)的结论,用
![](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/b0260317a23090e4a019f76ae08614f5.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c85b08638081ff0c9651e4ca5792669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e8454ef2c08a243be83057c34de2f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b7e12253044b5abff2a56dcd730ced8.png)
您最近一年使用:0次
9 . 在平面四边形
中(如图1),
,
,
,E是AB中点,现将△ADE沿DE翻折得到四棱锥
(如图2),
平面
;
(2)图2中,若F是
中点,试探究在平面
内是否存在无数多个点
,都有直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfaca9396f85c0137b534903321fcbe.png)
平面
,若存在,请证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb52f9b226b1db3f6f9f055948bd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995f8d5c1e57b541c10f7c29645add31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec43f7352b3a8c194b4c37485fb4ffd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee4a6b8ef3e79b4482388c3391d8b18.png)
(2)图2中,若F是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9b32570d553161be04d13954e92a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfaca9396f85c0137b534903321fcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在三棱柱
中,若G,H分别是线段AC,DF的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
;
(2)在线段CD上是否存在一点
,使得平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2c1789c5361169483df2924acd7321.png)
平面BCF,若存在,指出
的具体位置并证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0147945bdf3db4bf5e40be746ef2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)在线段CD上是否存在一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2c1789c5361169483df2924acd7321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2023-04-13更新
|
3157次组卷
|
9卷引用:立体几何专题:立体几何探索性问题的8种考法
(已下线)立体几何专题:立体几何探索性问题的8种考法(已下线)13.2.4 平面与平面的位置关系 (1)(已下线)8.5.3 平面与平面平行【第三练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)11.3.3平面与平面平行-同步精品课堂(人教B版2019必修第四册)(已下线)专题突破:空间几何体的动点探究问题-同步题型分类归纳讲与练(人教A版2019必修第二册)浙江省宁波市三锋教研联盟2022-2023学年高一下学期期中联考数学试题河北定州中学2022-2023学年高一下学期5月月考数学试题新疆阿克苏市实验中学2022-2023学年高一下学期第三次月考数学试题江西省宜春市第十中学2024届高二上学期开学检测数学试题