解题方法
1 . 已知函数
(
且
).
(1)求证:函数
的图象过定点,并写出该定点;
(2)设函数
,且
,试证明:函数
在区间
上有唯一零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d76ee3b131ecd6aa1aacf7fb7b3eb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ca4e405c12786846c4450743cd23bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b4b1cc7b0ac8c601e981710d5edb73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(1)求证:
是奇函数;
(2)用单调性的定义证明:
在
上是增函数.
(3)若
对任意
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbd9e52b79fb84c320dc522e13d4f0b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)用单调性的定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a414b95cb362b1e9a251977c36b452b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca97e3aa8061c4d8e621c5598c69b13b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253c838949b6987206019864d07eafde.png)
您最近一年使用:0次
2021-12-24更新
|
1157次组卷
|
4卷引用:云南省大理州祥云祥华中学2021-2022学年高一上学期期末考试数学模拟(四)试题
云南省大理州祥云祥华中学2021-2022学年高一上学期期末考试数学模拟(四)试题(已下线)期末考试模拟卷03-【一堂好课】2021-2022学年高一数学上学期同步精品课堂(人教A版2019必修第一册)云南省临沧市临翔区第一中学2022-2023学年高一下学期3月月考数学试题新疆师范大学附属中学2021-2022学年高一12月月考数学试题
3 . 已知函数
,函数
.
(1)判断函数
在其定义域上的单调性(不需要证明);
(2)对任意的实数
,都有
.
①求证:
;
②若存在a的两个取值
,
,使得
(c为常数),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b21c310a00732a9eda5489e225bd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df06bdef1d4a203b4174851bc270cfe5.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40295c491170bcf632abafc92eecc33f.png)
(2)对任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fab2aa2162c65b3f30d2b9f4be1226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d682fefb826126ec14c09099eb329e3.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee246607e97330c07187ea9d748d6332.png)
②若存在a的两个取值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54eab256e011759f28bf281b74f52d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f074582e866194b78c3299d4796f418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d52943e3995bdda062b3f7930265682.png)
您最近一年使用:0次
2022-02-08更新
|
179次组卷
|
2卷引用:云南省曲靖市师宗县平高中学(第四中学)2023-2024学年高一上学期期末数学模拟试卷
2021高一·江苏·专题练习
名校
解题方法
4 . 如图,在梯形ABCD中,AD
BC,AB⊥BC,AB=BC=1,PA⊥平面ABCD,CD⊥PC.
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758325185167360/2758421906202624/STEM/336d6b2f10fe444d9db2ca99252edaab.png?resizew=176)
(1)证明:CD⊥平面PAC;
(2)若E为PA的中点,求证:BE
平面PCD;
(3)若直线PC与平面ABCD成角为45°,求三棱锥A﹣PCD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758325185167360/2758421906202624/STEM/336d6b2f10fe444d9db2ca99252edaab.png?resizew=176)
(1)证明:CD⊥平面PAC;
(2)若E为PA的中点,求证:BE
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(3)若直线PC与平面ABCD成角为45°,求三棱锥A﹣PCD的体积.
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2021-07-06更新
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848次组卷
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4卷引用:云南省昭通市绥江县第一中学2020-2021学年高一下学期期末考试数学试题
云南省昭通市绥江县第一中学2020-2021学年高一下学期期末考试数学试题(已下线)13.3 空间图形的表面积和体积-2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)吉林省长春市第八中学2020-2021学年高一下学期期中数学试题(已下线)13.3空间图形的表面积和体积-2021-2022学年高一数学10分钟课前预习练(苏教版2019必修第二册)
名校
解题方法
5 . 如图所示,在四棱锥
中,
平面
,底面
是菱形,
,
,
.
为
与
的交点,
为棱
上一点,
(1)证明:平面
⊥平面
;
(2)若三棱锥
的体积为
,求证:
∥平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a459372aa54090fcce9430a3cfa182f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b999123e51b75bfeea6bee373e1677e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/24/cde40a84-07f6-4a39-941e-abec3a77b9a3.png?resizew=170)
您最近一年使用:0次
2017-10-20更新
|
759次组卷
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3卷引用:云南省红河州泸西一中2017─2018学年高二上学期期末考试文科数学试题
名校
6 . 如图,在四棱锥
中,
平面
,底面
为正方形,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/bfadc127-02c1-494f-b74d-524aa467f8b3.png?resizew=151)
(1)求证:
平面
;
(2)若
,求平面
与平面
夹角的余弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/bfadc127-02c1-494f-b74d-524aa467f8b3.png?resizew=151)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca260f5f547cb9211d36ddb555fd34f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2024-02-20更新
|
513次组卷
|
2卷引用:云南省昭通市一中教研联盟2023-2024学年高二上学期期末质量检测数学试题(A卷)
解题方法
7 . 如图,在四棱锥
中,底面
为矩形,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
平面
,
,
,
为
的中点.
;
(2)求证:平面
⊥平面
;
(3)在棱
上是否存在一点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
平面
?若存在,求
的值;若不存在,请说明理由.
![](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/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a470095e295c734a2f368cc6baf1b6.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212a67f115d1cbe69f100b489babe5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fddc06fe64a538283be16c816f059e9.png)
您最近一年使用:0次
名校
8 . 如图,在三棱锥
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/c49f0574-ff3e-40e5-83c1-718d926d7753.png?resizew=161)
(1)求证:
;
(2)求二面角
平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48f1f0da5854716a873c9bd072693e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e1a727ba332984ad857b3d25344d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/c49f0574-ff3e-40e5-83c1-718d926d7753.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77e3c1c236141d6118429fade0a9b9d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c909cd1b6f3fa1ec39eb245e8f5c11c.png)
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2024-01-29更新
|
186次组卷
|
3卷引用:云南省保山市2024届高三上学期1月期末数学试题
9 . 已知离心率为
的双曲线
经过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/25/750c3d65-f4cc-4936-b6c9-767395750267.png?resizew=143)
(1)求
的方程;
(2)如图,点
为双曲线上的任意一点,
为原点,过点
作双曲线两渐近线的平行线,分别与两渐近线交于
、
两点,求证:平行四边形
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c8091d78595c42d437ff5766431a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17861339a3796ae59308b87a6e41ed29.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/25/750c3d65-f4cc-4936-b6c9-767395750267.png?resizew=143)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abdbb88112c8ed764e1cb9351a4a9e9.png)
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2024-01-25更新
|
322次组卷
|
2卷引用:云南省昆明市官渡区2023-2024学年高二上学期1月期末学业水平考试数学试题
解题方法
10 . 在四棱锥
中,底面
是直角梯形,
,E为
的中点,
是等边三角形,平面
平面
,且
.
(1)求证:直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/70c66b94f6bc54b0c75063052410cb4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78aafccd397e9c88a567abf4993d40f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/68b81a3d-3a6d-4cbc-b0bd-2b81a7606d76.png?resizew=190)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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