1 . 设
为正整数,
,
,令![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649309617a29d1b9d4b2373d3c1c2946.png)
.求证:存在
使得
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e65369cec2aac72a87c314f4c7ba143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be022d2478bb5f67d3e98f1319ea821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649309617a29d1b9d4b2373d3c1c2946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264d2ca5912fe1d6c354d7b0fd5efe4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f7741f4975d9df3daa0c1cdd23c9df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264d2ca5912fe1d6c354d7b0fd5efe4f.png)
您最近一年使用:0次
2 . 已知
、
、
都是正数,且
.
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff87256fdc337d698e6a9b9ebb48ea51.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d19dd46c292deb2b5113f9012b760ee.png)
您最近一年使用:0次
3 . 设
,
,
,
,直线
与双曲线
相交于
,
两点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289bcfd18f773ebabcfe06683b4ebc79.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec6a840369a7f6d3af9ec20dc066aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd653739edd1793d5e2f5bc2a1da6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e5f44f92c1622e4cd89b5f40b48437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0e05a41bd2560573dd2533f76a92b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed16a0a363ba8da5a730897dfd0658d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587d5d656482d60ae672024af4e37e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289bcfd18f773ebabcfe06683b4ebc79.png)
您最近一年使用:0次
4 . 设
是严格单调递增的函数,其反函数为
.设
,
分别是方程
和
的解,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b04a597429e99f3406acf168857b10.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f4eff3125c5e63a994ba1ad5be58e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f749e2471684db63546a9ce817a6415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9565876bc50bceb63e5793c8c67a9032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8506490bdfeef3771ca828e6ceac5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e124011e4d140a8ea89685b41b76f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b04a597429e99f3406acf168857b10.png)
您最近一年使用:0次
5 . 若长方体的长、宽、高都是自然数,且所有棱长之和等于它的体积,则称此长方体为“完美长方体”,“完美长方体”的体积的最大值为______ .
您最近一年使用:0次
6 . 设
,
且
,
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30800bcb030cf5ee97d0e21fbbe8c368.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb559ff1fd340bf86f4f857eea672ae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9467b82088c5ebcab031c03ac63fc798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b250172ed268999cdb7d38980855e6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264d2ca5912fe1d6c354d7b0fd5efe4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a2f8008f8af0bbec60ddaada7ce3f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30800bcb030cf5ee97d0e21fbbe8c368.png)
您最近一年使用:0次
7 . 设
为正整数,若
对所有正整数
成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22d7c214d9685da7be80319ed80d8df.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533674a39b4b03b2b25432840172aa22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22d7c214d9685da7be80319ed80d8df.png)
您最近一年使用:0次
8 . 设
、
是集合
的两个子集,
,且
时
.记
为
的元素之和,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6babc90c8f06732ddba8d859b0d5ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b4a0e6a36a55f3c64af3f773f05f8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eeaf2a98a9a852b45cec8eb35b0b110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6763f17351b124098a08ccca74bf85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f808411c86d3205fcd6050abc998ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f808411c86d3205fcd6050abc998ea8.png)
您最近一年使用:0次
9 . 已知
,
.设
,则
的整数部分为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7360cd8a3b80d6b572255042528f0740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3625fa11729e51745eee9ed2cfa29be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ee923e5c38b4cef1df8fd9f0f30e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
您最近一年使用:0次
名校
10 . 如图,在四棱锥
中,
平面ABCD,四边形ABCD是菱形,
,
,E是PB上任意一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/581c5ac5-aba7-4df4-80b6-a2337cdc78dd.png?resizew=230)
(1)求证:
;
(2)已知二面角
的余弦值为
,若E为PB的中点,求EC与平面PAB所成角的正弦值.
![](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/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1719410d21e3de1242366ce2965e838c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/581c5ac5-aba7-4df4-80b6-a2337cdc78dd.png?resizew=230)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b757706eee506a078fc25e3f33a70cb.png)
(2)已知二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5651e38293e0c42a7278af69fa53ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
您最近一年使用:0次
2022-09-29更新
|
1063次组卷
|
12卷引用:广西陆川县中学2016-2017学年高二下学期知识竞赛数学(理)试题
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