1 . “
数”在量子代数研究中发挥了重要作用.设
是非零实数,对任意
,定义“
数”
利用“
数”可定义“
阶乘”
和“
组合数”,即对任意
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95f14cc089b8615edde195eb449b48b.png)
(1)计算:
;
(2)证明:对于任意
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d17cd22aac1f1f0f8acb1d0b67bb2c7.png)
(3)证明:对于任意
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d774d4ac2fb5da679ac23e0dea64da0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6724c68c4206bd95683998d800f7f676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d774d4ac2fb5da679ac23e0dea64da0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0dee336ed12a9b1b273d7fada509737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d774d4ac2fb5da679ac23e0dea64da0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d774d4ac2fb5da679ac23e0dea64da0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3361528cb2e9a12d35acc0381e12564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d774d4ac2fb5da679ac23e0dea64da0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dba6a7ab114b2a921dd1099e90c8bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95f14cc089b8615edde195eb449b48b.png)
(1)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d61962da2ebd6382d99cf5f1232c7de.png)
(2)证明:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110cb021ccb99d1a30025c66b026812b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d17cd22aac1f1f0f8acb1d0b67bb2c7.png)
(3)证明:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41228f0077b249a875e69698fefb2081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985b5678fd36804e1a28fac1c7a57982.png)
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2024-04-02更新
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1217次组卷
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2卷引用:山东省菏泽第一中学南京路校区2024届高三下学期开学考试数学试题
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2 . 已知函数
是
的导函数,
.
(1)求
的单调区间;
(2)若
有唯一零点.
①求实数
的取值范围;
②当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483aa062b70c839cd5f693f23c6b94b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55506fc48681be9458f6b9cf443166ea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8230f1d8b297d825b95846bc2eb1b971.png)
您最近一年使用:0次
2024-03-26更新
|
758次组卷
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2卷引用:山东省实验中学2024届高三下学期2月调研考试数学试卷
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解题方法
3 . 已知椭圆
的右顶点为A,左焦点为F,椭圆W上的点到F的最大距离是短半轴长的
倍,且椭圆W过点
.记坐标原点为O,圆E过O、A两点且与直线
相交于两个不同的点P,Q(P,Q在第一象限,且P在Q的上方),
,直线
与椭圆W相交于另一个点B.
(1)求椭圆W的方程;
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014b99f5c93a4ce8cd6251c12c1d1b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cc033406da2cdd342308972c6701f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3306c91876abdcf71ac138b4077a9aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
(1)求椭圆W的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcde52c2e252ca18148cbb9e48d213e4.png)
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2024-03-24更新
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707次组卷
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5卷引用:山东省菏泽第一中学八一路校区2024届高三下学期开学考试数学试题
名校
解题方法
4 . 已知椭圆
的两个焦点与短轴的一个端点连线构成等边三角形,且椭圆C的短轴长为
.
(1)求椭圆C的标准方程;
(2)是否存在过点
的直线l与椭圆C相交于不同的两点M,N,且满足
(O为坐标原点)若存在,求出直线l的方程:若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆C的标准方程;
(2)是否存在过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef10b20903796c7d952b978a02b40da8.png)
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5 . 在四棱锥
中,
是矩形,
为棱
上一点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5130ddc74af23f8ccfaa5974a223e84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
A.点![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.四棱锥![]() ![]() |
D.直线![]() ![]() ![]() |
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解题方法
6 . 双曲线
的左、右顶点分别为
,曲线
上的一点
关于
轴的对称点为
,若直线
的斜率为
,直线
的斜率为
,则当
取到最小值时,双曲线离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce0d4ca414e9e870813ae89721e0fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a7bb0db495511d6eb060745ee0d0aa.png)
A.3 | B.4 | C.![]() | D.2 |
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解题方法
7 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d999cab1da214d9b16c06be3e5a80507.png)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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解题方法
8 . 已知双曲线
的左、右焦点分别为
,焦距为6,其中一条渐近线方程为
,点
,若点
在双曲线
上,且满足
,则
外接圆的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25869dd14f3e7412beda491bb83f982d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89cddda9100666fa42033cc4f2688fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f2f1168ab19c9571ac225949a6038e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
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9 . 已知函数
与
的零点分别为m和n,若存在m,n使得
,则实数a的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc9e9802ec71e863cde96cf2bcb5750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8dc1e48066c7d2722d3e0e94504155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4184c3549eb113697c3ca15e1cabf85.png)
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10 . 已知函数
的导数为
.
(1)若
恒成立,求实数k的取值范围;
(2)函数
的图象上是否存在三个不同的点
,
,
(其中
且
成等比数列),使直线
的斜率等于
?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4628a4bec344f42992fdf0d4fcd0e56e.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c16dac1e9bf5804c8907cbc59014d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2004890867828e45d2c2d6bb58ecab.png)
您最近一年使用:0次
2024-03-09更新
|
572次组卷
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2卷引用:山东省菏泽第一中学南京路校区2024届高三下学期开学考试数学试题