名校
1 . 信息熵是信息论中的一个重要概念.设随机变量
所有可能的取值为1,2,…,n,且
,
,定义
的信息熵
.下列正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c5252fe790b57fb917728e410ef925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c94a17b49550283be4ec1a348c8534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6aff1256960a159195ce0b1b8ff83c7.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2 . 函数
,若关于x的方程
恰好有4个不同的实数根,则实数t的取值范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dae08066247229136919391aa9704f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd910e8af089632e20f4fa350a864157.png)
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3 . 函数
,有
且
,则下列选项成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e863ea4f1e8af63d06ad88a235a48f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff39b4890d0c471065f7e6348301ab27.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 设定义在
上的函数
满足
为奇函数,当
时,
,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b81a59c1c237bb74e76b8485433efefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459d1d8477fd46ece5a65d40e32b4bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab30faa78cc53c104f61b1cd906c365.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 已知函数
,
.( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4a29fd093745c5c8602450709d66b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9ce4e82eec17b60cc0cf34f0394e42.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.对于![]() ![]() ![]() |
D.对于![]() ![]() ![]() |
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6 . 下列大小关系正确的是( )
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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7 . 已知
,则
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa9461e30578a920546141b81eabe16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 已知
,
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c02c66aa826a94e88b047064aa4e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f72d9b5bf2d3437c5073c30bd75311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 已知实数
,
满足
,则
的最小值是__________ .
![](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/9d5b348153da7b39bd95869d534f4f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28dc8fb2ef00c16567bfefeab15b2065.png)
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名校
10 . 对于函数
和
,设
,
,若存在
,
,使得
,则称函数
和
互为“零点相伴函数”,若函数
与
互为“零点相伴函数”,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18529cf8aa326a76997c276dcfaaeb1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ca5a94f583cc18b0a21b072c67863a.png)
![](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/e69cdbbc50bc4b9e58ce65068a5f38be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf43c2b73add71a234a76557a975003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a62bccbc7c4b5ef9d402cee298e69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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