1 . 计算下列各式的值:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847b092108a46a0b9f2f2a463b23946a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0ac518d8e161d490ee56b66ebf24f7.png)
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2024-03-06更新
|
336次组卷
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2卷引用:海南省定安县定安中学2023-2024学年高一下学期开学考试数学试题
2 . 求值:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94c1dc61a007d11af57489e1345b0e.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94c1dc61a007d11af57489e1345b0e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a9b56bf5f53791961fdd7142ea1ce5.png)
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3 . 艾宾浩斯遗忘曲线描述了人类大脑对新鲜事物遗忘的规律.基于此,某课题小组研究发现,在学习课程
后每经过一个星期,会遗忘掉所记忆内容的
.为使得所记忆的内容不低于原来的
,最多在
个星期之后对所学内容进行复习,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
__________ .(
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ee628efd6b2f7296c106dd5cbae42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d7abf02717d6e59d8a64a65a87c412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96209d77ac4893605e355c6597269492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8288e1d872c6b5872b84a32469ff9e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5114e1dbd4fc973e99293e1fdb3def.png)
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4 . 若函数
满足下列条件:在定义域内存在
,使得
成立,则称函数
具有性质
;反之,若
不存在,则称函数
不具有性质
.
(1)证明:函数
具有性质
,并求出相应的
;
(2)已知函数
具有性质
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110e5b2f8a412dc6528df8da2ed66cc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc4e3775c850f1c1804f9eb7a70153a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7099e54df7bf582badbca0e1d3794b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 已知正实数
,
满足
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967d662a83942b23f2029bb73aa59372.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
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6 . 求下列各式的值
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ae7fe2fd45f453cf60ebdf93e6302d.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ae7fe2fd45f453cf60ebdf93e6302d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6ca44d090e100a534875c059c8bce6.png)
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7 . 求下列各式的值
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ae7fe2fd45f453cf60ebdf93e6302d.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ae7fe2fd45f453cf60ebdf93e6302d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ab037392bf5f09447e5c8f5e34080b.png)
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8 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578bf56c33636a68f547abd5c954aea1.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efc0dd4a184c51caa3b4b6a7da09302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578bf56c33636a68f547abd5c954aea1.png)
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9 . 已知
为
上的奇函数,且
,当
时,
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b568b2cee9ef2a32d2f27305a9104d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b402181e8e0ec843d3d7f441e35bd28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246de316aacce5e2a1b482840ff02f82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769283338a97a882a7caa9438bccb2ac.png)
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10 . 计算与化简:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211daa3d89589b73f078a598ac57c974.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211daa3d89589b73f078a598ac57c974.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2a861e6c7a95fb3d3e1218607d1385.png)
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