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1 . 如图,是一座“双塔钢结构自锚式悬索桥”,悬索的形状是平面几何中的悬链线,悬链线方程为
(c为参数,
),当
时,该方程就是双曲余弦函数
类似的有双曲正弦函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b383983da73f97c0ec7922556b84c49.png)
和
的值;
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfa06870da52663bbb4c7e18217dd9.png)
(3)
不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad2f5a11d7437f506adab0996961269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594663e98b797cdc4efbd098cc15854f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d712038d937090679d0e8cee56b47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b383983da73f97c0ec7922556b84c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b3d6bb49565cf01620a0259431d7ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1272e4f338038b3b9468cb9ecc06fe26.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfa06870da52663bbb4c7e18217dd9.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d489d153159fcf945322bf0c6761a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3120403a25e9fc836f06a7781d23c6ec.png)
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2 . 已知函数f(x)的定义域为R,其图象关于点
中心对称,若
则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404893bd85cd20d82aabf9702d1e0638.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 已知函数
是定义在
上的奇函数,
,对任意的
,且
,均有
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff68d7374e6f548d902f18ed6b6e8c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69b5fe06c9706349fe0ee02322759f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6629a0a419062fd4e9d1b7672d4e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead2d84f44d15afd79c6410078da36a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55d110d3aff4a3758b3faff66f2ad6f.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.函数![]() |
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解题方法
4 . 已知
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1893ec3241bbeb7909e5a1ecfb7c1760.png)
___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254844facd7d30fb5bc2f52610bc5c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ae637ab2db7442c4fafb163c992e38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1893ec3241bbeb7909e5a1ecfb7c1760.png)
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5 . 已知函数
满足:
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3281c4c4415fc4bbb65214ca342c0083.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa9c65056ca90651cc680583e08b541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3281c4c4415fc4bbb65214ca342c0083.png)
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2024-06-05更新
|
1325次组卷
|
4卷引用:云南省昆明市昆明师范专科学校附属中学2023-2024学年高二下学期3月学业质量监测数学试题
云南省昆明市昆明师范专科学校附属中学2023-2024学年高二下学期3月学业质量监测数学试题2024届东北三省四市教研联合体高考模拟(二)数学试题吉林省长春市2024届向三第四次质量监测数学试卷(已下线)江苏省盐城市盐城中学2024届高三全仿真模拟考试数学试题
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解题方法
6 . 若定义在
上的函数
满足
,且值域为
,则以下结论错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805945d3a0fe7ac5b1637692732e9388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ca5e984d5e14b4be18a5ee99f80a4f.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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解题方法
7 . 已知函数
,其导函数记为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bee080faaa1aa10a87267098245ac42.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57762f410fc839804895bdf6fd0922d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bee080faaa1aa10a87267098245ac42.png)
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解题方法
8 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7adee6f47118caa72c1948c5542e661a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42bcd83df757ee29904639baaacc702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7adee6f47118caa72c1948c5542e661a.png)
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9 . 已知定义在
上的函数
满足:
.
(1)判断
的奇偶性并证明;
(2)若
,求
;
(3)若
,判断并证明
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca24be2290ac9cf976edce22eb8d060.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4886e28e9ecd40f7edd25f25bde28453.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146e32ccd4375d7898e8381ef7bee7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a360203717effe5e60f78c5b2b7a95d.png)
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10 . 已知函数
.
(1)求
的值;
(2)求函数
的对称中心;
(3)作出
在一个周期内的图象(将给定的表格中填全,并描点画图)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ab39f0922de3e4ad00f86d10591943.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65a3f7b33165d8682c1011811454b91.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![]() | 0 | ||||
![]() | |||||
![]() |
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