名校
解题方法
1 . 定义
为双曲正弦函数,
为双曲余弦函数,它们是一类与三角函数类似的函数.
(1)试判断双曲正弦函数
的单调性,并用定义证明;
(2)①类比同角三角函数的平方关系,试写出
与
的关系式,并给予证明;
②对
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e183cfec7ad0c15ba454415017e3ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3442020c24433f0e30b455d3e2bd0e3.png)
(1)试判断双曲正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ae841e173b7700db59a369202dcbcf.png)
(2)①类比同角三角函数的平方关系,试写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ae841e173b7700db59a369202dcbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499a131f534409ee96f17e1d9f44b9e.png)
②对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c08d4d681c6e84e695b2a467dde8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77474ddd5262fcbf0877981ce802adb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-03-17更新
|
472次组卷
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2卷引用:安徽省淮北一中、安师大附中、铜陵一中、中科大附中四校2021-2022学年高一下学期学业水平调研数学试题
2011高一·安徽黄山·学业考试
2 . 如图,⊙
与⊙
相交于点A和B,经过A作直线与⊙
相交于D,与⊙
相交于C,设弧
的中点为M,弧
的中点为N,线段CD的中点为K.
求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06e273fc52edb4e575f769b06e7248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06e273fc52edb4e575f769b06e7248.png)
![](https://img.xkw.com/dksih/QBM/2011/8/25/1570290075320320/1570290080645120/STEM/5b13ca37fbd54e1b9adf3cfb6c931a49.png?resizew=363)
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3 . 若数列
满足
.
(Ⅰ)求
,
的值;
(Ⅱ)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5b9960d7480b668f74db946202e5a6.png)
(Ⅲ)记
表示不超过
的最大整数,如
.设
,数列
的前
项和为
.求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec179a85be41204f85e4aa52d1fdbbef.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5b9960d7480b668f74db946202e5a6.png)
(Ⅲ)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc374c1224c7ba34bc9023aa6a49de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa5cb4b6c95aa717509129ee8dbdc34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef0459addf01ebfa44eb2368ecedb71.png)
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