1 . 已知幂函数
在
上单调递增.
(1)求
的函数解析式;
(2)设
,若
的零点至少有一个在原点右侧,求实数
的取值范围;
(3)若
,
,
,若
,求满足条件的
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c14aa8187552ea9709319e80d23d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5104b3421459142f5125c1cdb52ecc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b82de1f098bcf34fbd1aaf4326f5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f75446914cf9b3425cb0ddcd08fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097a9ab1898d84021c65b050101b0dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4578f38c7b8d01161469fcadfeff7c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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解题方法
2 . 已知实数a满足
,
.
(1)求实数a的取值范围;
(2)若
,
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bc7e2758fd2002fbeaef52ab14a8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618ddbf4f91ffd36c5cedede3802e8d5.png)
(1)求实数a的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd0d5ef0170d4d4dc056eed669807ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f293ebe90eaabc460d2e2713e4ab48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe653ed86488f8dcdf2612ac544fe2aa.png)
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3 . 如图,对数函数
图象上的点A与x轴上的点
,C构成以BC为斜边的等腰直角三角形,若
右侧的相似三角形
的顶点E在函数
上,顶点C,D在x轴上,且两三角形的相似比为2,则该对数函数的解析式为______ .,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c82cafa7ea341764fdccd42b2680200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/05791cd0-774c-44fd-accc-eae8a8e367c3.png?resizew=163)
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4 . 在一个空旷的房间中大声讲话会产生回音,这种现象叫做“混响”.用声强的大小来度量声音的强弱,假设讲话瞬间发出声音的声强为
,则经过t秒后这段声音的声强变为
(
为常数).把混响时间
定义为声音的声强衰减到讲话之初的
倍所需时间,则
约为( )
(参考数据
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b4faefb6ef84a8c02f148bb7c30479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f847447c16f40847c485b3d5b9956da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fed26fed14e8725107bd33c5417f59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74cd839272108fb3987867337a0e257d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462995b0e447d3a2f5796bab03dfadb6.png)
(参考数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12a76edbb3e98e3ff41c03401769d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e36492ded42e594c63855802dee601.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-11-09更新
|
231次组卷
|
2卷引用:河南省周口市项城市2023-2024学年高三上学期期中数学试题
5 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd3f2e385048434acbe8df39c38d0cf.png)
______________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd3f2e385048434acbe8df39c38d0cf.png)
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2023-11-08更新
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1167次组卷
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5卷引用:浙江省温州十校联合体2023-2024学年高一上学期期中联考数学试题
6 . 若
,则
__________ .(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17ff729653a1c5097e915975ee01367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b511bcbe94aa484c0a067891fbf7968.png)
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解题方法
7 . 下列命题为真命题的是( )
A.函数![]() ![]() |
B.若幂函数![]() ![]() ![]() |
C.若幂函数![]() ![]() ![]() |
D.若函数![]() ![]() ![]() |
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8 . 如果函数
的定义域为
,且
恒成立,则函数
的图像关于直线
对称.已知函数 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1603a9f6f5e0617db8a852a1a705e2f.png)
(1)若
,求
的值;
(2)证明:函数
的图像关于
对称;
(3)现在已经得知函数
在
上是严格减函数,在
上是严格增函数,关于
的不等式
恒成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc58a89f281be53f284c0ddb5b7fe828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a454588e9beb97c69a0332a7c5c796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1603a9f6f5e0617db8a852a1a705e2f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c24244b1fdbf1455087c2ebf41c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(3)现在已经得知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be381da62d4a042476aa11dbd5824e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a76f56568aa5a381aeda448d05476a.png)
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9 . 已知函数
为奇函数,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be7967ccfa7f3951ed5c657cbeec5cdf.png)
A.![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2023-11-07更新
|
734次组卷
|
4卷引用:河南省湘豫名校联考2023-2024学年高三上学期一轮复习诊断考试(二)数学试题
10 . 20世纪30年代,数学家柯布和经济学家保罗·道格拉斯共同提出一个生产函数理想模型:
其中Q表示收益(产值),K表示资本投入,L表示劳动投入;A为一个正值常数,可以解释为技术的作用;
,表示资本投入在产值中占有的份额,
表示劳动投入在产值中占有的份额.经过实际数据的检验,形成更一般的关系:
,
,
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5dabd9e26cd28d0a4131a1f3baa2bb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2905ef7674574749b4ca9dd9cfe58cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fc97b0acc21bf52197d5a1e793671a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d9cd42d845f73ff619d50fe21db6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31ac41d9a862e90bb090c2c3e2fb623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a1a5a87f43705de6f8115981e68477.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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