名校
1 . 已知
(
、
)是奇函数.
(1)求实数
的值;
(2)判断函数
在
上的单调性,并给出证明;
(3)当
时,
的值域是
,求实数
与
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1a4fa622dcfa9d561ea48fdf085a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46c4820255b5f59cea43df6941a2178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-01-15更新
|
258次组卷
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4卷引用:上海市杨浦区控江中学2020-2021学年高一上学期期末数学试题
名校
2 . 设
,
是函数
的图像上任意两点,点
满足
.
(1)若
,求证:
为定值;
(2)若
,且
,求
的取值范围,并比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05193d9096bd9da9230acc14228aa4e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4920bf4db93b18d4ecfdc05e310dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21de984f69bcc0bec2c5580d2dc6b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/961e120bfd1da71d31f9dc204c0e851c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5f702b56a32a3b31c8eee63fbcf8be.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e099a6abe3e9566b2ad385906e323fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a86d65aab881fdd06a05ce47d09c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e7dc5d31b6378f40d36b132857e1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
您最近一年使用:0次
2020-05-21更新
|
291次组卷
|
3卷引用:2020届上海市黄浦区高三二模(阶段性调研)数学试题
名校
解题方法
3 . 已知函数
(
且
)是定义域为
的奇 函数,且
.
(1)求
的值,并判断
的单调性(不要求证明);
(2)是否存在实数
,使函数
在
上的最大值为0?如果存在,求出实数
所有的值;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a0efb23a59a82e6dd3252778f04ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a98186dcca4e3093a3e910b705b087.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1533fdab20809be5fa471a8d34e9e456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd9c440eb35d3edc3516a8ac4358e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-12-01更新
|
462次组卷
|
4卷引用:大题能力提升考前必做30题-2020-2021学年高一数学期末考试高分直通车(沪教版2020,必修一)
(已下线)大题能力提升考前必做30题-2020-2021学年高一数学期末考试高分直通车(沪教版2020,必修一)湖北省荆州中学2020-2021学年高一上学期期中数学试题(已下线)第四单元 (综合培优)指数函数与对数函数 B卷-【双基双测】2021-2022学年高一数学同步单元AB卷(人教A版2019必修第一册)(已下线)第四单元 (基础过关)指数函数与对数函数 A卷-【双基双测】2021-2022学年高一数学同步单元AB卷(人教A版2019必修第一册)
名校
解题方法
4 . 设集合
存在正实数
,使得定义域内任意x都有
.
(1)若
,证明
;
(2)若
,且
,求实数a的取值范围;
(3)若
,
,
且
、求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a831c679879f4a82dab89102a4f96588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da75dc1a74e80f86bc09281adedd7701.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c298e3b72856ab70082079d5105e8873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa335fe09eebdc9884934d1cbc16918.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021f43d4d536af9301adad72758d3355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764df344e05f8ef1a97b346ddf44a5a0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8c242fdc562359f5e4ecce57309060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97148e04ca6a9f9dca0aba91ce4e1d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9511a2031188decf655cdfc0302b4740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
您最近一年使用:0次
2021-01-18更新
|
533次组卷
|
3卷引用:上海市延安中学2020-2021学年高一上学期期末数学试题
解题方法
5 . 圆周率π的定义为:圆的周长与其直径之比,魏晋数学家刘徽注疏《九章算术》时,采取了增加圆的内接正多边形的边数,用正多边形周长逼近圆周的方法求π的近似值.
(1)据此,在单位圆内构造恰当的内接正多边形,证明:
;
(2)试借助计算器,列表描点,在直角坐标系中画出大致图象,描述函数
在区间D上的单调性,不必证明.根据D的不同情况,任选下列一题作答(都做的话,只选前者评分).
①
;
②
;
(3)根据(1)(2)证明:
.
(1)据此,在单位圆内构造恰当的内接正多边形,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7b90758b160fde273f833c0ead73b5.png)
(2)试借助计算器,列表描点,在直角坐标系中画出大致图象,描述函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa332d83f2f258a49d0636279be11a6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169ab597aa0807cacbcf52fad1efa63a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c8a116f962ae769863da8cf8e8b1b3.png)
x | |||||||||
![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc7d795a5b254d956664cb8335aaa31.png)
您最近一年使用:0次
6 . 已知函数
,常数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)已知
,若
的定义域关于原点对称,求实数
的值;
(2)当
时,判断
在区间
上的单调性,并利用定义证明您的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2476a8ea0b6d2183d3198f00436fdd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff33b4b5897c2736e3d237f0ab1afdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
您最近一年使用:0次
名校
解题方法
7 . 判断及证明函数
.在定义域上的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee916722bf805d52412e5bc3836daada.png)
您最近一年使用:0次
8 . 定义:对函数
,对给定的正整数k,若在其定义域内存在实数
,使得
,则称函数
为“k性质函数”.
(1)若函数
为“1性质函数”,求
;
(2)证明:函数
不是“k性质函数”;
(3)若函数
,为“2性质函数”,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f817309cf3a487af5d19e577c8b9dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ede389b43c78417912542746d91d00.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73ba53ae6166fea57c9c5a0840b3cfc.png)
您最近一年使用:0次
名校
9 . 已知函数
.
(1)求函数
的定义域并证明该函数是奇函数;
(2)若当
时,
,求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344d591ddf40ec7c27aa95c54eea961f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/737c165baced95d7095d9f918a9cc110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885c4da4b527adc76223d595a835bcd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
您最近一年使用:0次
10 . 已知定义在实数集
上的偶函数
和奇函数
满足
.
(1)求
与
的解析式;
(2)求证:
在区间
上单调递增;并求
在区间
的反函数;
(3)设
(其中
为常数),若
对于
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.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/b41ae210dd892fc5428a51dd409aa69d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b029e85e686623cdef977b2cb1f207a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b029e85e686623cdef977b2cb1f207a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4db4036616944674cc36bb1388a2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10dc986f44a2f80e9b8d192eb3521398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-02-04更新
|
649次组卷
|
2卷引用:2016届上海市静安区高考一模(文科)数学试题