名校
1 . 已知函数
.
(1)若函数
有3个不同的零点,求a的取值范围;
(2)已知
为函数
的导函数,
在
上有极小值0,对于某点
,
在P点的切线方程为
,若对于
,都有
,则称P为好点.
①求a的值;
②求所有的好点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/261bed360289f37d94f742ab63676e45.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25be20e3724274132cb83b16deaeecfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02af34501d48e2349967ecdfbfa6c1f8.png)
①求a的值;
②求所有的好点.
您最近一年使用:0次
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1392次组卷
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4卷引用:河北省部分学校联考2024届高三下学期3月模拟(二)数学试题
名校
解题方法
2 . 某商场周年庆进行大型促销活动,为吸引消费者,特别推出“玩游戏,送礼券”的活动,活动期间在商场消费达到一定金额的人可以参加游戏,游戏规则如下:在一个盒子里放着六枚硬币,其中有三枚正常的硬币,一面印着字,一面印着花;另外三枚硬币是特制的,有两枚双面都印着字,一枚双面都印着花,规定印着字的面为正面,印着花的面为反面.游戏者蒙着眼睛随机从盒子中抽取一枚硬币并连续投掷两次,由工作人员告知投掷的结果,若两次投掷向上的面都是正面,则进入最终挑战,否则游戏结束,不获得任何礼券.最终挑战的方式是进行第三次投掷,有两个方案可供选择:方案一,继续投掷之前抽取的那枚硬币,如果掷出向上的面为正面,则获得200元礼券,方案二,不使用之前抽取的硬币,从盒子里剩余的五枚硬币中再次随机抽取一枚投掷,如果掷出向上的面为正面,则获得300元礼券,不管选择方案一还是方案二,如果掷出向上的面为反面,则获得100元礼券.
(1)求第一次投掷后,向上的面为正面的概率.
(2)若已知某顾客抽取一枚硬币后连续两次投掷,向上的面均为正面,求该硬币是正常硬币的概率.
(3)在已知某顾客进入了最终挑战环节的条件下,试分别计算他选择两种抽奖方案最终获得的礼券的数学期望,并以此判断应该选择哪种抽奖方案更合适.
(1)求第一次投掷后,向上的面为正面的概率.
(2)若已知某顾客抽取一枚硬币后连续两次投掷,向上的面均为正面,求该硬币是正常硬币的概率.
(3)在已知某顾客进入了最终挑战环节的条件下,试分别计算他选择两种抽奖方案最终获得的礼券的数学期望,并以此判断应该选择哪种抽奖方案更合适.
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2139次组卷
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4卷引用:河北省部分学校联考2024届高三下学期3月模拟(二)数学试题
名校
解题方法
3 . 临沂一中校本部19、20班数学小组在探究函数的性质时,发现通过函数的单调性、奇偶性和周期性,还无法准确地描述出函数的图象,例如函数
和
,虽然它们都是增函数,但是图像上却有很大的差异. 通过观察图像和阅读数学文献,该小组了解到了函数的凹凸性的概念. 已知定义:设连续函数f(x)的定义域为
,如果对于
内任意两数
,都有
,则称
为
上的凹函数;若
,则
为凸函数. 对于函数的凹凸性,通过查阅资料,小组成员又了解到了琴生不等式(Jensen不等式):若f(x)是区间
上的凹函数,则对任意的
,有不等式
恒成立(当且仅当
时等号成立). 小组成员通过询问数学竞赛的同学对他们研究的建议,得到了如下评注:在运用琴生不等式求多元最值问题,关键是构造函数.小组成员选择了反比例型函数
和对数函数
,研究函数的凹凸性.
(1)设
,求W=
的最小值.
(2)设
为大于或等于1的实数,证明
(提示:可设
)
(3)若a>1,且当
时,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7cd59277a15b4d9063be84a40d5541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a4ab6155e1fd2c8f9508efa3adcda0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f87a3affc8cd30c21af57157d156c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6933733e82337e6d4a95fc2946ff26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2697ef67790838c84cc238a0334c5d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83aa9d22736190332e01260e5a7803de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b7a76267b71e6fc828cf2a2e81173d.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dd60e2cd1a1aae21a9c07820214290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0823f59998a025e80b46881993e89d1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01262e3dd65728a29f3bbfa584dccede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7425d1d31f6188375d44137c2b219b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cda4049695561dab3e0803c3a287fe.png)
(3)若a>1,且当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89c2336e46cbbe2b978d7d8fcd340be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc069f6b9d1623e1c06879cef933e42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-02-20更新
|
345次组卷
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2卷引用:山东省临沂第一中学2023-2024学年高一上学期期末模拟数学试题
解题方法
4 . 摩天轮是一种大型转轮状的机械建筑设施,游客坐在摩天轮的座舱里慢慢地往上转,可以从高处俯瞰四周景色.如图,某摩天轮最高点距离地面高度为
,转盘直径为
,设置有48个座舱,开启后按逆时针方向匀速旋转,游客在座舱转到距离地面最近的位置进舱,转一周大约需要
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/b9e74533-cc76-4962-a0c8-e7a1b7e7f98d.png?resizew=156)
(1)游客甲坐上摩天轮的座舱,开始转动
后距离地面的高度为
,求在转动一周的过程中,
关于
的函数解析式;
(2)求游客甲在开始转动
后距离地面的高度;
(3)若甲、乙两人分别坐在两个相邻的座舱里,在运行一周的过程中,求两人距离地面的高度差
(单位:
)关于
的函数解析式,并求高度差的最大值(精确到0.1).
(参考公式与数据:
;
;
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6363a9c7ab19b53bc1ddae6521a30a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba52ced0811df98fedb575535b24257b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a628160b971aca3528d447882fa45fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/b9e74533-cc76-4962-a0c8-e7a1b7e7f98d.png?resizew=156)
(1)游客甲坐上摩天轮的座舱,开始转动
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cec183057249005d5f234c4bea5de7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d847196d7a43900fb1ea0d95cd6fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)求游客甲在开始转动
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276544dddf27f079144b8db1e570b9ed.png)
(3)若甲、乙两人分别坐在两个相邻的座舱里,在运行一周的过程中,求两人距离地面的高度差
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(参考公式与数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258529c3397cff79706c3b62bdf3809e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5784c7060dacfbf93a57a81c97798a45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c57f1b3142e091f1ef8e596ad675d42.png)
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2024-02-05更新
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432次组卷
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2卷引用:北京市大兴区2023-2024学年高一上学期期末检测数学试题
5 . 对于给定的奇数
,设
是由
个实数组成的
行
列的数表,且
中所有数不全相同,
中第
行第
列的数
,记
为
的第
行各数之和,
为
的第
列各数之和,其中
.记
.设集合
或
,记
为集合
所含元素的个数.
(1)对以下两个数表
,
,写出
,
,
,
的值;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/e69407e7-892f-4a4f-952f-72fcf655e5f4.png?resizew=138)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/c396e40f-d96e-4dad-b60b-54bbd480977d.png?resizew=138)
(2)若
中恰有
个正数,
中恰有
个正数.求证:
;
(3)当
时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84de01db26d435ab45acdf26cfefe625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823b5260d6b24cc69747c0455c879b7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267e1fe5e16e9dc9641c7736528e1235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449fa836b7477adb5c394b8e67af6a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02eca2f89985a104ddeebdf89629ade7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f76063c9d41d3398308bf7d25938d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9164331fb78ebe6059e69060f3ab302a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d418009b040d5e5192d28417b459890.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e75ee8469247f599502aec2f2ee552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b811354062228d1e2e090aa587259c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)对以下两个数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d98b87ea379019dea6dbd58ebaf19f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebed69dd5f3ef7ff5eccd8031e4771ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8b030e661224065ec16aa272782b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a135dc0cf986199b13a3ce1106379e16.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/e69407e7-892f-4a4f-952f-72fcf655e5f4.png?resizew=138)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/c396e40f-d96e-4dad-b60b-54bbd480977d.png?resizew=138)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de7bdfbb18abcc2d1575d1228489f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f4518b3c93a17e13fc06affa23e519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31eb153a2133b41486193e3c3b633d3c.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7a1d739890a8951586e23b78b035bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8181afecca9a1adc761a2184543fd2e5.png)
您最近一年使用:0次
6 . 给定正整数
,设集合
.若对任意
,
,
,
两数中至少有一个属于
,则称集合
具有性质
.
(1)分别判断集合
与
是否具有性质
;
(2)若集合
具有性质
,求
的值;
(3)若具有性质
的集合
中包含6个元素,且
,求集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe04c33e38708c81ac8773e298dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059a6c5a965c335b8da05e697da2c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8692a851a72427d95eac78f2efd9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26bbb11e932ddb26a9088e7fc33e87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3ed03b0f8fb8b88d7edf6165345c6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7167aef3e4628ac67872117cdac32978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)若具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0d1c7c644d841c90d84dd75c562d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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7 . “函数
的图象关于点
对称”的充要条件是“对于函数
定义域内的任意x,都有
”,已知函数
.
(1)证明:函数
的图象关于点
对称;
(2)若函数
的图象关于点
对称,且当
时,
.若对任意
,总存在
,使得
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7f8871c0da18d18c0eaa5313861e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce90386fd6b7dfd5399cd372fa9103c3.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac7c28099bfbb7dc2a45ad166eace05.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca40ec1d89d7959b07f5394435c0224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e121df04531e9275387071a88cb9bb8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff565afbddafe8625ef376d7eb3fa649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
您最近一年使用:0次
8 . 若
,对
,都有
成立,则称函数
在
上具有性质
.
(1)分别判断函数
与
在区间
上是否具有性质
,如果具有性质
,写出
的取值范围;
(2)若函数
在
上具有性质
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36338db3cdaf11194eb0d9e29100a457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea232de27d21a2646fd4520ea0726bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f561d3fa34fe62678ab200340e1c1486.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8279cac23c4cc22c28b135580b22bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58df46e8e9a43fe549a00269ca3d1d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda591d3909af06eabf6b37c65bfe571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f561d3fa34fe62678ab200340e1c1486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f561d3fa34fe62678ab200340e1c1486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48cd0519bdbf3d782432c3a321b0ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6318e3429cac968a7adf8758b3493b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
9 . 已知集合
,其中
且
,非空集合
,记
为集合B中所有元素之和,并规定当
中只有一个元素
时,
.
(1)若
,写出所有可能的集合B;
(2)若
,且
是12的倍数,求集合B的个数;
(3)若
,证明:存在非空集合
,使得
是
的倍数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcbde10b7bc82536072ca38f32b2f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe11d564517c04437b9884da859002b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9bc3a22bc9cb056df1e6d5218877c8c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6e90ea92c80c31653e4ac972bf56c8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d725be6acff620b47bb7a8a7a0c6e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af5e68b8592c14157df8db05904c8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
您最近一年使用:0次
2024-01-20更新
|
316次组卷
|
2卷引用:北京市朝阳区2023-2024学年高一上学期期末质量检测数学试题
名校
解题方法
10 . 若函数
在定义域内存在实数
满足
,
,则称函数
为定义域的“
阶局部奇函数”.
(1)若函数
,判断
是否为
上的“二阶局部奇函数”?并说明理由;
(2)若函数
是
上的“一阶局部奇函数”,求实数
的取值范围;
(3)对于任意的实数
,函数
恒为
上的“
阶局部奇函数”,求
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82835a8d22c41dc902a1a5ff44595b78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a173784888adf2946382fa093ba53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936661e7a7a5bd6134053d38f80a7adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6934c9da2af4092391b69b036c88c661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25a4b68d7be63ec223f642976a1087ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)对于任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f70e7c2235fc7a25655a6c04fa89b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d857046139daeb7609ea60058d169e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2024-01-14更新
|
318次组卷
|
3卷引用:云南省昆明市云南师大附中2023-2024学年高一上学期教学测评期末数学试题