2022·上海浦东新·模拟预测
名校
解题方法
1 . 已知定义域为
的函数
.当
时,若
(
,
)是增函数,则称
是一个“
函数”.
(1)判断函数
(
)是否为
函数,并说明理由;
(2)若定义域为
的
函数
满足
,解关于
的不等式
;
(3)设
是满足下列条件的定义域为
的函数
组成的集合:①对任意
,
都是
函数;②
,
. 若
对一切
和所有
成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24600bfcfb91c661eb9d237956e011ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0a5af03cc59bf58c1385988a746668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd5f68f8223717c5f9e7a35da919f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5707b77c17eca36e53457fdbc7912ae.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b0cf56d1d3347f1301e42197259c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59df0f69cdcb8bbd1e7369d3b730ab6.png)
(2)若定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72dfa26de75e699e91401e1c7769db70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78db8978ef52545c2d1effc0f52b7f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e8528f8c2cefedbaedb13cd43540357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8562a7044c527888e2dd7fa42feda7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8321b2ac0cb0a0d6aa579dcbc9578ec.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac532cbc6695639c3816e49c809aed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2288a34a490fd0c8f4d566959a1e97b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2972af8c65701183de194c358b83256c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7576241e80f3fdd887fed12ebb5d2273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a824bb87d715617e270c800204d7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01d67fd2a155c3dd322dc971370a4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ae7943f38c810776e3dab3a8587f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa10bec00d5ea02234be29a9fd92a647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-07-05更新
|
1746次组卷
|
8卷引用:上海市华东师范大学第二附属中学2022届高三考前模拟数学试题
(已下线)上海市华东师范大学第二附属中学2022届高三考前模拟数学试题(已下线)考向10函数与导数(重点)-2上海市行知中学2023届高三上学期10月月考数学试题上海市曹杨第二中学2023届高三上学期12月月考数学试题2024届高三新高考改革数学适应性练习(九省联考题型)广东省广州市华附2023-2024学年高一上学期期中数学试题(已下线)第三章 函数的概念与性质单元测试基础卷-人教A版(2019)必修第一册广东省茂名市电白区第一中学2023-2024学年高一下学期4月月考数学试题
名校
2 . 已知函数
,
.
(1)若直线
是曲线
在
处的切线,求
的表达式;
(2)若任意
且
,有
恒成立,求符合要求的数对
组成的集合;
(3)当
时,方程
在区间
上恰有1个解,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4935611969e644511329f6b0dbbf3b.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779857e2a9f13158fb4cf5988debceca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5223ece2f8f76850c49e2505304532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eaa16e4de765a7127b2a4aa8302cef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a5286cdf08218995b1514c195494e3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298b861acdad2f218a882319c1a3280a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a531b9769bfba66a10139b153f09307c.png)
您最近一年使用:0次
名校
3 . 对于求解方程
的正整数解
(
,
,
)的问题,循环构造是一种常用且有效地构造方法.例如已知
是方程
的一组正整数解,则
,将
代入等式右边,得
,变形得:
,于是构造出方程
的另一组解
,重复上述过程,可以得到其他正整数解.进一步地,若取初始解时满足
最小,则依次重复上述过程 可以得到方程
的所有正整数解 .已知双曲线
(
,
)的离心率为
,实轴长为2.
(1)求双曲线
的标准方程;
(2)方程
的所有正整数解为
,且数列
单调递增.
①求证:
始终是4的整数倍;
②将
看作点,试问
的面积是否为定值?若是,请求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09e7065aa112872161285c5f3bfc022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3460cd2f27a53941986606734a9b479a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ca4e60aab76ce3be3b5ffb9137f163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef282595213e6ac1c04b09c8703e176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62b8fca47d65828c45fc8e38fe8beb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c804f8356fa6120aa13b2d11bfea10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f33dbb2fc073ae2d62891732e52dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e31df193bb9a9b93b02f2daa2fb747c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1e81a0995ee5492c4281539c65bf00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb4c637bd4364a8d3b8d13889befd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba78250f4e67347c7e80c543078d02e6.png)
②将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb4c637bd4364a8d3b8d13889befd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b66d595bfea3722fbc56e2fdccd548.png)
您最近一年使用:0次
4 . 在概率较难计算但数据量相当大、误差允许的情况下,可以使用UnionBound(布尔不等式)进行估计概率.已知UnionBound不等式为:记随机事件
,则
.其误差允许下可将左右两边视为近似相等.据此解决以下问题:
(1)有
个不同的球,其中
个有数字标号.每次等概率随机抽取
个球中的一个球.抽完后放回.记抽取
次球后
个有数字标号的球每个都至少抽了一次的概率为
,现在给定常数
,则满足
的
的最小值为多少?请用UnionBound估计其近似的最小值,结果不用取整.这里
相当大且远大于
;
(2)然而实际情况中,UnionBound精度往往不够,因此需要用容斥原理求出精确值.已知概率容斥原理:记随机事件
,则
.试问在(1)的情况下,用容斥原理求出的精确的
的最小值是多少(结果不用取整)?
相当大且远大于
.
(1)(2)问参考数据:当
相当大时,取
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54262f37f86a8b1320d22ffc3f5d3477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd780f6da9abba35cb0d9ad56ce2bd2c.png)
(1)有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8f69402300f6ed932697689212e91c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81bb4a9294276b027fecd5dd7f848412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)然而实际情况中,UnionBound精度往往不够,因此需要用容斥原理求出精确值.已知概率容斥原理:记随机事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54262f37f86a8b1320d22ffc3f5d3477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2833ccb3e3d658fa090f7bc327abd34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)(2)问参考数据:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e875164c06cd47489aee8c9f77af495.png)
您最近一年使用:0次
2024-05-16更新
|
1354次组卷
|
3卷引用:浙江省杭州学军中学2024届高三下学期4月适应性测试数学试题