1 . 已知
和数表
,其中
.若数表
满足如下两个性质,则称数表
由
生成.
①任意
中有三个
,一个3;
②存在
,使
中恰有三个数相等.
(1)判断数表
是否由
生成;(结论无需证明)
(2)是否存在数表
由
生成?说明理由;
(3)若存在数表
由
生成,写出
所有可能的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1b76c6898e230717d3daed334b0303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbda44091b0da7321b26722d6ab78845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac56300140ed9e27f8dff86ef1eaea0c.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/24c7d6627a568c6eaae35260d53dfb29.png)
①任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f29210b9144737a127a428679c58f406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd600b451b2b7f1680cbbcf36a49703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5137f97e66d136940d82a4027cd4fa2b.png)
(1)判断数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a97e4a4a351df2053a3cab244213d41c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e88b1329f12c3b53e86627d04f5e5a3.png)
(2)是否存在数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79dc44942df9856c903cd70e4776e86b.png)
(3)若存在数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0808a749c7fe9d45bea1edbd3ee96e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f44f67ab69be2217f7884536cfa53aa.png)
您最近一年使用:0次
2024-01-17更新
|
1084次组卷
|
6卷引用:北京市第一次普通高中2023-2024学年高二上学期学业水平合格性考试数学试题
北京市第一次普通高中2023-2024学年高二上学期学业水平合格性考试数学试题辽宁省沈阳市第二中学2024届高三下学期开学考试数学试题(已下线)第一套 新高考新结构全真模拟1(艺体生)(模块二)(已下线)微考点8-1 新高考新题型19题新定义题型精选北京市第二中学2023-2024学年高一下学期期中考试数学试题2024届河北省名校联盟高考三模数学试题
解题方法
2 . 已知函数
,(
,
为常数).
(1)若函数
是偶函数,求实数
的值;
(2)若函数
有
个零点,求实数
的取值范围;
(3)记
,若
与
在
有两个互异的交点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a39a5005c53d0e72546c0dfda5fdd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b348ef9ae62245f05324c52dc03e53.png)
您最近一年使用:0次
解题方法
3 . 俄国数学家切比雪夫(П.Л.Чебышев,1821-1894)是研究直线逼近函数理论的先驱.对定义在非空集合
上的函数
,以及函数
,切比雪夫将函数
,
的最大值称为函数
与
的“偏差”.
(1)若
,
,求函数
与
的“偏差”;
(2)若
,
,求实数
,使得函数
与
的“偏差”取得最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefd4b8569af51ff09803173f4e317d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefb4b25c31f33f979610ae52c79960c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9642df8f7f47962daeab61e8874a135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacc9308da40e8852e9c00db0eb1391a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6dbdc6df07aaa13b26b250f314f4c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5c448025ea7b5e428a7344e1ecd31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
2023-02-26更新
|
1265次组卷
|
4卷引用:广西2021-2022学年高二上学期12月高中学业水平考试数学试题
广西2021-2022学年高二上学期12月高中学业水平考试数学试题(已下线)第二篇 函数与导数专题5 切比雪夫、帕德逼近 微点2 切比雪夫多项式与切比雪夫逼近重庆市2023届高三下学期3月月度质量检测数学试题专题03E函数解答题
4 . 定义在R上的偶函数
满足
,且当
]时,
,若关于x的方程
至少有8个实数解,则实数m的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aeeb9b81e3c6a0d36add7093b657832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5f9c171f3c43a9b6ce7c0b8332fe31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42078dd3210cb53547efa1267777165d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11bf5ec5ef43915a517c09a8ae2009a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2022-11-22更新
|
2155次组卷
|
13卷引用:2023年3月河北省普通高中学业水平合格性考试模拟(十)数学试题
2023年3月河北省普通高中学业水平合格性考试模拟(十)数学试题广东省广州市二中2021-2022学年高二下学期期中数学试题广东省汕头市2022届高三第一次模拟数学试题天津市十二区县重点学校2022届高三下学期一模考前模拟数学试题天津市新华中学2022届高三下学期3月统练5数学试题(已下线)专题03 函数性质-2022届高考数学一模试题分类汇编(新高考卷)(已下线)考点03函数及其性质-4-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)天津市耀华中学2022-2023学年高三上学期统练(二)数学试题宁夏石嘴山市第三中学2023届高三上学期期末考试数学(理)试题吉林省长春市第二中学2022-2023学年高一下学期期初考试数学试题四川省阆中中学校2023届高三第五次检测(二模)数学(理)试题第一章 三角函数 单元测试卷(A卷)山东省济南市山东师大附中2022-2023学年高一下学期数学竞赛选拔(初赛)试题
名校
解题方法
5 . 对于函数
.
(1)若
,且
为奇函数,求a的值;
(2)若方程
恰有一个实根,求实数a的取值范围;
(3)设
,若对任意
,当
时,满足
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11be7eddb9524892c60b99356c5ce555.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0120d4566cc9889481c7d783a7bb9bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a852eb3b8feb1dc29a34318d678af1.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac3bf8d695b528cb2f81ca18575bb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f46d2ca347857b6a55e1aceafb47d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5049dfb734d7776ea05f8cf09b28a9.png)
您最近一年使用:0次
2022-04-23更新
|
2680次组卷
|
7卷引用:浙江省杭州市“桐·浦·富·兴”教研联盟2023-2024学年高二下学期6月学考模拟数学试题
名校
解题方法
6 . 已知三棱锥
三条侧棱
,
,
两两互相垂直,且
,
、
分别为该三棱锥的内切球和外接球上的动点,则线段
的长度的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f65a7b230807b683d18bb7415473de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-01-25更新
|
3549次组卷
|
9卷引用:2023年3月河北省普通高中学业水平合格性考试模拟(十)数学试题
7 . 已知圆
过点
.
(1)求圆
的方程;
(2)已知点
,
,点
是圆
上任意一点,求
的最大值,并求出此时点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78daa72a59c90db0c7d94cf76d527623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15530f883ddb1b04d38453ddd92ed36.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f39e4fe279f78b0bbc005bb1b7e862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2767866dc6472299128b8bd074e384fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b17e28ce88e9a94b0584fed68b4adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2021-12-24更新
|
608次组卷
|
2卷引用:贵州省2021-2022学年高二12月学业水平考试数学试题
名校
8 . 设函数
.
(1)判断
能否为函数
的极值点,并说明理由;
(2)若存在
,使得定义在
上的函数
在
处取得最大值,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2f38cf1aca37d11a488c573818bfcc.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce8f59639f85ce4771b178b3f9dd6d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d747e07c2f9c4bf8fed76b88fb47f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61bf1ec26825646e2a51a4b9cef8126d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2017-04-15更新
|
903次组卷
|
2卷引用:河南省郑州市2019-2020学年高二下学期阶段性学业检测题5月数学(理)试题
9 . 设函数
的定义域为
,其中
.
(1)当
时,写出函数
的单调区间(不要求证明);
(2)若对于任意的
,均有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e89adf24b5653e711db2013b6d906c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d217c7b12e12e5fb67472452518859ec.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8e1dd8da540badcb9a8f427c5b202e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0313347c4fb22b033bac5074d9631e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c538cb679f324eed97878398996a377c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2016-12-04更新
|
1133次组卷
|
3卷引用:浙江省2016年10月普通高中学业水平考试数学试题2
10 . 设
,
为椭圆
的左、右焦点,动点
的坐标为
,过点
的直线与椭圆交于
,
两点.
![](https://img.xkw.com/dksih/QBM/2016/10/26/1573106686074880/1573106692562944/STEM/00407d23c08f4f0b88bac947f489a5a9.png)
(3)求
,
的坐标;
(4)若直线
,
,
的斜率之和为0,求
的所有整数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36bfda1001f393f13d41531d6b7af50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2016/10/26/1573106686074880/1573106692562944/STEM/00407d23c08f4f0b88bac947f489a5a9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(4)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-04更新
|
1086次组卷
|
3卷引用:浙江省2016年10月普通高中学业水平考试数学试题2