1 . 如图,已知抛物线与坐标轴分别交于A
、B
、C
三点,过坐标原点O的直线
与抛物线交于M、N两点.分别过点C、D
作平行于
轴的直线
、
.(1)求抛物线对应的二次函数的解析式;(2)求证:以ON为直径的圆与直线
相切;(3)求线段MN的长(用
表示),并证明M、N两点到直线
的距离之和等于线段MN的长.
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/4fbddbdfabab4550bfb83c4a46fda115.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/28c38477a2914d08bf56d2768b291972.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/50ae5727b62d4679bdd6542feadbc2ac.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/15a03c0f8234483e834cd3969fb73c58.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/b3bc8f851d394332b24cab8ca34b570e.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/c8e31e3a457f47eda0042ba68a5abd4e.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/02e26592ab7546678bb399f665cd0e99.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/eb5ae2f76bd4437097ad0cc25765eb30.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/02e26592ab7546678bb399f665cd0e99.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/2ba5c2ddc3324d15a776a0334d36274d.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/eb5ae2f76bd4437097ad0cc25765eb30.png)
![](https://img.xkw.com/dksih/QBM/2012/11/9/1571058669568000/1571058675179520/STEM/8073397b2f20477895392153773e3195.png)
您最近一年使用:0次
名校
解题方法
2 . 已知不等式
的解集为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa70fa7eb86c3733e2c1f1c7d07dd802.png)
(1)求证:方程
必有两个不同的根;
(2)若方程
的两个根分别为
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5f28031b036e4a37be931d5ff28368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa70fa7eb86c3733e2c1f1c7d07dd802.png)
(1)求证:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54610fc51fb1a700d9977ec678c74392.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54610fc51fb1a700d9977ec678c74392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4e94463a0f22990789c5494916e844.png)
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2023-10-08更新
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3卷引用:江西省丰城市第九中学2023-2024学年高一上学期11月期中数学试题
江西省丰城市第九中学2023-2024学年高一上学期11月期中数学试题吉林省长春吉大附中实验学校2023-2024学年高一上学期10月月考数学试题(已下线)第二章 一元二次函数、方程和不等式-【优化数学】单元测试能力卷(人教A版2019)
名校
3 . 已知函数
,
.
(1)判断
的单调性,并利用单调性的定义加以证明;
(2)设
,
,求函数
的最小值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a2299ba8b37e81821f1a2dcfaba653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05c3469207680b78060b5182857c4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
您最近一年使用:0次
2024-01-25更新
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244次组卷
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2卷引用:江西省上饶市私立新知学校2023-2024学年高一上学期期末数学试题
2023高一上·上海·专题练习
解题方法
4 . 已知函数
,
.
(1)证明
的单调性并求值域;
(2)设
,
,
,求函数
的最小值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a2299ba8b37e81821f1a2dcfaba653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05c3469207680b78060b5182857c4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
您最近一年使用:0次
名校
解题方法
5 . 给定整数
,由
元实数集合
定义其相伴数集
,如果
,则称集合S为一个
元规范数集,并定义S的范数
为其中所有元素绝对值之和.
(1)判断
、
哪个是规范数集,并说明理由;
(2)任取一个
元规范数集S,记
、
分别为其中最小数与最大数,求证:
;
(3)当
遍历所有2023元规范数集时,求范数
的最小值.
注:
、
分别表示数集
中的最小数与最大数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825aebd95112da4ea868624c6a8d5e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f292ceb39541a09e4e0895236888b758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1caf54f3f842ff7aef9ad1383a8631f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f786ac371d6a08506bffda41dcac71.png)
(2)任取一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a74839dfa76d4637641dcb41270e0618.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dfa7b5f718ed24cde77b169b3d76f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f5e363bbded380a6c6e5d51405e5fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3ba68338f7e2594df13b30ed67ecfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
2023-02-24更新
|
4250次组卷
|
12卷引用:江西省南昌市江西师范大学附属中学2024届高三下学期开学考(数学)试卷
江西省南昌市江西师范大学附属中学2024届高三下学期开学考(数学)试卷北京市清华大学附属中学望京学校2022-2023学年高一下学期2月统练(开学考试)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3 切比雪夫函数与切比雪夫不等式(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-19安徽省合肥一六八中学2024届高三“九省联考”考后适应性测试数学试题(一)2024届高三新高考改革数学适应性练习(一)(九省联考题型)(已下线)黄金卷03(2024新题型)(已下线)信息必刷卷05(已下线)信息必刷卷04(江苏专用,2024新题型)河南省信阳市新县高级中学2024届高三下学期3月适应性考试数学试题(已下线)数学(九省新高考新结构卷01)(已下线)压轴题01集合新定义、函数与导数13题型汇总-2
名校
解题方法
6 . 已知函数
.
(1)当
时,求函数
的单调递增区间(不必写明证明过程);
(2)判断函数
的奇偶性,并说明理由;
(3)当
时,对任意的
,恒有
成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3411c6dd7f98eb07a9067a4e204b3d64.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998485ffeb46a0412ff1a0f814429257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911ef39b13a09894783851f7da24c1a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163836ab07d982556c85ac2e6a13ae72.png)
您最近一年使用:0次
2023-12-15更新
|
303次组卷
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2卷引用:江西省宜春市丰城拖船中学2023-2024学年高一上学期期中数学试题
7 . 如图所示,在
中,点D是边BC的中点,点E是线段AD的中点.过点E的直线与边AB,AC分别交于点P,Q.设
,
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ee44c8ad5792736787bb903ca273db.png)
![](https://img.xkw.com/dksih/QBM/2022/10/10/3084552225349632/3085931629084672/STEM/99cbf902e79b456d83a8b162745b5770.png?resizew=199)
(1)试用
与
表示
、
;
(2)求证:
为定值,并求此定值;
(3)设
的面积为
,
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93179982551da01266d5f1bc177fb4ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe91df8a5a97bf49ab8004f07f64e908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ee44c8ad5792736787bb903ca273db.png)
![](https://img.xkw.com/dksih/QBM/2022/10/10/3084552225349632/3085931629084672/STEM/99cbf902e79b456d83a8b162745b5770.png?resizew=199)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228f4ddbb8959f904d71259be7c6ab36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1da92a2fc2ce861e82f7192fe4e648f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fe2d802f2b37e7db198c5a3c1df9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b680f91c4a693cc9ab2c23f2e9114ce.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac8a4086cd8af00e89c57fdfd905114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd72016a9855cbf0056ff732fe872612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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2022-10-12更新
|
440次组卷
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3卷引用:江西2023届高三联合测评卷数学(文)试题
名校
8 . 已知定义在R上的奇函数
和偶函数
满足
.
(1)判断函数
的单调性,并用单调性的定义证明;
(2)求函数
,
的最小值.
![](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/563d34c1f9b294a226c6a007d85bd1ef.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fdca52eaaa472aa46c7c64119de509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
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2023-10-01更新
|
1171次组卷
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6卷引用:江西师范大学附属中学2022-2023学年高一上学期期中考试数学试题
江西师范大学附属中学2022-2023学年高一上学期期中考试数学试题(已下线)模块四 专题7 大题分类练(幂函数、指数与指数函数)拔高能力练(人教A)广东省广州市第八十六中学2023-2024学年高一上学期期中数学试题(已下线)第6章 幂函数、指数函数和对数函数综合能力测试-【帮课堂】(苏教版2019必修第一册)(已下线)6.2 指数函数(2)-【帮课堂】(苏教版2019必修第一册)宁夏石嘴山市第三中学2023-2024学年高一上学期期中考试数学试卷
名校
解题方法
9 . 已知函数
.
(1)当
时,证明:当
时,
.
(2)当
时,对任意的
都有
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2fd4de38f1bb92c496df614ee6a92ee.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcace0fa79086824913868b25cadd916.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f671822e561d7500591ba2eba241b028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-01-10更新
|
483次组卷
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3卷引用:江西省吉安市第三中学2022-2023学年高一上学期期末数学试题
名校
10 . 已知函数
,
.
(1)若
的值域为
,求a的值.
(2)证明:对任意
,总存在
,使得
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3f58722394cad3df7234b543be4587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30bf0418560efb017338a9778bd13d72.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(2)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d5a5e70f64f0933ae1e4ddec5fa2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e4c91f4e75c07fe50ba226b419c5e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
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2022-01-24更新
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11卷引用:江西省抚州市临川区第一中学2021-2022学年高一下学期第一次月考数学试题
江西省抚州市临川区第一中学2021-2022学年高一下学期第一次月考数学试题山西省吕梁市2021-2022学年高一上学期期末数学试题湖北省十堰市2021-2022学年高一上学期元月期末数学试题河北省秦皇岛市2021-2022学年高一上学期期末数学试题重庆市复旦中学2021-2022学年高一下学期开学考试数学试题(已下线)专题19 函数的基本性质 (2)安徽省滁州市定远县民族中学2021-2022学年高一下学期开学摸底考试数学试题河南省洛阳市第一高级中学2023-2024学年高一上学期期中达标数学测评卷(A卷)(已下线)专题07 函数恒成立等综合大题归类宁夏石嘴山市平罗中学2023-2024学年高一上学期第二次月考数学试题(已下线)培优专题01 二次函数含参数最值问题-【同步题型讲义】(人教A版2019必修第一册)