解题方法
1 . 已知集合
(其中
是虚数单位)
,定义:
,
.
(1)计算
的值;
(2)记
,若
,且满足
,求
的最大值,并写出一组符合题意的
、
;
(3)若
,且满足
,
,记
,求证:当
时,函数
必存在唯一的零点
,且当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531f55c9de4647282bc0424a81f4fd25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ddb621d78a738eba6ebafecbbd7d06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47aa3fcf666d1169ceca5e1e720b926e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ccc73232efc9d641adcbae21035944.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0ff8b406a295a58f4fbb36b4c292fa.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be674fcbd2fd1a608fd4a9705c70db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e7c6170cd75c5a40d7e695eda15e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e95d018246b699601d127e79ec46131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f82089a3186fdffaa2535faebd3d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b54286fe72b8305272c36c0a3a8d2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f7d480cfc89b872404666083e62db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546ababc482b51df95c4aba05ee18c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d828db2a08e2a1da164a0012cc6627a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661249bf6499017f9e5e03db3fcd93d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d5ec74c81f7d02f273f7eecefaf9a7.png)
您最近一年使用:0次
解题方法
2 .
中,
,当
时,
的最小值为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6060d9a82ed5405a1ea8cd824448b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3ede869e508a8c8bda34a16782f863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9baf78638bf6a9798800efc59248d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c54fccc669a643c76daccc13562e265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
您最近一年使用:0次
解题方法
3 . 已知实数
满足
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde3da412c997c926ae842ddc107cf35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095354f5d4e5dc28402af7b089ebb2f9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
20-21高一下·浙江·期末
名校
4 .
中,内角
,
,
的对边分别为
,
,
,
为
的面积,且
,
,下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d556015a8e1a6214d8fd240e85b66cc7.png)
A.![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-05-11更新
|
579次组卷
|
17卷引用:上海交通大学附属中学2021-2022学年高一下学期3月线上测试数学试题
上海交通大学附属中学2021-2022学年高一下学期3月线上测试数学试题(已下线)【新东方】双师265高一下(已下线)【新东方】高中数学20210527-027【2021】【高一下】浙江省“七彩阳光”新高考研究联盟2020-2021学年高一下学期期中联考数学试题(已下线)专题6.10 解三角形综合练习(一)-2022届高三数学一轮复习精讲精练(已下线)第28讲 平面向量范围与最值问题-2022年新高考数学二轮专题突破精练陕西省西北工业大学附属中学2022-2023学年高二上学期1月期末数学试题福建省福州日升中学2022-2023学年高一下学期期中考试数学试题河南省开封市河大附中实验学校2022-2023学年高一下学期第一次月考数学试题广东省湛江市雷州市第一中学2022-2023学年高一下学期第一次月考数学试题重庆市第十八中学2023-2024学年高一下学期3月月考数学试题江苏省无锡市辅仁高级中学2023-2024学年高一下学期3月月考数学试卷重庆市第八中学校2023-2024学年高一下学期4月阶段练习数学试题 湖北省武汉市第六中学2023-2024学年高一下学期4月月考数学试卷广东省茂名市高州中学2023-2024学年高二上学期12月月考数学试题江苏省?邮市第?中学2023-2024学年高一下学期4月阶段测试数学试卷(已下线)专题4 解三角形中的最值与范围问题【讲】(高一期末压轴专项)
5 . 函数
的表达式为
.
(1)若
,直线
与曲线
相切于点
,求直线
的方程;
(2)函数
的最小正周期是
,令
,将函数
的零点由小到大依次记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c032d50e3dde09f453adc34a1c5353ea.png)
,证明:数列
是严格减数列;
(3)已知定义在
上的奇函数
满足
,对任意
,当
时,都有
且
.记
,
.当
时,是否存在
,使得
成立?若存在,求出符合题意的
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0923a929dbc45520103daa8a889b60.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcee772e6187ac31d7f8d69b0487000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea3733e989ba820120027e2c3664285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba2967e52115b6f3f668116ed021199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c032d50e3dde09f453adc34a1c5353ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30af9e4dbb01b5db338a2cd88cb1cc01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bef0ef12869d633d4592adec26ea6a.png)
(3)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b8ca7bca7dd23fa9e18073ad4636dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344008f3ab39f3923a971a44c2c4bbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd5f68f8223717c5f9e7a35da919f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca34074d548c4b6c3cd3a1006895fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbda8d24ba7efec06837fc39824d7e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15c2171c1be9ec394494ad822a048d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf88dc817c8fdbd8730f52ff5ed4cd43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8f180b0f0fcbf29811f39603ecaba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5223ece2f8f76850c49e2505304532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e34fd6b3b3243aa66337886d067021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
您最近一年使用:0次
解题方法
6 . 已知双曲线
的左、右顶点分别为
、
,设点
在第一象限且在双曲线上,
为坐标原点.
(2)若
,求
的取值范围;
(3)椭圆
的长轴长为
,且短轴的端点恰好是
、
两点,直线
与椭圆的另一个交点为
记
、
的面积分别为
、
求
的最小值,并写出取最小值时点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d34cf4ed961f4052ed35c7475c7d32e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58a8ca834f54630a35eec57044a9376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b14123852c3e17f0a519282e076797.png)
(3)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a36a9dc09e4ed89c47993141ea124fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e534b545e86c02abd2a0dc75d32b407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a1568c0bf07f285b2e01c3a3a55900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b1ab746f3773e5989f4d18fb3072a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
7 . 已知
是各项均为正实数的数列
的前n项和,
,若
,则实数m的取值范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55cfe3500a7c74bbe92c6c77a8ce3ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3cb49234c927b2564c980c2bccb4f2.png)
您最近一年使用:0次
2024-03-31更新
|
453次组卷
|
6卷引用:上海市宝山区吴淞中学2024届高三下学期3月月考数学试题
上海市宝山区吴淞中学2024届高三下学期3月月考数学试题1号卷·A10联盟2022届全国高考第一轮总复习试卷数学(文科)试题(十一)江西省南昌市江西师大附中2023-2024学年高二下学期3月月考数学试题(已下线)专题8 数列与不等式恒成立问题(一题多解)四川省成都市玉林中学2023-2024学年高二下学期3月诊断性评价数学试题(已下线)高二数学期末模拟试卷02【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
8 . 设抛物线
,过焦点
的直线与抛物线
交于点
、
.当直线
垂直于
轴时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/4aa9e607-413f-4aea-bdbc-427ada0cd9a0.png?resizew=164)
(1)求抛物线
的标准方程.
(2)已知点
,直线
、
分别与抛物线
交于点
、
.
①求证:直线
过定点;
②求
与
面积之和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544fc1ddf9f59d08c9feb5df9b4080d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e39fda3cda5ddc03b085413f2030aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/4aa9e607-413f-4aea-bdbc-427ada0cd9a0.png?resizew=164)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96499747e4aea990f4b878eea8d73ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
您最近一年使用:0次
2024-02-28更新
|
1076次组卷
|
4卷引用:上海市宝山区吴淞中学2024届高三下学期3月月考数学试题
名校
解题方法
9 . 考虑这样的等腰三角形:它的三个顶点都在椭圆
上,且其中恰有两个顶点为椭圆
的顶点.关于这样的等腰三角形有多少个,有两个命题:命题①:满足条件的三角形至少有12个.命题②:满足条件的三角形最多有20个.关于这两个命题的真假有如下判断,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069ffc1e3936d254303d588e1a70a3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.命题①正确;命题②错误. | B.命题①错误;命题②正确. |
C.命题①,②均正确. | D.命题①,②均错误. |
您最近一年使用:0次
10 . 如图,在棱长为2的正方体
中,点
分别在线段
和
上,给出下列命题:(1)
长的最小值为2;(2)四棱锥
的体积为定值;(3)有且仅有一条直线
与
垂直;(4)存在点
,使
为等边三角形;其中真命题的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
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