1 . 已知函数
,
.
(1)讨论函数
的单调性;
(2)若
,且对任意
(其中
)都有
,求实数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e99119d426e266f76b858b0bfb1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46844bfd93548d0f3e7338b02921849.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574c9d9c90d4ef56d665cf8413975c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a65cccb4906515dcf25d662176a86dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . 已知函数
,若存在实数
,满足
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d9d16ded71a64119d8833c2f2c3854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f74cb3f9906bdbb0e6d9cf69fa2190b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81a4c1e314c88a485aada08d9be2031.png)
您最近一年使用:0次
2023-07-08更新
|
847次组卷
|
5卷引用:广东省东莞市2022-2023学年高二下学期期末数学试题
广东省东莞市2022-2023学年高二下学期期末数学试题黑龙江省大庆市萨尔图区第二十三中学2022-2023学年高二下学期期末数学试题江苏省南京师范大学苏州实验学校2023-2024学年高三上学期7月阶段性调研数学试题(已下线)模块二 专题2 导数 A基础卷(人教A)(已下线)考点2 分段函数 2024届高考数学考点总动员 (讲)
3 . 甲、乙、丙、丁4名志愿者参加创文巩卫志愿者活动,现有
三个社区可供选择,每名志愿者只能选择其中一个社区,每个社区至少一名志愿者,则甲不在
社区的概率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e30c0a5c92f50dce1f7624709950ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-07-08更新
|
369次组卷
|
2卷引用:广东省茂名市2022-2023学年高二下学期期末数学试题
4 . 已知函数
.
(1)当
时,求
在点
处的切线方程;
(2)若
有两个零点
,求实数
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2265e7209eee6b98cd2484d68d9b427b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df5ab740f56f319c91c2a7a83013e2f.png)
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解题方法
5 . 在棱长为2的正方体
中,动点
满足
,其中
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6b545127bd51036a5a7b0d3cd5b320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() |
D.有且仅有两个点![]() ![]() |
您最近一年使用:0次
2023-07-08更新
|
395次组卷
|
3卷引用:广东省佛山市普通高中2022-2023学年高一下学期期末数学试题
6 . 在
中,
,将
分别绕边
,
,
所在直线旋转一周,形成的几何体的侧面积分别记为
,
,
,体积分别记为
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2217dfd3de10c834acb8aea9ec9e3a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040e42893ef55c07146018f4013550f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0d979724886e8312e4135bc5e8e6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e29d496af9b75c1cba59c089ffb1dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d257782662b2fc1658523ea79d0d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d247755e1b97bb243d7146801c13267.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
7 . 如图,在棱长为4的正方体
中,
为
的中点,经过
,
,
三点的平面记为平面
,点
是侧面
内的动点,且
.
,求证:
;
(2)平面
将正方体
分成两部分,求这两部分的体积之比
(其中
);
(3)当
最小时,求三棱锥
的外接球的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7146a372ce6a346fae937622a89d6589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021a0a080f9ce719709a73a46c3459de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e0bdfd5676792840d607096ae0555b.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1daf42c1a89bda5f17ce22e49dda533.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8049311621004b8d0f2637d13010db7.png)
您最近一年使用:0次
8 . 如图,已知长方体
的三条棱长分别为
,
,
,
,
,
为常数,且满足
,
.点
为
上的动点(不与
,
重合),过点
作截面
,使
,
分别交
,
于点
,
.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d42e97eee705d164e6ac6de9ecd6d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a88b719166fcc1431f876bc8c5656c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8c82a8fc85d59983aec24a60485ad2.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/d2c659396f6a0f72e213185b1ab2e198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18af922d7bcd7a1bfbd89398d86eda5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe02e0d5ca5bb845c0d22f30e6a3af6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/11/3f0987be-b642-4af9-bed2-2162aebd45b7.png?resizew=114)
A.截面![]() | B.截面![]() |
C.存在点![]() ![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 已知函数
在点
处的切线方程为:
.
(1)求实数a,b的值;
(2)证明:
;
(3)若方程
有两个实数根
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e43c48834ba7d527e4314281cfe6a80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d983f1213ce474227e80c41d7fba6374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(1)求实数a,b的值;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf53f2c62deafc1c3d79c84122aeaeb.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb2e46f49adba6036e2624639a1b966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cd30fa62f6b73633cfbf66b5a6bc6e.png)
您最近一年使用:0次
2023-07-08更新
|
341次组卷
|
3卷引用:广东省梅州市2022-2023学年高二下学期期末数学试题
解题方法
10 . 已知随机变量
的取值为不大于n的正整数值,它的分布列为:
其中
满足:
,且
.定义由
生成的函数
.现有一个装有分别标记着1,2,3的三个质地均匀和大小相同小球的箱子,若随机从箱子中摸出一个球,记其标号为
,由
生成的函数为
,
;若连续两次有放回的随机从箱子中摸出一个球,记两次标号之和为
,此时由
生成的函数为
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
1 | 2 | |||
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c635004284b1a7a03967f3daaf41c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475c0990ebac8c24ea0cbfc7a79e3f63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11eb77d5348ea270cae8e679b410ad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c020a5a9b3c8fe9f6f04cf5d5ab66a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebef85c05f6d84ceb67d92abf77ba2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af0f47ecd097ee9a5b89932c8cb9cbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ace630100e64ed290d82936ad249c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f134d219f03890bcca95b2dac11759.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次