1 . 如图,在正四棱柱
中,四边形
是边长为2的正方形,
分别是棱
的中点,
分别是棱
上动点.当直线
与底面
所成角最小时线段
的长度是__________ ,四面体
的体积是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc814fa51a659b3eb6b11ab4770df0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46c696ff5f123a482bae81cf9a1b570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570661f3cd27119447394748b3bae6bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e33929752b1cb4dd36ee9b98b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e33929752b1cb4dd36ee9b98b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cfd0530c5623a89ec6a6652a367e2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/20/264bcff6-4d98-4a29-95dc-bf7e77eb8a9d.png?resizew=135)
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2 . 已知函数
,若直线
是曲线
的切线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ ;若直线
与曲线
交于
,
两点,且
,则
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb4c3b570cb1f80cf3d01b38d8cdd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff26491b344566f7bb04cbb7deb6baa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deee3d8693da1fe9d74749a5fabe7ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 已知正四棱锥
的底面边长为
,侧棱长为2,则该正四棱锥相邻两个侧面所成二面角的余弦值为______ ;该正四棱锥的外接球的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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2023-07-16更新
|
400次组卷
|
4卷引用:福建省漳州市2022-2023学年高一下学期期末教学质量检测数学试题
22-23高二下·福建宁德·期末
名校
解题方法
4 . 设函数
,若
,
恒成立,则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9473df0378e20dbb674d5bd3d698bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-07-16更新
|
538次组卷
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6卷引用:福建省宁德市2022-2023学年高二下学期7月期末数学试题
(已下线)福建省宁德市2022-2023学年高二下学期7月期末数学试题江苏省部分四星级高中2023-2024学年高三上学期期初调研数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期期初调研数学试题江苏省南京外国语学校2023-2024学年高三上学期期中模拟数学试题安徽省淮北市树人高级中学2023-2024学年高二下学期开学考试数学试卷(已下线)专题5 指数对数同构问题【讲】(压轴题大全)
5 . 已知
的内解
所对的边分别为
,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
______ ;若
内有一点
,使得
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f4e4f04a1991a014b77e37f1aeb915.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab1c19b66cda3fb899f06d9a25e973c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae7888d643678ea18f83f3237732052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfeaf26f178031f78a5545233a2a73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858ebd49a89f0269c554b7bc9a3c6606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e879b16b727b9e19517aceaa4c0efc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f4e4f04a1991a014b77e37f1aeb915.png)
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6 . 已知函数
及其导函数
的定义域均为R,若
,
都为偶函数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3feb35ac391ed43c53402c7938bfbbed.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f704425f97fded12f1962eb33e6f66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949dbd290631733ffb77c8413c6ad97e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3feb35ac391ed43c53402c7938bfbbed.png)
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2023-07-11更新
|
434次组卷
|
4卷引用:福建省泉州实验中学2024届高三上学期10月月考数学试题
名校
解题方法
7 . 已知函数
,函数
有三个不同的零点
,且
,则实数
的取值范围是______ ;
的取值范围是______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b307491561ce76e263b1eddd7ff20e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29145ea38299ebe4c2424013b73e2043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628739d6d557640291283f074ffbdad.png)
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2023-07-11更新
|
343次组卷
|
5卷引用:福建省厦门双十中学漳州校区2024届高三上学期10月月考数学试题
福建省厦门双十中学漳州校区2024届高三上学期10月月考数学试题山东省滨州市2022-2023学年高二下学期期末数学试题福建省莆田第二中学、仙游第一中学2023-2024学年高二下学期期中联考数学试题(已下线)模块五 专题2 全真基础模拟2(已下线)重组1 高二期末真题重组卷(山东卷)B提升卷
解题方法
8 .
=___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161e98ff486182015a2f5fe795e6e10b.png)
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9 . 已知定义在
上函数
满足:
,写出一个满足上述条件的函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b711eb80f9577f22a675b81148338fea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
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10 . 已知函数
有三个零点
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a1cbc2cf5b7b5ba8f731e35aeead37.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc5c68b57d4e10c796a45d345ed1c4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed2edae42fa90deb0e4f3d24589a78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a1cbc2cf5b7b5ba8f731e35aeead37.png)
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