1 . 已知函数
.
(1)证明:
,有
;
(2)设
(
),讨论
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2827943eee7716dc5609485eef4f846a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cc25a7cf28ed096549fbae97fce40a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1635473a4200e29e0cd13dffa54f7571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
2 . 已知函数
.
(1)讨论函数
的单调区间;
(2)若
为函数
的极值点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a32017ba8a1d4613cfd9ec6d030d016.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd4a25c61167cd73dd176d2c39b4b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07238e4e1f21841ecc5a8daaf3b5ade.png)
您最近一年使用:0次
2023-08-20更新
|
470次组卷
|
2卷引用:西藏昌都市第一高级中学2023届高三高考全真仿真考试数学(理)试题
名校
解题方法
3 . 已知函数.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fc14e0e9de52e4d6a36af83854f15f.png)
您最近一年使用:0次
2023-08-13更新
|
592次组卷
|
5卷引用:西藏自治区拉萨市2024届高三一模数学(理)试题
解题方法
4 . 《九章算术·商功》:“斜解立方,得两堑堵.斜解堑堵,其一为阳马,一为鳖臑.阳马居二,鳖臑居一,不易之率也.合两鳖臑三而一,验之以棊,其形露矣.”刘徽注:“此术臑者,背节也,或曰半阳马,其形有似鳖肘,故以名云.中破阳马,得两鳖臑,鳖臑之起数,数同而实据半,故云六而一即得.”
如图,在鳖臑ABCD中,侧棱AB⊥底面BCD;
(1)若
,
,
,试求异面直线AC与BD所成角的余弦值.
(2)若
,
,点P在棱AC上运动.试求
面积的最小值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/22/84152742-e106-43ca-a408-c3b4449bce08.png?resizew=416)
如图,在鳖臑ABCD中,侧棱AB⊥底面BCD;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/22/6476cb57-a508-4f63-868c-6a74790b42f7.png?resizew=301)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9c7cbcc38b28d45c8539710e5b260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e1ab67f8e48ad3340cf9d165cd75f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
您最近一年使用:0次
解题方法
5 . 已知椭圆
:
(
)的左、右焦点分别为
,
,
是椭圆
上异于左、右顶点的动点,
的周长为6,椭圆
的离心率为
.
(1)求椭圆
的标准方程;
(2)若圆
与
的三边都相切,判断是否存在定点
,
,使
为定值.若存在,求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](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/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.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/ea0200b028c8a4e40b9987a4b1d5e486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
您最近一年使用:0次
名校
6 . 对任意的
,不等式
恒成立,则实数
的取值集合是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5663adc9b7b68dcf3557efcc35a2ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-04-18更新
|
577次组卷
|
4卷引用:西藏拉萨市2023届高三一模数学(理)试题
解题方法
7 . 已知函数
.
(1)求曲线
在
处的切线方程
,并证明:当
时,
恒成立;
(2)若
有两个不同的实数根
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/586ac14c735533a982d8029c21e4f09b.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a06acf17d7c28fa264c03224226951b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684bcf84f0a266515bfafde0da903050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a797b151c88c427c45b142e4eb5405e1.png)
您最近一年使用:0次
8 . 已知用周长为36的矩形截某圆锥得到椭圆
与矩形的四边都相切且焦距为
,__________.
①
为等差数列;②
为等比数列.
(1)在①②中任选一个条件,求椭圆的标准方程;
(2)(1)中所求
的左、右焦点分别为
,过
作直线与椭圆
交于
两点,
为椭圆的右顶点,直线
分别交直线
于
两点,求以
为直径的圆是否过定点,若是求出该定点;若不是请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b428e657cfaa28a1d5a151a256493ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dcc91c2ffb5571eaf944c34f5e8ffe.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f8721d6b1c5504e9945af537390de9.png)
(1)在①②中任选一个条件,求椭圆的标准方程;
(2)(1)中所求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d021e137803a9ad95ec600a33e5662a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2023-02-17更新
|
865次组卷
|
7卷引用:西藏日喀则市2023届高三第一次联考模拟数学(文)试题
西藏日喀则市2023届高三第一次联考模拟数学(文)试题西藏日喀则市2023届高三第一次联考模拟数学(理)试题山西省临汾市2023届高三下学期第一次高考考前适应性训练数学试题(已下线)模块十二 解析几何-2(已下线)专题16圆锥曲线(解答题)(已下线)专题15 圆锥曲线综合(已下线)专题7-4圆锥曲线五个方程型大题归类-2
名校
9 . 在数学中,布劳威尔不动点定理是拓扑学里一个非常重要的不动点定理,它可应用到有限维空间,并且是构成一般不动点定理的基石.简单地讲就是对于满足一定条件的连续函数
,存在点
,使得
,那么我们称该函数为“不动点”函数.若函数
为“不动点”函数,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069951b1d05cecf782b8c9d9f6cf0d89.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-12-09更新
|
1119次组卷
|
5卷引用:西藏日喀则市2023届高三第一次联考模拟数学(文)试题
西藏日喀则市2023届高三第一次联考模拟数学(文)试题河南省开封市2023届高三年级第一次模拟考试文科数学试题 (已下线)第二篇 函数与导数 专题7 函数不动点定理 微点2 函数不动点定理综合训练上海市延安中学2022-2023学年高二下学期期中数学试题(已下线)模块二 情境9 经典数学问题
名校
10 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,若关于x的不等式
恒成立,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3960dc7474b60e405b6a9f5e3cb483ac.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b3cacc24c7cd34a4a7c20292ad5382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14be21f2377d2f42ba3fd5e62ff3e1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed7aeaf9930f1d650f8acb0356b233b.png)
您最近一年使用:0次
2022-03-16更新
|
739次组卷
|
7卷引用:西藏林芝市第一中学2020届高三上学期模拟考试数学(理)试题
西藏林芝市第一中学2020届高三上学期模拟考试数学(理)试题广西南宁市东盟中学2021届高三5月考数学(理)试题广西南宁市东盟中学2021届高三5月考数学(文)试题西藏林芝市、日喀则市2021届高三下学期第二次联考数学(文)试题河北省邯郸市大名县第一中学2022届高三上学期强化训练(三)数学试题(已下线)第06讲 函数的单调性-【帮课堂】2021-2022学年高二数学同步精品讲义(人教A版2019选择性必修第二册)(已下线)5.3.1 函数的单调性(3)