名校
1 . 已知函数
,其中
,函数
在
上的零点为
,函数
.
(1)证明:
①
;
②函数
有两个零点;
(2)设
的两个零点为
,证明:
.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7495c0f25cf04e5e59bb4ae43ffc4fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c940cb46e4a6eae0b7172414c965b66f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c353f6bf5422164ef1496838ba1e6de0.png)
(1)证明:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffa38ec984cae2089a6061c5b231dc5.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f127c78da4fd62e8e98f2262400bda.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2995cf1665e01b853555e62aeaf0ac31.png)
您最近一年使用:0次
2022-12-16更新
|
1827次组卷
|
4卷引用:T8(华师一附中、湖南师大附中等)2023届高三上学期第一次学业质量评价数学试题
2022·全国·模拟预测
名校
2 . 已知
,
,
是互不相等的非零向量,其中
,
是互相垂直的单位向量,
,记
,
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff983823af408d32b203381c8f86665d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14390e9b6b44472bdc7a131133ab39b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cd14dfc0024459f9d8e594c95c5106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07dcf0b16163e0e0e0c0f248466ee7e.png)
A.若![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2022-12-05更新
|
1172次组卷
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4卷引用:2023年普通高等学校招生全国统一考试数学领航卷(九)
(已下线)2023年普通高等学校招生全国统一考试数学领航卷(九)黑龙江省牡丹江市第一高级中学2022-2023学年高一下学期4月月考数学试题黑龙江省哈尔滨市第九中学校2023-2024学年高一下学期4月月考数学试题浙江省温州中学2023-2024学年高一下学期期中考试数学试题
2022·全国·模拟预测
解题方法
3 . 已知函数
,
.
(1)当
时,求证:
.
(2)令
,若
的两个极值点分别为m,n(m<n).
①当
时,求曲线
在
,
处的切线方程(
为
的导函数);
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a39fb4746011157bdfceae7315ea11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959e6ffc5dac0d71aa0393c0877dc91f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a6252e652cf095ea30565dc53dee64.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4633de9335d15d7685bdecb007a3678c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adca47fb3667e6707265f5279688cf1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be7302f2e9ff02fee3fcf26e77b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c985d6a1e024804ccd86092e4e020cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628255703e0ab0e9eed8106850e81bb.png)
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名校
4 . 已知函数
.
(1)当
时,对任意的
,令
,求
关于
的函数解析式,并写出
的取值范围;
(2)若关于x的方程
有3个不同的根,求n的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7377b0ccd2e4c7a69919758edfc40ef.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8beee95c6754ae92beb5b5765599744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec18b3959c5e7d6cf9c79064e285ff15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
您最近一年使用:0次
2022-11-08更新
|
1868次组卷
|
9卷引用:四川省成都市第七中学2022-2023学年高一上学期期中数学试题
四川省成都市第七中学2022-2023学年高一上学期期中数学试题第4章 指数概念与对数函数(基础、典型、易错、新文化、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)(已下线)第二篇 函数与导数专题5 切比雪夫、帕德逼近 微点4 切比雪夫逼近与帕德逼近综合训练(已下线)第13讲函数的应用(二)(5大考点)(1)(已下线)专题4.9 指数函数与对数函数全章综合测试卷(提高篇)-举一反三系列(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】(人教A版2019必修第一册)湖南省永州市祁阳市第一中学2023-2024学年高一上学期第一次段考数学试题广东省深圳市宝安区2022-2023学年高一上学期期末数学试题浙江省湖州市长兴县雉城中学2023-2024学年高一上学期期末数学复习卷一
2022高三·全国·专题练习
5 . 已知
,
分别是椭圆的左、右焦点,B为椭圆上一点,延长
到点A,满足
,
的中点为H,则下列两个结论是否正确:结论1:
;结论2:BH为椭圆的切线.
![](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/4c429b542abf0ebee74a239b4857cf88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798a7e5c77491778e51f61844699c57a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c34f36a5ea5950cfaa9cdae38602081.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/58898a54-dbe4-47f4-a686-cc6532fde891.png?resizew=195)
您最近一年使用:0次
6 . 设
为实数,定义
生成数列
和其特征数列
如下:
(i)
;
(ii)
,其中
.
(1)直接写出
生成数列的前4项;
(2)判断以下三个命题的真假并说明理由;
①对任意实数
,都有
;
②对任意实数
,都有
;
③存在自然数
和正整数
,对任意自然数
,有
,其中
为常数.
(3)从一个无穷数列中抽出无穷多项,依原来的顺序组成一个新的无穷数列,若新数列是递增数列,则称之为原数列的一个无穷递增子列.求证:对任意正实数
生成数列
存在无穷递增子列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796bb39a2ab23cfdb6e463ab30a7af2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4758b555ca9b157cc074f1e4a092e34a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f61c0bb2370087736c8e00e108b48c8.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c051dc675bcca6a8f70a3dbe922354.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3121951a9b059eef49b4a346d3aa2b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400b893304c51631873ded41027cf48.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e0c84de10f0f2186313169c3dc997b.png)
(2)判断以下三个命题的真假并说明理由;
①对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fbdf49cd00af1ff87259836ddd9f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508cd31480a898a71472e2d5d22377c7.png)
②对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fbdf49cd00af1ff87259836ddd9f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c99515d9952f2f7739fd750a31128f.png)
③存在自然数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a178f2c27906fc74afee1b7d7d52746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1563da7b0f046a469476668a3686e8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59a60eb4d63ebc879ae5c26413bcdcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)从一个无穷数列中抽出无穷多项,依原来的顺序组成一个新的无穷数列,若新数列是递增数列,则称之为原数列的一个无穷递增子列.求证:对任意正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da069077c220af26b9e77b02baeee4a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4758b555ca9b157cc074f1e4a092e34a.png)
您最近一年使用:0次
名校
解题方法
7 . 对于集合A,称定义域与值域均为A的函数
为集合 A上的等域函数.①若
,则A上的等域函数有_______ 个;②若
,使
为A上的等域函数,a的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9a1e9dd14cbd2271ba2f472664ad57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c98e68600297a331aa206425a138ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c92b9847324883eeaa7002c72e7cd81.png)
您最近一年使用:0次
2022-11-04更新
|
788次组卷
|
3卷引用:北京市海淀区中国人民大学附属中学2022-2023学年高一上学期期中练习数学试题
8 . 已知双曲线E:
(
,
)一个顶点为
,直线l过点
交双曲线右支于M,N两点,记
,
,
的面积分别为S,
,
.当l与x轴垂直时,
的值为
.
(1)求双曲线E的标准方程;
(2)若l交y轴于点P,
,
,求证:
为定值;
(3)在(2)的条件下,若
,当
时,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ab02a01fa41c784b688575fe90539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74110bc818c2f5a53d63451c5251eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436a2732e9c9d5ce401c448cd9de80e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b72cb228a0747bf4b779cc337749a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3a5255a0a61f4d297874ecd1967b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b690956d61cb5a9f955a87093856eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc2628ebeec39f2ff82e216e780e3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9cdbc51da77d74d60ef8e2878fa2dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac8a4086cd8af00e89c57fdfd905114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd72016a9855cbf0056ff732fe872612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac8a4086cd8af00e89c57fdfd905114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa84eb397ffcbbf3a26d95e50f0e7db.png)
(1)求双曲线E的标准方程;
(2)若l交y轴于点P,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8f34c9aba5a3834c8d2c76701366c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ccee36f0ebe053f4bd976b31aab0efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff141a77e796894f84d0104f8f947e8a.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165e3984c374e63ff90022b333efa103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a11319d09d138b1ecc48692209ceec.png)
您最近一年使用:0次
2022-10-25更新
|
2089次组卷
|
5卷引用:重庆市第八中学校2023届高三上学期高考适应性月考(二)数学试题
名校
9 . 如图,在五面体
中,底面
为矩形,
和
均为等边三角形,
平面
,
,
,且二面角
和
的大小均为
.设五面体
的各个顶点均位于球
的表面上,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/9922bed7-bbff-4246-a837-64a6972fd2e9.png?resizew=215)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a04a2b317c5a6b8b7eb5d760fbd818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e2bf04b646d77e272034198d21a1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5219d5b2c63eded763670e5800dd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ba310682e25a0c6d488e6aff816614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5292af357a9c81f104ff2237053a4d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c2044ecc165365634e21f3e95ec7f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8b7a29b332ac3a192a2c19efa1f886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadd8e8730b81d153ffa6c55a3ac68e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a04a2b317c5a6b8b7eb5d760fbd818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/9922bed7-bbff-4246-a837-64a6972fd2e9.png?resizew=215)
A.有且仅有一个![]() ![]() |
B.有且仅有两个![]() ![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() |
您最近一年使用:0次
2022-10-11更新
|
2326次组卷
|
6卷引用:浙江省杭州学军中学2022-2023学年高二上学期期中模拟数学试题
浙江省杭州学军中学2022-2023学年高二上学期期中模拟数学试题(已下线)专题06 一网打尽外接球与内切球问题(精讲精练)-3湖北省云学新高考联盟学校2022-2023学年高二上学期10月联考数学试题2023年普通高等学校招生星云线上统一模拟考试Ⅰ数学试卷(已下线)模拟卷02广东省广州七中2023届高三上学期1月月考数学试题
10 . 已知函数
.
(1)若
存在两个极值点
,
,求
的取值范围;
(2)若
,证明:当
时,函数
在
上有
个零点.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836c9a0f2574ab8e06dcb19aede1c015.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/c847f857b8d1788d4ba414b82840ef5e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/474eb9ce16cccdd7173bbae1df2c6680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04bc9df77bcb5daee8c8663d094cbc1d.png)
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