解题方法
1 . 已知实数
满足
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c057ea2ec9fef49befe17571794aeb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d4fcb22b9ef5b847927d6d3437e024.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
2 . 有如下条件:
①对
,
,2,
,均有
;
②对
,
,2,
,均有
;
③对
,
,2,3,
;若
,则均有
;
④对
,
,2,3,
;若
,则均有
.
(1)设函数
,
,请写出该函数满足的所有条件序号,并充分说明理由;
(2)设
,比较函数
,
,
值的大小,并说明理由;
(3)设函数
,满足条件②,求证:
的最大值
.(注:导数法不予计分)
①对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de1fa20e0bb8fa1d5a4f4bfc471139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2f24b4fa5308650a244d954f78f09b.png)
②对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de1fa20e0bb8fa1d5a4f4bfc471139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3ecbbaca8eeb1cfa8f4035f7d5726.png)
③对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de1fa20e0bb8fa1d5a4f4bfc471139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c8f1c6b5fa1bd63ca493856b8e600b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5141a62d81c04d7c20f4135cc7f1dbb.png)
④对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de1fa20e0bb8fa1d5a4f4bfc471139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c8f1c6b5fa1bd63ca493856b8e600b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa8e4c6783752d1090385ff08a9f7a7.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38724fa88a08e6b45a5eb248ca8807b9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1c7571006978c5115a9a6bd764698a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ed4309f300802aef509cf52bd754ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da281ccca7c32c2052b29c83383fcc5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb71a578b8da093174f94e14fe4cb4bb.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbdd006d6c6aa4c00282f564718a03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db7f4871ab297375b0e1598479164f5.png)
您最近一年使用:0次
2024-02-23更新
|
511次组卷
|
5卷引用:北京市海淀区北京大学附属中学行知学院2022-2023学年高一下学期期中数学试题
名校
解题方法
3 . 已知函数
的定义域为
.若存在实数
,使得对于任意
,都存在
,使得
,则称函数
具有性质
.
(1)分别判断:
及
是否具有性质
;(结论不需要证明)
(2)若函数
的定义域为
,且具有性质
,证明:“
”是“函数
存在零点”的充分非必要条件;
(3)已知
,设
,若存在唯一的实数
,使得函数
,
具有性质
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cb15d282a40c780c2b68287e47867e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce602f345fcda5fe07be7237af78cdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbde2170c24819edd47db617810bf47.png)
(1)分别判断:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6342e0a5a8942cfb1cf535ceb2c50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba837ccb2f36f9dcef19706e5a1f27.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c2b4e2e5fc950391a87556e0c24577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b1cddd7e5a1be825ca185ee0243fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbde2170c24819edd47db617810bf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d57778bc0e184610f507559a89d96c2.png)
且
是奇函数.
(1)当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
为自然对数底数)时,解不等式:
;
(2)关于x的不等式
解集中有且仅有3个整数,讨论实数n的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d57778bc0e184610f507559a89d96c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d74d706d2e4392e25016e9101d07ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18375771aceaae2c20130efa961bb12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c04e8f899f16999d2068364f1b81e71.png)
(2)关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971183b60f6287e9b39bcf5d21dcba85.png)
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解题方法
5 . 定义在D上的函数
,如果满足:存在常数
,对任意
,都有
成立,则称
是D上的有界函数,其中M称为函数
的上界.
(1)判断函数
是否是
上的有界函数并说明理由;
(2)已知函数
,若函数
在
上是以4为上界的有界函数,求实数a的取值范围;
(3)若
,函数
在区间
上是否存在上界
,若存在,求出
的取值范围,若不存在请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea232de27d21a2646fd4520ea0726bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee40803bfd576cf49b85c8b567fc5b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec10b6e8f27dbd5828fe782565f6d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03e44339cab84ec913c77675935f763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0058182e412897c5f51e8360a43c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0058182e412897c5f51e8360a43c0c.png)
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解题方法
6 . 知函数
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7192d87d0fa400d5d7dba57924bbbe3.png)
A.若x为锐角,则![]() |
B.![]() |
C.方程![]() ![]() |
D.方程![]() |
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名校
解题方法
7 . 已知函数
和
的定义域分别为
和
,若对任意
,恰好存在
个不同的实数
,使得
(其中
),则称
为
的“
重覆盖函数”.
(1)判断
是否为
的“
重覆盖函数”,如果是,求出
的值;如果不是,说明理由.
(2)若
为
的“2重覆盖函数”,求实数
的取值范围;
(3)函数
表示不超过
的最大整数,如
.若
为
的“5重覆盖函数”,求正实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eddf991be37d25d033f78bd3511809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d5df7922a4e98e8e07bf418dd48a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44a5aed663a9b61ef7355b38c77d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9870d9b876542c26c7fba4f7076313a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dccee4b9a920071470ebff237be05dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6cfa19dda8748dba2d549d885def27d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5b1a2cc7ff59a5d7b500f84ae4bb13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f3417c317fecfdb3895460a6867630.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d82bab9f2808b11904d680eae089356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63dd6c8dd0f888235902849d9d7b2ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353e46e2ea602f47eda40d420e633af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 已知函数
为常数).函数
定义如下:对每个给定的实数
.
(1)若
,求
在
上的最大值;
(2)若
且
,求函数
在区间
上的单调增区间的长度之和.(闭区间
的长度定义为
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095878335d1f0c342afc4a2a300edfe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f842876e8f512903598574fa62e86e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e1c681b27df538bd4742f6cd8298ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575002003f89bc8309a2c7f206761794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa21416f901e005780f383fb029e86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede949a2fe7bf9f1f98f5457d408b41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
您最近一年使用:0次
2023-11-18更新
|
746次组卷
|
2卷引用:浙江省宁波市镇海中学2023-2024学年高一上学期11月期中考试数学试题
名校
解题方法
9 . 已知函数
(
且
),若
,
是假命题,则实数a的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2fce82d8b7bf78e4325fbfab8fc5f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37681b22f24c571f1a8e5ec2bfaa0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0858003218792d1824757534478b8c.png)
您最近一年使用:0次
2023-09-27更新
|
1374次组卷
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7卷引用:高一数学上学期期中考试模拟卷
(已下线)高一数学上学期期中考试模拟卷湖南省邵阳市第二中学2023-2024学年高一上学期基础知识竞赛数学试题河北省尚义县第一中学等校2024届高三上学期9月联考数学试题重庆市北碚区西南大学附属中学校2024届高三上学期11月期中数学试题(已下线)北京市第四中学2024届高三上学期10月月考数学试题变式题11-15安徽省江南十校2024届高三联考信息卷数学模拟预测卷(一)(已下线)专题11 不等式恒成立、能成立、恰好成立问题(过关集训)
名校
10 . 已知指数函数
满足
.
(1)求
的解析式;
(2)设函数
,若方程
有4个不相等的实数解
.
(i)求实数
的取值范围;
(i i)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff1bd5b2a54dd2a75ef06da67134511.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fc80bf7788fa16d89e381455476c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3de7ba1d8ceff5bec47ae0636b6a3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
(i)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(i i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d131856631aca8c08e326881caf776.png)
您最近一年使用:0次
2023-01-10更新
|
948次组卷
|
3卷引用:江苏省南通市通州区2022-2023学年高一上学期期末数学试题