21-22高三上·北京·期中
名校
1 . 已知函数
.
(1)求
的单调递增区间;
(2)若
在区间
上的最大值是
,求
的取值范围;
(3)令
,如果曲线
与直线
相邻两个交点间的距离为
,求
的所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f734c7bab5a46c252054c0c7c58c1c38.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb37d173605f006df4c51ba63b1841d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2665cce8924f0d96c37e25ffdc982d7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d74c0570f3ef4fff3e0ba34204f8d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
您最近一年使用:0次
名校
2 . 已知函数
,
.
(Ⅰ)求证:曲线
在点
处的切线方程与实数
的取值无关;
(Ⅱ)若
对
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f2544eee2be0a0880d60cc4c22ed61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(Ⅰ)求证:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd78eaaea022ca802d231c741ac2779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-11-07更新
|
544次组卷
|
3卷引用:北京大学附属中学2021届上学期高三阶段性检测数学试题
3 . 数列
中
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6a2f1bfdc4c1f262d7775ad7f6ce4e.png)
(1)
时,求
;
(2)证明:若存在
,其中
,设
的取值范围设为
,
;
(3)若
,求
的取值个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e076d53e0fab96afda46ff7ac1689dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6a2f1bfdc4c1f262d7775ad7f6ce4e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3129ddd2ea97fd010b9e0b644225da8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6fe44bc49b478979589face327799.png)
(2)证明:若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd42f8e3f220a7b1c6f6945e73bc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153fb853cd99beec9e600a4eaf73fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5b5f7e398a382c96b3bdcb0b4b2a6f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc473418716524061f271116d3f0b065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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4 . 设
,函数
,函数
,
.
(Ⅰ)判断函数
在区间
上是否为单调函数,并说明理由;
(Ⅱ)若当
时,对任意的
, 都有
成立,求实数
的取值范围;
(Ⅲ)当
时,若存在直线
(
),使得曲线
与曲线
分别位于直线
的两侧,写出
的所有可能取值. (只需写出结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e4b994dbe43b3dc59409507791ae05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b44ce1f38097acac14cd28b5dc07fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096f1be1cd0f6fb6856e9d147f076c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db2eb29042782efa4f96d82e6aa35d6.png)
(Ⅰ)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a141e697b1a31a9a4e759984e899a5.png)
(Ⅱ)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9234e2ee3ebf72645582a8319a0168b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bd3b259fabe06824f1abeca77a3dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c61ed9bb08a0a1bfff16f95ea95098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307da948a9e2f6f48cf86295bff9a61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f869c504d225b642b67137595a8be7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
5 . 已知函数
(
)在其定义域内有两个不同的极值点.
(I)求a的取值范围;
(II)记两个极值点分别为
,且
.已知
,若不等式
恒成立,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5124251b521fb2525f55b99ee9ff6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(I)求a的取值范围;
(II)记两个极值点分别为
![](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/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5def2e680848aaf69b5a8c0f50ce05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2016-12-04更新
|
781次组卷
|
10卷引用:北京东城五中2017-2018学年高三上期中数学真题卷
2014·江西宜春·一模
名校
解题方法
6 . 已知函数
,
.
(1)若
在区间
上不是单调函数,求实数
的范围;
(2)若对任意
,都有
恒成立,求实数
的取值范围;
(3)当
时,设
,对任意给定的正实数
,曲线
上是否存在两点
,
,使得
是以
(
为坐标原点)为直角顶点的直角三角形,而且此三角形斜边中点在
轴上?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c067e6d907f6c0fdfa9be70bbc027595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2905c314cbffa446435bd56c760097e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99f1bc6895934a9e2a6d659383ded9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6eefb2d02e54ce0ce4c9931ef774b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd94098e98d90588cb74c1429033a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efd09912705e08177bc86e839c41b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次
2016-12-03更新
|
2201次组卷
|
7卷引用:【全国百强校】北京市第四中学2019届高三高考调研卷(二)文科数学试题
【全国百强校】北京市第四中学2019届高三高考调研卷(二)文科数学试题(已下线)2014届江西省宜春市高三考前模拟理科数学试卷(已下线)2015届山东省淄博实验中学高三第一次诊断性考试理科数学试卷湖南师大附中2019届高三月考试题(七)数学(文)【市级联考】江西省萍乡市2019届高三一模考试数学(文)试题湖南师范大学附属中学2018-2019学年高三第七次月考数学(文)试题山东省济宁市第一中学2020届高三考前冲刺测试(一)数学试题
7 . 已知关于
的不等式
的解集是
.
(1)若
,求实数
的取值范围;
(2)若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc657da2ede4b9cb3c91c0d8a4bfabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681068041dd133845a2a5c79214eefe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d07972d88302df1ae58b765103548e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f48697046ef1531aaaf9e18cfb27254.png)
您最近一年使用:0次
名校
8 . 已知
,函数
,当
时,不等式
的解集是________________ .若函数
恰有2个零点,则
的取值范围是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1158df70ea7d665cd0a43fe98ba11375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-09-09更新
|
221次组卷
|
3卷引用:北京市第八十中学2023-2024学年高三上学期10月月考数学试卷
名校
解题方法
9 . 已知函数
给出下列四个结论:
①若
有最小值,则
的取值范围是
;
②当
时,若
无实根,则
的取值范围是
;
③当
时,不等式
的解集为
;
④当
时,若存在
,满足
,则
.
其中,所有正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff4e0cfa86f6d91ff0b3cdb3251393b.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6cc71d0c988d725b25c55c2672919c.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976d18a5396ba232f0aa38d136f1d749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1606791e5eeefbf298210543e01dd4.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5bcfb3bafe8373dd907e0e55d08f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168fef6477a494abceae56fb6c2e4c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339de01d9636343c484391b421c31301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec808ad60dbf016632ec816eaca1df.png)
其中,所有正确结论的序号为
您最近一年使用:0次
2023-11-02更新
|
825次组卷
|
5卷引用:北京市第一零一中学2024届高三上学期10月月考数学试题
名校
10 . 设函数
,
①若
,则不等式
的解集为___________ ;
②若
,且不等式
的解集中恰有一个正整数,则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711a65c36cdd87a7cdf26f9b84e5c49b.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3b43fb07a1d631b294dbf6f0f58713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a023ef8a7a5d94029b08b4cb30422e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-05-05更新
|
1054次组卷
|
3卷引用:北京市海淀区2023届高三二模数学试题