名校
1 . 已知函数
.
(Ⅰ)若
,求
的单调区间;
(Ⅱ)是否存在实数
,使得
的最小值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fe7f3e7af7c1899cad2c8db79ac766.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed670b1f668778c6243f3f7470ee7d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(Ⅱ)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
2 . 定义在R上的函数
,当
时,
,且对任意的
都有
.
(Ⅰ)求证:
是R上的增函数;
(Ⅱ)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db40d5295942e85ec07a3728c7ad308d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402dc8125eed2dac02913f5eaaf7fc5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9308bb553e88185db6f98a757f0aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01948906f3b7096a102f2b52d1ccbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb81baf89ef03f986cc1e41aaa5b3ce.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
(Ⅱ)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b53901a96f93dce5b59b117f78eaa4d.png)
您最近一年使用:0次
2019-01-08更新
|
748次组卷
|
2卷引用:福建省泉州市南安第一中学2017-2018学年高一上学期期中考试数学试题
3 . 已知向量
,函数
的最小值为
.
(1)当
时,求
的值;
(2)求
;
(3)已知函数
为定义在上的增函数,且对任意的
都满足
,问:是否存在这样的实数
,使不等式
对所有
恒成立,若存在,求出
的取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48a908ba3b4cfdd7214e8d2a5f2058d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f6c6915a9efda53dee8443337af8bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1987ecbd076d89da5ef1e2561d79d857.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1987ecbd076d89da5ef1e2561d79d857.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1987ecbd076d89da5ef1e2561d79d857.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2101050389dd439511d14dcbaa829637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0fcb2ae19e92827bce37e8942e0b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce64c8664618915a32b8ae004e68c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2018-07-05更新
|
1498次组卷
|
4卷引用:福建省长汀、连城、上杭、武平、永定、漳平一中六校2016-2017学年高一年下学期期中联考数学试题
4 . 已知圆心在
轴上的圆
与直线
切于点
.
(1)求直线
被圆
截得的弦长;
(2)已知
,经过原点,且斜率为正数的直线
与圆
交于
两点.
①求证:
为定值;
②若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bba5922f974abd7883d7a5dcddb8e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ef056e640b447c4a7c6ad5372831d6.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa104036e085e83aeee77bd84f21499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612ddc716903a6e71d88e8dd377c822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976a13bcc46b77df6805d88275b3616b.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fef976a0230bdfe3bc758e93987ba8.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c705887eb3c4f31eb3d43e9ae8e5c9ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
您最近一年使用:0次
2017-02-17更新
|
61次组卷
|
2卷引用:2016-2017学年福建省南平市高一上学期期末质量检查数学试卷
解题方法
5 . 已知函数
是偶函数.
(1)求
的值;
(2)若
,求
的取值范围;
(3)设函数
,其中
.若函数
与
的图象有且只有一个交点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb165f6f9fe5908cb2ac7e9f988c8f92.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13319759ccc41989d123904c7c47c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd5988b69a792a8de6c513f03dd281d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](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/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
6 . 若函数
满足下列条件:在定义域内存在
,使得
成立,则称函数
具有性质
;反之,若
不存在,则称函数
不具有性质
.
(Ⅰ)证明:函数
具有性质
,并求出对应的
的值;
(Ⅱ)试分别探究形如①
(
)、②
(
且
)、③
(
且
)的函数,是否一定具有性质
?并加以证明.
(Ⅲ)已知函数
具有性质
,求
的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c3f77c4d399c6ce669406032c7b7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅰ)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(Ⅱ)试分别探究形如①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.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/82869dad28f771d088772a2c2b08b187.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/ac047e91852b91af639feec23a9598b2.png)
(Ⅲ)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d17ccc5aa295cfc6b892cd45986fd25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
7 . 定义在
的函数
满足:①当
时,
;②对任意
,总有
.
(1)求出
的值;
(2)解不等式
;
(3)写出一个满足上述条件的具体函数(不必说明理由,只需写出一个就可以).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0606c4ffcfe6f4709155d1e8671ee57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db51af23fe06951a95cc040644f6b253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f174ccd8cac2694c230b1764be2c81.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7846930759271646d8ee762dfd38ed.png)
(3)写出一个满足上述条件的具体函数(不必说明理由,只需写出一个就可以).
您最近一年使用:0次
2017-12-08更新
|
560次组卷
|
2卷引用:福建省厦门市双十中学2017-2018学年高一上学期期中考试数学试卷
名校
8 . 已知函数
的图象过点
.
(1)求
的值并求函数
的值域;
(2)若关于
的方程
有实根,求实数
的取值范围;
(3)若函数
,则是否存在实数
,使得函数
的最大值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821477acdf93de938c08d3a1cc2e9832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eca0b64bb0fbfbcf6bcc2926f401aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3096ca57200cf8cb9457b1c97fc7b495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2017-11-22更新
|
1782次组卷
|
9卷引用:福建省福州市八县一中(福清一中,长乐一中等)2017-2018学年高一上学期期中考试数学试题
福建省福州市八县一中(福清一中,长乐一中等)2017-2018学年高一上学期期中考试数学试题福建省福清华侨中学2018-2019学年高一下学期期中考试数学试题安徽省淮南市第二中学2017-2018学年高一上学期期末考试数学试题(已下线)期中重难点突破专题01-【尖子生专用】2021-2022学年高一数学考点培优训练(人教A版2019必修第一册)湖南省常德市汉寿县第一中学2023-2024学年高一上学期12月月考数学试题河南省南阳市新野县第一高级中学校2023-2024学年高一上学期期末预测数学试题(一)辽宁省盘锦市高级中学2017-2018学年高二下学期期末考试理数试卷安徽省滁州市定远县育才学校2018-2019学年高二(实验班)下学期期末考试数学(文)试题(已下线)考点12 指数与指数函数(考点专练)-备战2021年新高考数学一轮复习考点微专题
名校
9 . 已知
.
(1)设
,
,若函数
存在零点,求
的取值范围;
(2)若
是偶函数,设
,若函数
与
的图象只有一个公共点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f2491e5537940eaeec5978cc8e961.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0384a0466920e5bf00231a5c5bf77969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/739ddca433c4b5f3935ebfda60770f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2017-12-08更新
|
1079次组卷
|
6卷引用:福建省厦门市双十中学2017-2018学年高一上学期期中考试数学试卷
解题方法
10 . 设函数
,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4360ce512aea78e001e81beaf19e1b9c.png)
(1)当
时,解关于
的不等式:
;
(2)若
且
,已知函数
有两个零点
和
,若点
,
,其中
是坐标原点,证明:
与
不可能垂直.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d4985bfa06dbd6c3d8faff88b0d192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64afd5ad06ba91a2f620fa81fec3894c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4360ce512aea78e001e81beaf19e1b9c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01162b9ae6aa69dd858f7d807c708f4e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e7deb668cee7b52f8b35ae95ed4d0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9eea5fd36d96291ce2e62d24d9f75a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ce91cc8d671a51948e8aae8e12f8fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
您最近一年使用:0次