名校
解题方法
1 . 椭圆
与双曲线
有相同的焦点
、
,记椭圆
的离心率为
,双曲线
的离心率为
,则下列关系式一定正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6155c590302cdf30e3b428726855aef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69aef6ec665a785ed201645999c1add.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
2 . 已知函数
.
(1)若方程
恰有两个不同的正根,求实数
的取值范围;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e379be7e59917c3048773005d72568.png)
①求
在
上的最大值
;
②若
,对
有:
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962c3a71145a926d4d5a93e7c0ca0bb2.png)
(1)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72887c5ebdf00bf0e33c675bc1c3fab3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e379be7e59917c3048773005d72568.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb4068ea539526f142b8d26dbb622be.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7725e8ffa805d7744a46bde68549e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c7e73075eb82517587ea69bb59ecc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed61ead7b2076e3fb8742eebb8d875f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
为定义在
上不恒为
的函数,对定义域内任意
,
满足:
,
.且当
时,
.
(1)证明:
;
(2)证明:
在
单调递减;
(3)解关于
的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e2db881e8f568503e74978583d01dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed670b1f668778c6243f3f7470ee7d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccaa6e503b61e9ae78d8439cba2e328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bfb865cbc42d512717bc7fd9acfb3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6374a0510e93e18f5db8d1db8a02c2.png)
您最近一年使用:0次
名校
4 . 重庆南开中学作为高中新课程新教材实施国家级示范校,校本选修课是南开中学课程创新中的重要一环,学校为了支持生物选修课程开展,计划利用学校面积为
的矩形空地建造试验田,试验田为三块全等的矩形区域,分别种植三种植物,相邻矩形区域之间间隔
,三块矩形区域的前、后与空地边沿各保留
宽的通道,左、右两块矩形区域分别与相邻的左右边沿保留
宽的通道,如图.设矩形空地长为
,三块种植植物的矩形区域(如下图中阴影部分所示)的总面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/8b2abb79-2891-4b3e-b5a9-88feed5fbf82.png?resizew=245)
(1)求
关于
的函数关系式;
(2)求
的最大值,及此时长
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8096e96ff8e83d2f402717a06c3566ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8081b57f0de3c86904a8da282b8fc872.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8081b57f0de3c86904a8da282b8fc872.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5769e5c0f48564c08bdd2f0af5bf94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ffd001ed78d9a6617d6a17afb25c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fcd969158dcf1cbe6c59cd601bd9b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/8b2abb79-2891-4b3e-b5a9-88feed5fbf82.png?resizew=245)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
解题方法
5 .
为定义在
上的函数,且对任意实数
均满足
.
(1)求
的解析式;
(2)若存在
使得不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb2ef34e9e57ca06060612a0b045b0a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538193a4717d564c01145e82314c2d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682bdc466189886ccd85cbb46ab16c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-11-10更新
|
364次组卷
|
2卷引用:重庆市南开中学校2023-2024学年高一上学期期中数学试题
名校
解题方法
6 . 已知幂函数
,且
在
上单调递增.
(1)求实数
的值;
(2)求函数
,
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0884cbe08c0158af277c31855f00bc42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d921aca43e63056d9dddc42240eade9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
您最近一年使用:0次
名校
7 . 已知集合
,
.
(1)当
时,求
;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6975154019f7034ce45849b85fbcd2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4ee5ef5bd9c9b6702b43eac016ff52.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
8 . 已知函数
,若
,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffcbb0542caa0773caea739e61ecb9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a56e3f8f312a8953a377935af87d872.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
名校
9 . 求函数
,
的最小值__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f7446cd9bd23b107687f96b62f24c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
您最近一年使用:0次
名校
解题方法
10 . 若函数
为奇函数,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ce9222702c10c312495d1cf63fbc41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
您最近一年使用:0次