名校
1 . 若函数
有
个零点,且从小到大排列依次为
,定义
如下:
.已知函数
(其中
为实数).
(1)设
是
的导函数,试比较
和
的大小;
(2)若
,求
的取值范围;
(3)对任意正实数
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ae738aa8389e3b7902ea5055a4f279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e73582d71d8dafbe53f55bbde3c99f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926a1586c9457dd1996157096eb23f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301bbd5742966ec13edf24d7a3b150e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ac79984ad2022bf411890562910d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034f4c179b838bf595faede7eafb86e4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33d620bf581ebbe4c9fea0ee549fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)对任意正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793927fab6e6256ea2eeb70334a9db31.png)
您最近一年使用:0次
2 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a670e5d56fcdd3cc214064c5d3d3b1.png)
(1)当
时,解关于
的不等式
;
(2)若
有两个零点
,求
的值;
(3)当
时,
的最大值
,最小值为
,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a670e5d56fcdd3cc214064c5d3d3b1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ef9f9f0a79e61a30f7da782cbb2fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5f18a08ed6cf92b894ea722af72862.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)
您最近一年使用:0次
解题方法
4 . 已知定义在区间
上的函数
,其中常数
.
(1)若函数
分别在区间
上单调,试求
的取值范围;
(2)当
时,方程
有四个不相等的实根
.
①求
的乘积;
②是否存在实数
,使得函数
在区间
单调,且
的取值范围为
,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/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528c47af5e756030df86aef0798acc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbaabfaec35591078715d268d9325ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
②是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e333c856d24ba160c4623cbe335ca4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8af7bed124f00c8e19b52d028b4d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
5 . 函数
,方程
有三个互不相等的实数根,从小到大依次为
,
,
.
(1)当
时,求
的值;
(2)若对于任意的正实数
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b4a647a94dca12e07814d9d9f7a79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c543b45884d75765b16c78bcd0e149.png)
(2)若对于任意的正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e18c65d75a24393e4d814da3b8f9f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
6 . 对于函数
, 若存在
,使得
,则称
为函数
的 “不动点”;若存在
,使得
,则称
为函数
的“稳定点”.记函数
的“不动点”和“稳定点”的集合分别为A和B,即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732c1cd5c72ed679ddcb0e3b1e08138d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a087d67f13276fbef8eaa8e82718dc8.png)
(1)设函数
,求A和B;
(2)请探究集合A和B的关系,并证明你的结论;
(3)若
,且
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea844642720c083f09f158f56dabccd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b359345c5afa1739bf5ebf8982e1d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b359345c5afa1739bf5ebf8982e1d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374054f44b9a52668f91ac7601e63c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732c1cd5c72ed679ddcb0e3b1e08138d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a087d67f13276fbef8eaa8e82718dc8.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c07bd1bced5e02c11b99392f9526f7d.png)
(2)请探究集合A和B的关系,并证明你的结论;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afafcdd19ed39cf1c3682bfea3825b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d02e5de0c92487382f4b98376e9740.png)
您最近一年使用:0次
2022-11-16更新
|
994次组卷
|
5卷引用:山东省潍坊市2022-2023学年高一上学期期中考试数学试题
名校
7 . 已知函数
.
(1)求函数
的零点;
(2)证明:当
时,函数
是
上的严格增函数;
(3)设
,若对任意
,
恒成立,求正实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da5bf1fbb7d7339058beb960a4c6ae5f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76507928e4468b7e3b096bc7f3e62cd.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01890ce9d5ecec35eb0d4ef26ad9481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e23b1beceb47324577bfbfc118cf00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41e0308d7fbdecab686b8f7ee4838d0.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ab976d37f4b11aa304628295d53cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efaa6571bd68afbbf09a6cc86e7236d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f4d3e19d974d600e9df098fd4699fa.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
8 . 已知函数
,其中
.
(1)当
时,求函数
的零点;
(2)若
,
,当
时,关于
的方程
有3个不同的实数解,求实数
的值及该方程的解;
(3)若对任意
,都有
恒成立,求实数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11976693acdf39ca341f1a2e115ba075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbbc8994aeede020660affa4b73cf49.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48adb8a59b5c02fad5eada1b35171cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a79d7f73b6128650bf7aed538260c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fb831c75ae371c30b63adc23dde09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47545bd5310d9c5c8de5f64a2a6e2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5aa200de40134d6c0c865a9bc7ecb3b.png)
您最近一年使用:0次
名校
解题方法
9 . 对于函数
.
(1)当
向下和向左各平移一个单位,得到函数
,求函数
的零点;
(2)对于常数
,讨论函数
的单调性;
(3)当
,若对于函数
满足
恒成立,求实数
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3036cf2c106f2b3a0880b43a9a226d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6df3dd28c2fa75007f9fc3ac08b2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)对于常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7a54ead79841d64b18c5ea1a09ae4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
10 . 定义在
上的函数
,如果对任意
,恒有
成立,则称
为
阶缩放函数.
(1)已知函数
为二阶缩放函数,且当
时,
,求
的值;
(2)已知函数
为二阶缩放函数,且当
时,
,求证:函数
在
上无零点;
(3)已知函数
为
阶缩放函数,且当
时,
的取值范围是
,求
在
上的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa3d426f89f0d61420658729e35208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46ecf935049473045cdebae68415657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa9ae68588aca912bf1ad4f6c9febc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b5bfb104d79b8242e8faaf7a8f17ca.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46ecf935049473045cdebae68415657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b4163b626b28fdefa38cbda9f73b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac5b738cd5ea12f6d93e9c5fc6bcd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc07b986f375453663b3e5c93eb1e0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2fc9e0dce53875ba108a4a041fcbf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6567b9bfcbc9b17b5d3988c86361b4fd.png)
您最近一年使用:0次
2020-02-05更新
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670次组卷
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2卷引用:上海市七宝中学2016届高三上学期期中(理科)数学试题