2024高三·上海·专题练习
解题方法
1 . 已知函数
,设
的最大值、最小值分别为
,
,若
,则正整数
的取值个数是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bada3e4ca7dfec636a7ebec3f48405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cfd57b8405efd0e3bfc03b7a78c5a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 . 若函数
无最大值,则实数a的取值范围____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95782758bafbe17a661efd8395055121.png)
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3 . 已知函数
,
.
(1)解方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9708c59f51c8ed59a859e288e9ac024.png)
(2)当
时,有
最大值为1,求实数
的值;
(3)若方程
在
上有4个实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1697647bba92906e733fb696f622a2e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4139cddc2af2ef0900496dce24274d2.png)
(1)解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9708c59f51c8ed59a859e288e9ac024.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f955a011428f5e0d962cd57f8e73b396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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23-24高一上·上海浦东新·期末
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解题方法
4 . 记
在区间
(
为正数)上的最大值为
,若
,则实数
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9db9ce814f08447762530cac61202bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93c82944db4a310a2047dd6d8966162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe13bedc59eb296d5948c2c59d702b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8238dfbbcf90b6ffa1a66eb214cc68d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
5 . 已知正项数列
的前
项和
满足
(
为正整数).记
,若函数
的值域为
,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f60e9a26a3784940b7c5b40ca3eeef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2a0686fb74ed14df00e0efefc354d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9d233a5992384c318b88bc065983c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
6 . 若函数
在区间
上的函数值的集合恰为
,则称区间
为
的一个“
区间”.设
.
(1)若函数
在区间
上是严格增函数,请直接写出区间
(一个即可);
(2)试判断区间
是否为函数
的一个“
区间”,并说明理由;
(3)求函数
在
内的“
区间”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e5aa1bde431ba57857f6b30033095e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f69506035da4e8d4adaf6d2fb24218.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)试判断区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745eb631342dcfee91d7d7e8ccb4375b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03db4ea1dcb63b22cf4e917df5db581e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
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解题方法
7 . 已知
,其中
是常数,
.
(1)若函数
为奇函数,求实数
的值;
(2)若对任意实数
,均有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd870f1f669420f3c8caf96faec7cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2608a57caffde627dbf140ca22a2ff8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 如果函数
满足以下两个条件,我们就称
为
型函数.
①对任意的
,总有
;
② 当
时,总有
成立.
(1)记
,求证:
为
型函数;
(2)设
,记
,若
是
型函数,求
的取值范围;
(3)是否存在
型函数
满足:对于任意的
,都存在
,使得等式
成立?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
①对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
② 当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfdccde6a17dc78bec232630577f99d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d5873aa225a83805e1072ef8119b7a.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc540d6c4de05039557cdfe8c78ceeec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54428f4829c8061f79df9f492305c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951b05c96af4f7704de24ac541b3f172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb679de6747c1a9147225d7b61c436f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe0c952b97016a6816cfca66e024ef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdc6e6a0e6584bea7deb91b0841fa28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe8e17429b079c4965fae3bef4e6b25.png)
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2024-01-10更新
|
420次组卷
|
2卷引用:上海市静安区2024届高三上学期期末教学质量调研数学试题
名校
解题方法
9 . 已知函数
.
(1)当
时,解不等式:
;
(2)若函数
在
上的最大值为
,求
的值;
(3)当
时,记
,若对任意的
,函数
的图像总在函数
的图像的下方,求正数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc391884cb2d4e69c318015ed1cc5724.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41bec4d534507843da676c3cf84acdd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1230fedeac230a151ba0d84bfc275d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b081b1439dd4a3f6dafec805b6785700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6070f2ee5e48cce77eb4a2cb9f11ccfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4096ebda06e298e48c475986932e4829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ad4b6efae29ab7dec69eedf348eaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58427d5aa7deeca47c8789241913f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 已知函数
的定义域为
,其最小值为2.点
是函数图象上的任意一点,过点
分别作直线
和
轴的垂线,垂足分别为
.其中
为坐标原点.给出下列四个结论:
①
; ②不存在点
,使得
;
③
的值恒为
; ④四边形
面积的最小值为
.
其中,所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e29a631e052d3a682b025e512f0618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c037b199f33cbed1efcffdd2376d8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeab2a468fa7034c7d50644d1fc92a23.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9486e4e76ff07c6c47091e0e4b8bcd7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6c989fd224866658230526892e2bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2cc049891e859c6ca7e84db4562650.png)
其中,所有正确结论的序号是
您最近一年使用:0次
2023-11-04更新
|
495次组卷
|
6卷引用:第1章 坐标平面上的直线 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
(已下线)第1章 坐标平面上的直线 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)陕西省西安市西安中学2024届高三上学期期末数学(理)试题(已下线)专题02 直线和圆的方程(5)(已下线)黄金卷01北京市清华大学附属中学2023-2024学年高二上学期期中考试数学试题(已下线)2.3.2 点到直线的距离公式、两条平行直线间的距离【第三练】