解题方法
1 . 设函数
的定义域为
,若存在实数
,使得对于任意
,都有
,则称函数
有上界,实数
的最小值为函数
的上确界;记集合
{
在区间
上是严格增函数};
(1)求函数
的上确界;
(2)若
,求
的最大值;
(3)设函数
一定义域为
;若
,且
有上界,求证:
,且存在函数
,它的上确界为0;
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a82f9ed1fed1e3aa42434da4671b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5830648092860499a7017d2ee157e77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617da64f56745521a83fe4b4bf5f20a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf860993c4cee78cdfed6d29273cf76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c28c7adedb14985ec58d6a016770706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21f0ef09f65ef153b4df26a5b9b7d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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2 . 若函数
与
满足:对任意
,都有
,则称函数
是函数
的“约束函数”.已知函数
是函数
的“约束函数”.
(1)若
,判断函数
的奇偶性,并说明理由:
(2)若
,求实数
的取值范围;
(3)若
为严格减函数,
,且函数
的图像是连续曲线,求证:
是
上的严格增函数.
![](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/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec6c7a1da7ecaef51a3d08fbcdf2821.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/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a6aefe8450e0c625ee979ecaef16384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bc9c32ab68ddb51b1a4196f50081f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
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2023-12-12更新
|
694次组卷
|
4卷引用:2024届上海市长宁区高考一模数学试题
2024届上海市长宁区高考一模数学试题(已下线)专题09 导数(三大类型题)15区新题速递(已下线)专题03 函数(三大类型题)15区新题速递河南省信阳高级中学2024届高三5月测试(一)二模数学试题
名校
解题方法
3 . 已知A是直线
和曲线
的一个公共点.
(1)若直线
与曲线
相切于点A,求
的值;
(2)设点A的横坐标为
,当
在区间
上变化时,求
的最大值;
(3)若直线
与曲线
另有一个不同于A的公共点
,求证:线段
中点的纵坐标大于1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9136761fe20df42369e5bf110229e9.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设点A的横坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94beb083d48ef4a8e0556dc1e2339c7b.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
解题方法
4 . 已知函数
的定义域为
,其中
.
(1)若
是函数
的一个驻点,求a的值;
(2)函数
在区间
上严格增,求a的取值范围;
(3)当
时,若函数
,
在
处取得最大值,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e51abbb93b730a3ac6e719d1cfeb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b538da8582fb32f6d40c6754bda8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
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5 . 已知
.
(1)当
时,求函数
的单调减区间;
(2)当
时,曲线
在相异的两点
点处的切线分别为
和
和
的交点位于直线
上,证明:
两点的横坐标之和小于4;
(3)当
时,如果对于任意
,总存在以
为三边长的三角形,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50a5b1b35f29dfec58eb44bcc9a89f2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c7d2c85e7878b6cbfb45b71ffb60b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5631bc68728bbf17b87c3e7e7f8e425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bc82aed391363566b80c93ddfab5111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
6 . 已知复数
是纯虚数,
是实数.
(1)求
;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f775cc22daf5bd923288efb777741f01.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02670a0e20ea7d6740abb69844615e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c264cca2d434effa117b1b1bdd392142.png)
您最近一年使用:0次
2023-05-05更新
|
1464次组卷
|
6卷引用:上海市延安中学2022-2023学年高一下学期期末数学试题
名校
解题方法
7 . 某公园有一块如图所示的区域OACB,该场地由线段OA,OB,AC及曲线段BC围成;经测量,
,
米,曲线段BC是以OB为对称轴的抛物线的一部分,点C到OA,OB的距离都是50米;现拟在该区域建设一个矩形游乐场OEDF,其中点D在线段AC或曲线段BC上,点E,F分别在线段OA,OB上,且该游乐场最短边长不低于25米;设
米,游乐场的面积为S平方米;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/1/7819bba1-0508-4ffb-a8bb-f75d8e46834e.png?resizew=133)
(1)以点O为原点,试建立平面直角坐标系,求曲线段BC的方程;
(2)求面积S关于x的函数解析式
;
(3)试确定点D的位置,使得游乐场的面积S最大(结果精确到0.1米);
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce1435622e153e6d5d6a417fd51b277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d30747569ae3b6b493273f0b190e1932.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/1/7819bba1-0508-4ffb-a8bb-f75d8e46834e.png?resizew=133)
(1)以点O为原点,试建立平面直角坐标系,求曲线段BC的方程;
(2)求面积S关于x的函数解析式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3105bd82be20cc7540d68aa81fb0cb27.png)
(3)试确定点D的位置,使得游乐场的面积S最大(结果精确到0.1米);
您最近一年使用:0次
2023-04-26更新
|
293次组卷
|
2卷引用:上海市延安中学2022-2023学年高二下学期期中数学试题
名校
8 . 求函数
,
的单调区间和极值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcde82aabb8f1c0761351fda95c6b012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a68eadbcb9953c6d7fc17ef2763ce5.png)
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9 . (1)求简谐振动
的振幅、周期和初相位
;
(2)若函数
在区间
上有唯一的极大值点,求实数m的取值范围;
(3)设
,
,若函数
在区间
上是严格增函数,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c793183ec51b2304e5f3eb0e422a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44e89f32c090e204068d3ab249e7d40.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/939d602a617905899df2f5cfc46eda2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d45c738904d7aea7b2aa9caa2aa315.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daed7d15d3b8296ed1b51d14822f51c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
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名校
10 . 如图,
是曲线
上的
个点,点
在
轴的正半轴上,且△
是正三角形
是坐标原点).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/86311efd-f7c4-4a46-8bfb-5e6933f9905a.png?resizew=249)
(1)求
、
、
的值及数列
的递推公式;
(2)猜想点
的横坐标
关于
的表达式,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857d97c35c872937e4172dbc2ede1af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956620959792f8c3a28ed0fc4bf053d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f94253ca8e33eca70b1a9ee6c2a0e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27853b475a8bc2bfe297bbdbdaaa86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a617f7ebacc3d380868cf6e002c0be3e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/86311efd-f7c4-4a46-8bfb-5e6933f9905a.png?resizew=249)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)猜想点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b25286f6029da66ce5270aacd05184f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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