名校
解题方法
1 . 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)求符合题意的
的取值范围;
(3)若对于任意符合题意的
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f95842e86d20c4cfb0db08675cbc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c543b45884d75765b16c78bcd0e149.png)
(2)求符合题意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若对于任意符合题意的
![](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
2022-12-01更新
|
912次组卷
|
2卷引用:重庆市南开中学2022-2023学年高一上学期12月月考数学试题
解题方法
2 . 俄国数学家切比雪夫(П.Л.Чебышев,1821-1894)是研究直线逼近函数理论的先驱.对定义在非空集合
上的函数
,以及函数
,切比雪夫将函数
,
的最大值称为函数
与
的“偏差”.
(1)若
,
,求函数
与
的“偏差”;
(2)若
,
,求实数
,使得函数
与
的“偏差”取得最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefd4b8569af51ff09803173f4e317d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefb4b25c31f33f979610ae52c79960c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9642df8f7f47962daeab61e8874a135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacc9308da40e8852e9c00db0eb1391a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6dbdc6df07aaa13b26b250f314f4c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5c448025ea7b5e428a7344e1ecd31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
2023-02-26更新
|
1253次组卷
|
4卷引用:重庆市2023届高三下学期3月月度质量检测数学试题
重庆市2023届高三下学期3月月度质量检测数学试题广西2021-2022学年高二上学期12月高中学业水平考试数学试题(已下线)第二篇 函数与导数专题5 切比雪夫、帕德逼近 微点2 切比雪夫多项式与切比雪夫逼近专题03E函数解答题
3 . 设O为坐标原点,动点P在圆
上,过点P作
轴的垂线,垂足为Q且
.
(1)求动点D的轨迹E的方程;
(2)直线
与圆
相切,且直线
与曲线E相交于两不同的点A、B,T为线段AB的中点.线段OA、OB分别与圆O交于M、N两点,记
的面积分别为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e01ab2367599ebef5d70bebe1e2b78.png)
(1)求动点D的轨迹E的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4445624a29fa285ca1cce7ebe9adeba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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2022-01-25更新
|
1206次组卷
|
2卷引用:重庆市西南大学附属中学2021-2022学年高二上学期期末数学试题
名校
解题方法
4 . 对于两个函数:
和
,
的最大值为M,若存在最小的正整数k,使得
恒成立,则称
是
的“k阶上界函数”.
(1)若
,
是
的“k阶上界函数”.求k的值;
(2)已知
,设
,
,
.
(i)求
的最小值和最大值;
(ii)求证:
是
的“2阶上界函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6afd1b3aeae1bd415dba90e50c001c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffea0f7bb26c02be91008a3a992a27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5289677c3bf66194c475c4c44f4a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06f45220c23094a3d9ef53b54b89d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2bc8d66faac1a06acfec68e28086bf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b89d55ca6a541bce15e141a7e38285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f0ca536621ec8db02707ba65917029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ff2689759a35f3a8030b02be7a22c3.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49794721f5504dd828acf49be37ff42.png)
您最近一年使用:0次
2022-01-24更新
|
1602次组卷
|
2卷引用:重庆市巴蜀中学2021-2022学年高一上学期期末数学试题
名校
解题方法
5 . 已知函数
对任意的实数m,n都有
,且当
时,有
恒成立.
(1)求
的值;
(2)求证
在R上为增函数;
(3)若
,
,对任意的
,则关于x的不等式
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053e4e1dc1431145c998c014b8fc0c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
(2)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9bf4ec57e9172349be55e4527214acc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2188e898a6af08a1e4f4001001194bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab099277f1ca651f5acca46ca054844c.png)
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