名校
解题方法
1 . 设常数
,
.若函数
在区间
上恰有2024个零点,则所有可能的正整数n的值组成的集合为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171849cbf36955fcdad36feaf1cb5f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c07c496500d66cbd74e1070e1c7c1d5.png)
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名校
解题方法
2 . 若函数
有2个零点,则m的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94dadacc20558af802e1f7a204b6d05.png)
您最近一年使用:0次
2024-06-01更新
|
550次组卷
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2卷引用:上海市金山中学2023-2024学年高一下学期5月月考试卷
名校
3 . 已知函数
在区间
上恰有两个零点,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8f65737dc55384c57c6a3f1f0a87e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-10更新
|
650次组卷
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2卷引用:上海市格致中学2023-2024学年高一下学期5月月考数学试卷
名校
解题方法
4 . 已知函数
.
(1)当
时,求函数
的单调递增区间;
(2)对于
为任意实数,关于
的方程
恰好有两个不等的实根,求实数
的值;
(3)在(2)的条件下,若不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52301f311b021f7d04bfdca8c3aaf00.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1986ee008f64fc4fb6dddad020e2cdb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1017a21be2a73738eb51d22771329929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8b002680c476b8323c4b67e8bc999e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(3)在(2)的条件下,若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b791ef4858df886be749c11a7690f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0a5133b8460df6c46da0e44051e2a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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5 . 设函数
与
的定义域为
与
分别为函数
与
的导函数,若存在
,满足
且
,则称函数
与
为“优美函数”.已知函数
与
.
(1)已知
和
,求证:
和
;
(2)当
时,若函数
与
为“优美函数”,求
的取值范围;
(3)当
时,已知函数
与
为“优美函数”,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6085b118b86f7f4dd54864e113cd595c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc4a85bbf152031dc8ebd182e44ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5685f66553971f62cb1d8cee9a49244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59ef75c0e906e108cad5f4d34ae21ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6085b118b86f7f4dd54864e113cd595c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc4a85bbf152031dc8ebd182e44ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3102c0a2f53b80f9dddbf9352537e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a4a84e03dab8e8aa04f597b4fcf998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c668385fc2475e2600074c350d961a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6085b118b86f7f4dd54864e113cd595c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc4a85bbf152031dc8ebd182e44ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d6c95ea3b9d0ff3e90a702d2db77d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7024f7708dcc7deba3b8baa1afe6b40a.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155672d8c17847792e73c07cb94fcff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7300497edb92cd1fedd641dd1c5a364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6694d977c5ac4d7b5342d18728f4c489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e549248d2c6d1c8706ec49f19a59b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4acc891e024b77f174039085580e48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83dcde657544ded718d8b7b0ff0537a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7139148f3c934fdf505f2f020f023d.png)
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6 . 已知函数
满足:在定义域
内存在实数
,使得
.设集合
是满足上述性质的函数
的全体.
(1)若
,判断函数
是否属于集合
,并说明理由;
(2)设
,若函数
属于集合
,求
的取值范围;
(3)设
,求证:对任意实数
,函数
均属于集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c413f613d1bb2dfbfc9969f82416196a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2f84a6e2b68badd47734f36fd546d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b734eb2bc8266344b97f7f970c2481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c820f55a65ea1de54613f35123f362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d0d134d0cf0d456e1eaf2887174c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
7 . 将函数
的图像进行如下变换:先向下平移
个单位长度,再向左平移
个单位长度,得到函数
的图像
(1)求
的最小正周期及单调增区间
(2)当
时,方程
有两个不等的实根
,求实数
的取值范围
(3)若函数
在区间
内恰有2022个零点,求
的所有可能取值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84005158547c0dfe3fd36a54fa06c20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2818807dce7e9ec5514de572c3cc644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adb4910475f817ded8ada2da36b1a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4c1927483c5074919ea78503186f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024-03-20更新
|
307次组卷
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2卷引用:上海市金山中学2023-2024学年高一下学期3月月考数学试卷
8 . 已知函数
.
(1)某同学打算用“五点法”画出函数
再某一周期内的图象,列表如下:
请填写上表的空格处,并写出函数
的解析式;
(2)若函数
,将
图象上各点的纵坐标不变、横坐标扩大到原来的2倍,再向右平移
个单位,得到函数
的图象,若
在
上恰有奇数个零点,求实数a与零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e613ec74a2f330b57a235439510dc5.png)
(1)某同学打算用“五点法”画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
x | ![]() | ![]() | ![]() | ||
![]() | 0 | ![]() | ![]() | ![]() | ![]() |
![]() | 0 | 1 | 0 | ![]() | 0 |
![]() | 0 | ![]() | 0 | 0 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfa338e78c528663f0602c60f3f594d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdb2704ea6bc44b5a75fb3c8a100353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aab44d48c65864b1f46ea3647437bbe.png)
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9 . 已知函数
在
上恰有两个零点,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af043b008f98634cfa3a287c25b1a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
您最近一年使用:0次
2024-02-05更新
|
1059次组卷
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8卷引用:上海市浦东新区上海实验学校2024届高三下学期3月月考数学试题
上海市浦东新区上海实验学校2024届高三下学期3月月考数学试题上海市向明中学2023-2024学年高一下学期期中考试数学试题 上海市实验学校2023-2024学年高三3月数学练习试卷 辽宁省沈阳市翔宇中学2023-2024学年高一下学期第一次月考数学试卷山西省太原市2023-2024学年高一上学期期末数学试题安徽省马鞍山市劲松学校2023-2024学年高一下学期开学考试数学试题(已下线)1.6 函数y=Asin (ωx+φ)的性质与图象4种常见考法归类(2)-【帮课堂】(北师大版2019必修第二册)(已下线)专题02三角函数的图像与性质期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)
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解题方法
10 . 已知函数
,若关于x的不等式
恰有一个整数解,则实数a的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768f54d2c84689f7441ce490aaf286ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fca994e8d5b7ec2c2cb7b390f1a939.png)
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2024-01-15更新
|
498次组卷
|
2卷引用:上海市黄浦区大同中学2024届高三下学期2月月考数学试题