1 . 已知直线
和
是函数
图像两条相邻的对称轴.
(1)求
的解析式和单调区间;
(2)保持
图像上各点的纵坐标不变,横坐标变为原来的
倍,得到函数
的图像.若
在区间
恰有两个极值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c6cb0cc172657611e286e7fa669584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4eae5056ae4e4f11c49fe4b1fb67908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f26765b493dcb0cb3ebe4f7ef74c3c6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)保持
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ca7d2fde2a0ab2398185e87db8c4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 . 在
的展开式中,若
的系数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
______ ;若展开式中有且仅有
项的系数最大,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd03f26e21d9427fd15f9c6f8ae8956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d800f03de80068a1172beac3a2c75587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e60696d1c681628c57bb2c7e9d1814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3336c8ed5361c10c37300e41e03f9f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 设
为坐标原点,椭圆
的左、右顶点分别为
,
,点
为椭圆上一点,直线
的斜率为
,
的斜率为2,则
的斜率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
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解题方法
4 . 已知凸四边形
内接于圆
,
,
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847c3d6a96fd48180d52a1872d0dd2a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f37c0a85ae2cfc261c9b010624619d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78c44f837a63101c19745cc1a79a740.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-12更新
|
1017次组卷
|
6卷引用:2024年高三数学极光杯线上测试(一)
2024年高三数学极光杯线上测试(一) (已下线)专题18 三角形中关于角的最值问题2024届高三新改革数学模拟预测训练四(九省联考题型)(已下线)压轴小题14 定角类解三角形问题(已下线)专题09 余弦定理、正弦定理的应用-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)专题11 余弦定理、正弦定理的应用-《重难点题型·高分突破》(苏教版2019必修第二册)
名校
5 . 若5个正数之和为2,且依次成等差数列,则公差
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-12更新
|
1289次组卷
|
5卷引用:2024年高三数学极光杯线上测试(一)
2024年高三数学极光杯线上测试(一) (已下线)山东省部分学校2024届高三3月调研数学试卷(2024年普通高等学校招生全国统一考试数学模拟试卷)(已下线)2024年全国高考名校名师联席命制数学(理)押题卷(四)湖南师范大学附属中学2024届高三下学期模拟(二)数学试卷重庆市缙云教育联盟2023-2024学年高二下学期3月月度质量检测数学试题
6 . 设
是正实数数列.
(1)若
收敛,求证:存在严格递增的无界正实数数列
满足
收敛.
(2)若
收敛,是否一定存在严格递增的正整数数列
,满足
收敛,且
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7376941fa463c63b1d4d4ea866b78c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccecde965d7557d5ee35dea8ae7164a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c988a3683540149b687486af0ed3a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120dcd9c3adc5b08ab9d84f228cc4b90.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ad99ac2f9cbe69281dcdc7d4195d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba58d775c69de6d132c58581d614792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246e5563a2f86de45879b21393d814f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c69eef9b8e90f6a153b87738f759bcf.png)
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7 . 设
,满足
.
(1)证明:若
,则当
时,
.
(2)若存在
满足
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e761714f6940c2c06c5750e2ed80cc4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbd27b6b4143c730ab9d36393a5fe14.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c61cfbfd3bf888856b7dc9b2a84c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac247d375e0da7fddafad1aa8186aa51.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4439c7de7291f79def06d548603de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
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8 . 对有理数
,若
且
,定义
.求最大的正实数
,使得存在正常数
满足
对所有有理数
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee17bd1437d928f932fd1ebc1672d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee31d3aeb5cbb8275a25e762d55fdcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f03255ec0c937126b9a018f1f42cf85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3806a5fe77b4104d16b0623719ffc6c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 . 设
为全体由
和1构成的
元数组的集合,其中
为偶数.称
与
正交,若
.记
为可以从
中选出
元数组个数的最大值,满足选出的数组两两正交.求
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318f55d136f3b38a2a5f529fd17f1f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b4cd18676efcd11a591ab3e4d2085b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea378cc281cb24fc593bedb34dab3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc3f52cd9edf88e49e2409f050108d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d75967b4ca5e79d2493d1eac59d230.png)
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10 . 已知复数
,
,…,
,
,
,…,
,满足
,
,…,
互不相同,
,
,…,
互不相同.已知对任意正整数
,均有
.求证:
,
.
![](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/dad7f66c97bfce4c00c53d86700c961b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47233e81de2d9d728c80f02359f1af4a.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/dad7f66c97bfce4c00c53d86700c961b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47233e81de2d9d728c80f02359f1af4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c8214c80f9e949b1ac8d6e41b597e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddf38600954700caa8a227dae4e8ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8389928ac57b99f195e6bef80d2a28d3.png)
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