名校
解题方法
1 . 已知点
是椭圆
上的一点,经过原点
的直线
与椭圆
交于
两点(不同于左、右顶点),且
,直线
与
轴交于点
与
轴垂直,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7425f70eb9a4e532b4ab809917cb1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d390782b8ea7016628ee68403dcbfbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddb48d3d00c550dc4c6a4753f255d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.记直线![]() ![]() ![]() |
B.![]() |
C.![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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解题方法
2 . 双曲线
的左、右顶点分别为
,曲线
上的一点
关于
轴的对称点为
,若直线
的斜率为
,直线
的斜率为
,则当
取到最小值时,双曲线离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce0d4ca414e9e870813ae89721e0fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a7bb0db495511d6eb060745ee0d0aa.png)
A.3 | B.4 | C.![]() | D.2 |
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名校
解题方法
3 . 已知函数
,
为
的导函数.
(1)证明:
;
(2)设函数
有两个极值点
,
.
①求实数
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b26b3a2baf877660919f00eca68954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38657b66d50bfc41143e8efbd0cff817.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a93969738a9bb969f40cf587f1d5d5.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147f89995c5aa07ce7f797c308c9c7d2.png)
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名校
4 . 已知函数
,若函数
有三个零点
、
、
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bff1ac72e1e74f1a1e01059c530f4df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc046a7b475b5130da69bf537226ec8.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
A.![]() |
B.![]() |
C.函数![]() ![]() |
D.![]() ![]() |
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5 . 基本不等式:对于2个正数
,它们的算术平均数不小于它们的几何平均数,即
,当且仅当
时,等号成立.可以推广到一般的情形:对于
个正数
,它们的算术平均数不小于它们的几何平均数,
.当且仅当
时,等号成立.若无穷正项数列
同时满足下列两个性质:①
;②
为单调数列,则称数列
具有性质
.
(1)若
;求数列
的最小项;
(2)若数列
的前
项和为
,判断数列
是否具有性质
,并说明理由;
(3)若
,求证:数列
具有性质
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140564fb2e11f8411e353d2fa73fbee9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b2fb1017d5dfe3a300de3e14a71b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efff8ec14cb242e793afab4468bf2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2617515e5ce81b3f5d9f4e806b21b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6879960be91ea52297d587e9a014f54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17fac66473a039bdb47c2a248b0f4854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9bb1963d176a00c82828c93ca0e2c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247739746b8ddf1403541047e8b5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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名校
解题方法
6 . 已知
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ed49d83fd68e4b5a6a4215a8a8a3f1.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2024-03-07更新
|
658次组卷
|
3卷引用:江西省宜春市宜春中学2023-2024学年高一下学期开学考试数学试题
江西省宜春市宜春中学2023-2024学年高一下学期开学考试数学试题福建省泉州市2023-2024学年高一上学期1月期末教学质量监测数学试题(已下线)微考点1-1 新高考新试卷结构中不等式压轴4大考点总结
7 . 已知数列
满是
,
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc289d11d4e48c34874f5ee63e90212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd15336272a0bfbad4cbe768e26921bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576e6f82d809db1ce12ff4f7f3bd586b.png)
A.![]() | B.![]() | C.16 | D.18 |
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2024-02-27更新
|
682次组卷
|
3卷引用:湖南省长沙市第一中学2023-2024学年高二下学期开学自主检测数学试题
湖南省长沙市第一中学2023-2024学年高二下学期开学自主检测数学试题辽宁省丹东市凤城市第一中学2023-2024学年高二下学期第一次月考(4月)数学试题(已下线)专题3 复杂递推及斐波那契数列相关二阶递推问题【讲】(高二期末压轴专项)
名校
解题方法
8 . 如图,已知
,
,
为
边
上的两点,且满足
,
,则当
取最大值时,
的面积等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cc2450dc300ce26b513c2abae28cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab63989beb8972f172f67ddf6c72570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-02-27更新
|
1551次组卷
|
4卷引用:浙江省杭州第二中学2023-2024学年高三下学期开学考试数学试卷
名校
解题方法
9 . 基本不等式可以推广到一般的情形:对于
个正数
,它们的算术平均不小于它们的几何平均,即
,当且仅当
时,等号成立.若无穷正项数列
同时满足下列两个性质:①
;②
为单调数列,则称数列
具有性质
.
(1)若
,求数列
的最小项;
(2)若
,记
,判断数列
是否具有性质
,并说明理由;
(3)若
,求证:数列
具有性质
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efff8ec14cb242e793afab4468bf2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2617515e5ce81b3f5d9f4e806b21b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6879960be91ea52297d587e9a014f54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce59ae5baacab766b0915722377a746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bc99b9545c8c838e99b7be9c6d1046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20e03ee7d9307a0a4d242fffda381d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247739746b8ddf1403541047e8b5580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2024-02-21更新
|
3162次组卷
|
7卷引用:安徽省部分省示范高中2024届高三开学联考数学试卷
安徽省部分省示范高中2024届高三开学联考数学试卷湖南省2024年高三数学新改革提高训练三(九省联考题型)湖北省荆州市沙市中学2024届高三下学期3月月考数学试题(已下线)黄金卷04(2024新题型)广东省广州市西关外国语学校2023-2024学年高二下学期期中数学试题(已下线)压轴题03不等式压轴题13题型汇总-2辽宁省朝阳市建平县实验中学2024届高三第五次模拟考试数学试题
解题方法
10 . 某药品可用于治疗某种疾病,经检测知每注射tml药品,从注射时间起血药浓度y(单位:ug/ml)与药品在体内时间
(单位:小时)的关系如下:
当血药浓度不低于
时才能起到有效治疗的作用,每次注射药品不超过
.
(1)若注射
药品,求药品的有效治疗时间;
(2)若多次注射,则某一时刻体内血药浓度为每次注射后相应时刻血药浓度之和.已知病人第一次注射1ml药品,12小时之后又注射aml药品,要使随后的6小时内药品能够持续有效消疗,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964609698358e6e31673615f150802ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57fa6097197c6943c40394eaceae732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b35d774836119531a3eec0ee121a8585.png)
(1)若注射
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710dd2e08d422d57c65fd63f80509d84.png)
(2)若多次注射,则某一时刻体内血药浓度为每次注射后相应时刻血药浓度之和.已知病人第一次注射1ml药品,12小时之后又注射aml药品,要使随后的6小时内药品能够持续有效消疗,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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