名校
解题方法
1 . 若实数集
对
,均有
,则称
具有Bernoulli型关系.
(1)若集合
,判断
是否具有Bernoulli型关系,并说明理由;
(2)设集合
,若
具有Bernoulli型关系,求非负实数
的取值范围;
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2df79c96894e48585d810e2d1180b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de62c03953e609ea331280b1e27ba701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acae4bf2a6bead9d904b70d0480fc0.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5055c43ef4c493c056609f617f38e108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef4609431a6fc9f2755d8e8ca6617b0.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9d408eb7f234bea73e86bff6a453f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5596a9fe31bffbe73af20f611a9a574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953916e76840b10bf27302f42ad98cb9.png)
您最近一年使用:0次
2024-05-12更新
|
1006次组卷
|
3卷引用:安徽省六安第一中学2023-2024学年高三下学期期末质量检测卷(二)数学试题
2 . 已知函数
与
的图象关于直线
对称,若
,构造函数
.
(1)当
时,求函数
在点
处的切线与坐标轴围成三角形的面积;
(2)若
(其中
为
的导函数),当
时,
,证明:
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca5c70f5cb1caf91827aa7d3041f37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a3f617721f69da3649d17ec9c59602.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c97d54952104950bfd7afc0176bbd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339416541b598f3c1fd390ef1b3251b3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752bf766bc202c8cb83e4c6a9abe989f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51350a90203fcdc2d500a89061b7f52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424ef928fdc9de964b00ad253701959e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fed1a157dd189c3a1f20868a121cad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac07d4b1e7127c7eb1fb914837256d70.png)
您最近一年使用:0次
2023·全国·模拟预测
3 . 一类项目若投资1元,投资成功的概率为
.如果投资成功,会获得
元的回报
;如果投资失败,则会亏掉1元本金.为了规避风险,分多次投资该类项目,设每次投资金额为剩余本金的
,1956年约翰·拉里·凯利计算得出,多次投资的平均回报率函数为
,并提出了凯利公式.
(1)证明:当
时,使得平均回报率
最高的投资比例
满足凯利公式
;
(2)若
,
,求函数
在
上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893e658908683584084ea8cd2b1abb23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e4dfb68af91a58e45ca8596abc3d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821289d70c0fb192f97cd7e0c4030d3b.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882d11ef98daf356e7ce70c24d4b9cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25770560bdfb28b2b79f2900084057e8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee70e500750f7aeef9a15557433ad3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
您最近一年使用:0次
2024-01-17更新
|
831次组卷
|
5卷引用:安徽省六安市金寨第一中学2024届高三上学期期末适应性考试数学试题(二)
名校
4 . 为响应国家“乡村振兴”政策,某村在对口帮扶单位的支持下拟建一个生产农机产品的小型加工厂.经过市场调研,生产该农机产品当年需投入固定成本10万元,每年需另投入流动成本
(万元)与
成正比(其中x(台)表示产量),并知当生产20台该产品时,需要流动成本0.7万元,每件产品的售价
与产量x(台)的函数关系为
(万元)(其中
).记当年销售该产品x台获得的利润(利润=销售收入-生产成本)为
万元.
(参考数据:
,
,
)
(1)求函数
的解析式;
(2)当产量x为何值时,该工厂的年利润
最大?最大利润是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da77bb9b5ed5dbaa35e9d9817cc4b2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839dce8ab2307c7f40629cabef3d98f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a241cda471a5c3891a7eaef028ce186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d39ad065dd21c518980f725d4557b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8f8d3d05cc8ec8771e19c950b503f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56cd9fd1bf71d7bb19b29d9d326b73a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11070394a6405a0d5c0ff585f72fb810.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当产量x为何值时,该工厂的年利润
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2023-06-17更新
|
331次组卷
|
5卷引用:安徽省亳州市第二完全中学2022-2023学年高二下学期期末教学质量检测数学试题(B卷)
安徽省亳州市第二完全中学2022-2023学年高二下学期期末教学质量检测数学试题(B卷)福建省宁德市2022-2023学年高二下学期区域性学业质量监测(A卷)数学试题福建省宁德市2022-2023学年高二下学期期中数学试题(A卷)(已下线)专题10 导数12种常见考法归类(4)(已下线)模块四 期中重组篇(人教B版高二下福建)
5 . 函数
.
(1)当
时,求函数
的极值;
(2)当
,且
.
①证明:
有两个极值点;
②证明:对任意的
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f342a299466323139fff562334080372.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5309f8da13872b3cdc06c8ac378d3af6.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ab586aefae2e8c69d0b165f7a1a8ea.png)
②证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff358e2b863caff880bf134c2a27423.png)
您最近一年使用:0次
名校
6 . 若函数
的定义域为
,对任意的
,
恒成立,则称函数
为“有下界函数”,其中
的最大值称为函数
的“下确界”.已知函数
,其中
.
(1)若
,证明:
为“有下界函数”,并求出
的“下确界”.
(2)若函数
为“有下界函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796629d1136615f7891f0e5cd7f926ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d4409c3166f7229ca07183d3952085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
7 . 如图所示,两村庄
和
相距
,现计划在两村庄外以
为直径的半圆弧
上选择一点
建造自来水厂,并沿线段
和
铺设引水管道.根据调研分析,
段的引水管道造价为
万元
,
段的引水管道造价为
万元
,设
,铺设引水管道的总造价为
万元,且已知当自来水厂建在半圆弧
的中点时,
.
![](https://img.xkw.com/dksih/QBM/2022/1/24/2901456358277120/2909832154570752/STEM/6b61ee99-9aed-4b92-bfd3-0a87769f9561.png?resizew=178)
(1)求
的值,并将
表示为
的函数;
(2)分析
是否存在最大值,若存在,求出最大值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9600d011c14315338e99623269d3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355fe3d6107ed80ff49de68d3756fbe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355fe3d6107ed80ff49de68d3756fbe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1cdfe93a110796ba7592e5ef4f869aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126b6be076b1e9b257747b6e4e2c14ee.png)
![](https://img.xkw.com/dksih/QBM/2022/1/24/2901456358277120/2909832154570752/STEM/6b61ee99-9aed-4b92-bfd3-0a87769f9561.png?resizew=178)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)分析
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次
2022-02-05更新
|
780次组卷
|
5卷引用:安徽省亳州市普通高中2021-2022学年高三上学期期末理科数学试题
安徽省亳州市普通高中2021-2022学年高三上学期期末理科数学试题山东省日照市校际联考2021-2022学年高二下学期期中数学试题(已下线)专题13 函数模型及其应用上海师范大学附属中学2023届高三上学期10月月考数学试题(已下线)专题13 函数模型及其应用-2
解题方法
8 . 已知函数
,其中
为常数,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1cd0cf755cb75c35aff6dc911b52f0.png)
(1)求证:
时,
;
(2)已知a,b,p,q为正实数,满足
,比较
与
的大小关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d4d40d1e6f257935b3a52d9ffb17a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1cd0cf755cb75c35aff6dc911b52f0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e799e937076aa5a7dcd51cdc0f40f6b0.png)
(2)已知a,b,p,q为正实数,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b70d4a3fc3e01b5a6358cf4e57578e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6aaa9893d6dd865f68b1a0723d72f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1058544b35c6f5dfc023bec6dfcfd141.png)
您最近一年使用:0次
名校
9 . 函数
的图象为曲线
关于直线
的对称曲线,
,设
为函数
的导函数.
(1)当
时,求
的零点;
(2)
时,设
的最小值为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2eff609c6043c2a89a6dd163fe2244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bfa80344f93e9a2b42f32fbb2f405bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a90170d7ef5ff6d1d63517c166f7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6bf810e353d6f1318a898127d4823a3.png)
您最近一年使用:0次
2021-07-12更新
|
237次组卷
|
3卷引用:安徽省名校联盟2020-2021学年高二下学期期末联考文科数学试题