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1 . 宜昌一中江南新校区拟建一个扇环形状的花坛(如图所示),按设计要求扇环的周长为30米,其中大圆弧所在圆的半径为10米,设小圆弧所在圆的半径为
米,圆心角
(弧度).
![](https://img.xkw.com/dksih/QBM/2017/3/23/1650174128562176/1650788506591232/STEM/f5f59454d9a94421b90ea685e6914cb9.png?resizew=157)
(1)求
关于
的函数关系式;
(2)已知对花坛的边缘(实线部分)进行装饰时,直线部分的装饰费用为4元/米,弧线部分的装饰费用为9元/米,设花坛的面积与装饰总费用之比为
,求
关于
的函数关系式,并求出
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/2017/3/23/1650174128562176/1650788506591232/STEM/f5f59454d9a94421b90ea685e6914cb9.png?resizew=157)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知对花坛的边缘(实线部分)进行装饰时,直线部分的装饰费用为4元/米,弧线部分的装饰费用为9元/米,设花坛的面积与装饰总费用之比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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2017-03-24更新
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2 . 已知函数
若关于
的方程
恰有三个不同的实数解,则满足条件的所有实数
的取值集合为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6586be92b2725e2c5d29780b1c91d230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9058368324b4f846cefd4a834768c277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2017-03-20更新
|
922次组卷
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4卷引用:2017届江苏省如东高级中学高三2月摸底考试数学试卷
2017届江苏省如东高级中学高三2月摸底考试数学试卷【全国百强校】江苏省扬州中学2019届高三10月月考数学试题2019年江苏省扬州市高邮市高三上学期开学考试数学(文)试题(已下线)专题02 导数及其应用-《巅峰冲刺2020年高考之二轮专项提升》(江苏)
3 . 某湿地公园内有一条河,现打算建一座桥将河两岸的路连接起来,剖面设计图纸如下:
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647033146163200/1647946590740480/STEM/30f0c34163754a4a9e5609184b23ac76.png?resizew=489)
其中,点
为
轴上关于原点对称的两点,曲线段
是桥的主体,
为桥顶,且曲线段
在图纸上的图形对应函数的解析式为
,曲线段
均为开口向上的抛物线段,且
分别为两抛物线的顶点,设计时要求:保持两曲线在各衔接处(
)的切线的斜率相等.
(1)求曲线段
在图纸上对应函数的解析式,并写出定义域;
(2)车辆从
经
倒
爬坡,定义车辆上桥过程中某点
所需要的爬坡能力为:
(该点
与桥顶间的水平距离)
(设计图纸上该点处的切线的斜率),其中
的单位:米.若该景区可提供三种类型的观光车:①游客踏乘;②蓄电池动力;③内燃机动力.它们的爬坡能力分别为
米,
米,
米,又已知图纸上一个单位长度表示实际长度
米,试问三种类型的观光车是否都可以顺利过桥?
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647033146163200/1647946590740480/STEM/30f0c34163754a4a9e5609184b23ac76.png?resizew=489)
其中,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974bc22aed322f940bdd8a83de869edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e04a5b59cced25ab7057d03fe3c0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e04a5b59cced25ab7057d03fe3c0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fed19e09b52266a544aebf9077a1270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a1008494918681c42448ebef61dea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974bc22aed322f940bdd8a83de869edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc96ce462f6a456c6993588e8edb0af2.png)
(1)求曲线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
(2)车辆从
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b237a5e4df47a0a2cf6c468d39085bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1452ad51bc851e39fb45acb2825089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b418f716e6ea876faa7b003b8af56044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742145c3bfb5281e2e583e6405a3d4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f08d5e69543f99644ac3c8974c5b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
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4 . 定义在
上的函数
满足:
,并且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7aac41b55c039c3550f87d545704e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41c0b87a5b0cdbfd638a9f0f581a4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e630a93b3433bffa9521161469c7b23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c9ee5191aa96478eb5a4deb07ddacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7aac41b55c039c3550f87d545704e39.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 若实数
、
、
满足
,则称
比
接近
.
(1)若
比3接近0,求
的取值范围;
(2)已知函数
的定义域
.任取
,
等于
和
中接近0的那个值.写出函数
的解析式,并指出它的奇偶性、最小正周期、最小值和单调性(结论不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b64829ac929dfe6c4adced699ad2da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e1fbe0fb49725cf6d1e689ee8986d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a117cef9f5e2e304a88395d1f03dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d184609decfae5beb784ab6ca385803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e988af7b349ed5eb8312772ca6ce6b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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解题方法
6 . 在某次水下考古活动中,需要潜水员潜入水深为30米的水底进行作业.其用氧量包含3个方面:①下潜时,平均速度为
(米/单位时间),单位时间内用氧量为
(
为正常数);②在水底作业需5个单位时间,每个单位时间用氧量为0.4;③返回水面时,平均速度为
(米/单位时间), 单位时间用氧量为0.2.记该潜水员在此次考古活动中,总用氧量为
.
(1)将
表示为
的函数;
(2)设0<
≤5,试确定下潜速度
,使总的用氧量最少.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd5ed2da95cbfcf6ca66d919a0d6d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e36c53355664937aa548031db22e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
(2)设0<
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
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2016-12-03更新
|
591次组卷
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2卷引用:2015届江苏省如东高中高三上学期第8周周练理科数学试卷
2013·江苏·三模
7 . 某单位设计的两种密封玻璃窗如图所示:图1是单层玻璃,厚度为8 mm;图2是双层中空玻璃,厚度均为4 mm,中间留有厚度为
的空气隔层.根据热传导知识,对于厚度为
的均匀介质,两侧的温度差为
,单位时间内,在单位面积上通过的热量
,其中
为热传导系数.假定单位时间内,在单位面积上通过每一层玻璃及空气隔层的热量相等.(注:玻璃的热传导系数为
,空气的热传导系数为
.)
(1)设室内,室外温度均分别为
,
,内层玻璃外侧温度为
,外层玻璃内侧温度为
,且
.试分别求出单层玻璃和双层中空玻璃单位时间内,在单位面积上通过的热量(结果用
,
及
表示);
(2)为使双层中空玻璃单位时间内,在单位面积上通过的热量只有单层玻璃的4%,应如何设计
的大小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b432ad272dada9c6f397a0b47127ad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f86423acfd187cdf283d049ed77bf64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986a1f1c59a29ee365da1eb05a3ef286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a010df0727bb8fa9fe335e8b4e21b5.png)
(1)设室内,室外温度均分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd59e8a1a7c98c65bc485f96db60e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5296995fabbd85a155f72072bdbbae26.png)
![](https://img.xkw.com/dksih/QBM/2013/8/23/1571324929097728/1571324934766592/STEM/81441b355fe6465db426709c48038f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)为使双层中空玻璃单位时间内,在单位面积上通过的热量只有单层玻璃的4%,应如何设计
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2013/8/23/1571324929097728/1571324934766592/STEM/ec7321ea5ca943859a775056d8ebbee1.png)
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