2024高一·全国·专题练习
解题方法
1 . 判断下列各函数是否具有奇偶性
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d295a39a651ff4b182c792f746ebe7.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10103111f02bf84e12956a5c282a4ec1.png)
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686810dd2089a4a3a772b8a2546dfb37.png)
(4)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6070f2ee5e48cce77eb4a2cb9f11ccfb.png)
(5)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3df1b38fdab64521c3e0888876fa387.png)
(6)
;
(7)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990387f736ce73715cb41868664db7da.png)
(8)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d295a39a651ff4b182c792f746ebe7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10103111f02bf84e12956a5c282a4ec1.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686810dd2089a4a3a772b8a2546dfb37.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6070f2ee5e48cce77eb4a2cb9f11ccfb.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3df1b38fdab64521c3e0888876fa387.png)
(6)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ac4cdc066c910fca5966f968d3111a.png)
(7)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990387f736ce73715cb41868664db7da.png)
(8)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9117f2d12eb2294ddf3d2e33b52c8fdc.png)
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2 . 已知
是
上的减函数,且
,如图,记
为曲线
与直线
,直线
,以及
轴围成的图形的面积,并约定
.已知
,对任意正数
,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/578602c6-842e-4f6b-8da2-3553e172ac1a.png?resizew=157)
(1)求
与
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebadf71a3c73c1d82ae821018a7f67c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b8dc1c868e194693aca8526df70e93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae52fec0134afc670aed78812818bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0733a8512b7ec53396842328f6e7cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f34b3ff8c658fc5cf2c3b5ae5a9443dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3b4c102ae0e48d1a26964c466461800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94595481ba773bf66e7d3293b5318f59.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/578602c6-842e-4f6b-8da2-3553e172ac1a.png?resizew=157)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3724599ff059a3223fb4d51ae0febd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6aa67fa4d7e6697eefd238814004388.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93fd5334937da8063dee79c23bc05006.png)
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解题方法
3 . 已知幂的基本不等式:当
,
时,
.请利用此基本不等式解决下列相关问题:
(1)当
,
时,求
的取值范围;
(2)当
,
时,求证:
;
(3)利用(2)证明对数函数的单调性:当
时,对数函数
在
上是严格增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1419108104429f6df5d5352a05211e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e0630a1632f6368fb824ebfdead0d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1419108104429f6df5d5352a05211e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca16bee4a8ecee60c31f9aaac02539b0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27eb687fdf1568ab06ce8119845823c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92098b3da769963a2320cf1d8dad00a.png)
(3)利用(2)证明对数函数的单调性:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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解题方法
4 . 某乡镇为全面实施乡村振兴战略,大力发展特色农产业,提升特色农产品的知名度,邀请了一家广告牌制作公司设计一个宽为x米、长为y米的长方形展牌,其中
,并要求其面积为
平方米.
(1)求y关于x的函数
;
(2)判断
在其定义域内的单调性,并用定义证明;
(3)如何设计展牌的长和宽,才能使展牌的周长最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0086b15b30b83d428b35cdbe094810f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa49758e9976f1f99d53b270836dc0e.png)
(1)求y关于x的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)如何设计展牌的长和宽,才能使展牌的周长最小?
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2023-12-15更新
|
300次组卷
|
3卷引用:河南省八地市2023-2024学年高一上学期期中联考数学试题
河南省八地市2023-2024学年高一上学期期中联考数学试题河南省2023-2024学年高一上学期学业质量监测考试数学试题(濮阳、周口版)(已下线)3.4函数的应用(一)【第二练】“上好三节课,做好三套题“高中数学素养晋级之路
5 . 已知长方形的周长为10,一边长为x,其面积为S.
(1)写出S关于x的函数关系.
(2)当x从1增加到
时,面积S改变了多少?此时,面积S关于x的平均变化率是多少?解释它的实际意义.
(3)当长从x增加到
时,面积S改变了多少?此时,面积S关于x的平均变化率是多少?
(4)在
处,面积S关于x的瞬时变化率是多少?解释它的实际意义.
(5)在
处,面积S关于x的瞬时变化率是多少?解释它的实际意义.
(1)写出S关于x的函数关系.
(2)当x从1增加到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7c2d3c9d1233676abfa1e42fb93bd8.png)
(3)当长从x增加到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8620af3c7a01ebc1dbab875c3c7ec50e.png)
(4)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(5)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
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6 . 在某郁金香主题公园景区中,春的气息热烈而浓厚,放眼望去各色郁金香让人心潮澎湃,黑色“夜皇后”低调而奢华;白色“塔克马山”叶片叠层丰富,姿态雍容华贵;粉色“香奈儿”微微张开花瓣,自带芬芳.园区计划在如图所示的区域内种植樱花和风信子,让游客在花的海洋里有不一样的体验,其中
区域种植樱花,
区域种植风信子.为了满足游客观赏需要,现欲在射线
上分别选一处
,修建一条贯穿两区域的直路
与
相交于点
,其中每百米的修路费用为
万元.已知
,
百米,设
.
![](https://img.xkw.com/dksih/QBM/2023/4/28/3226149216370688/3262383766953984/STEM/1770c57f619e4687a2fe2618050a191e.png?resizew=214)
(1)试将修路总费用
表示为
的函数
;
(2)求修路总费用
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea77ba313fcc751481ac1ca214df3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b92dbe7d01d47d6c2db1396180caf76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01f2c492699e35cdb5242d1cff55f39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef670f42ee498d6d942d920c9b5ea1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afface6e34f75dc6fb982a423c08388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8873762fb8002050e8e261100dfcadb7.png)
![](https://img.xkw.com/dksih/QBM/2023/4/28/3226149216370688/3262383766953984/STEM/1770c57f619e4687a2fe2618050a191e.png?resizew=214)
(1)试将修路总费用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0496f7b645615d6cf59b8a7ec1fb6e.png)
(2)求修路总费用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0496f7b645615d6cf59b8a7ec1fb6e.png)
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2023-06-18更新
|
393次组卷
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2卷引用:湖北省荆州市部分校2022-2023学年高一下学期期中联考数学试题
7 . 利用课本中关于水库存水量的列表作出由水深确定存水量的函数图象,并根据图象估计出水深为7
和18
时的存水量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
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21-22高一·湖南·课后作业
8 . 学校要印刷一批资料,现要求纸面上、下各留4cm空白,左、右各留3cm空白,中间排版部分要求面积为
.写出纸张面积
与中间排版部分宽度
间的函数解析式
,确定其定义域,再计算出
,
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322daa37b361e169e9e05c04ce4246ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5f8148759352a4bd48e04403c54528.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da6a52e3eb6cef810c7770b8e53fdcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6520ab5cbfa43d94f411b88d05ccc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0725140bc9a0d20f5dccc9e2fa85b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bccaeb8de9c8d64846b53066536b4abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376f22b7b0615bf880affa42e759633d.png)
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21-22高二·江苏·课后作业
9 .
与
的含义有什么不同?
与
的含义有什么不同?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad19d1ad05a31122ad5163011c89572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad19d1ad05a31122ad5163011c89572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
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名校
解题方法
10 . 喷绘在商业广告、宣传等领域应用广泛,喷绘画面是使用喷绘机打印出来的,喷绘机工作时相当于一条直线(喷嘴)连续扫过一张画布.一家广告公司在一个等腰梯形OABC的画布上使用喷绘机印刷广告,画布的底角为45°,上底长2米,下底长4米,如图所示,记梯形OABC位于直线位于直线
左侧的图形的面积为
.
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897254977765376/2901291588763648/STEM/e86aa6f7-ea3c-47c0-b59d-44bed2d1da11.png?resizew=187)
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897254977765376/2901291588763648/STEM/91f4973d-7a68-4f54-9dd8-071588d69a95.png?resizew=200)
(1)试求函数
的解析式;
(2)定义“
”为“平均喷绘率”,求
的峰值(即最大值).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0c03f0156764e6358d83697ea14c5ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897254977765376/2901291588763648/STEM/e86aa6f7-ea3c-47c0-b59d-44bed2d1da11.png?resizew=187)
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897254977765376/2901291588763648/STEM/91f4973d-7a68-4f54-9dd8-071588d69a95.png?resizew=200)
(1)试求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
(2)定义“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d53aa74746a8f68b5011889d7edfe2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85a9bd008da608222ba5f6f895af4d4.png)
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2022-01-24更新
|
569次组卷
|
3卷引用:山东省聊城第一中学2021-2022学年高一上学期期末数学试题