解题方法
1 . 已知函数
,(其中
是自然对数的底数)
(1)判断函数
在
上的单调性(不必证明);
(2)求证:函数
在
内存在零点
,且
;
(3)在(2)的条件下,求使不等式
成立的整数
的最大值.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2449e5f1b9bb4207c417e54c015159ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f935fa5d0ae1b208aff21aa468ecf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4015b3933584f7e0b4b27ee20aec5aa4.png)
(3)在(2)的条件下,求使不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7e97df7844dd6633cfa48c0dcc385a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670fe3513adf8e865c006336f75077ff.png)
您最近一年使用:0次
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解题方法
2 . 已知函数
.
(1)当
时,直接写出函数
的单调区间(不需证明);
(2)当
时,求
在区间
上的最大值和最小值;
(3)当
时,若函数
在
上既有最大值又有最小值,求证:
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edebc46619f44fc7db7a82b55754ca78.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fab11f38ab8593932082ec4d9c8c91f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a3a7a0d64b9c01ccecd21cc97beb80.png)
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解题方法
3 . 已知
.
(1)求证函数
是奇函数:
(2)判断函数
的单调性并用定义法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c34d64a7bea0629324b9105d94556ff.png)
(1)求证函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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2022-12-13更新
|
340次组卷
|
4卷引用:上海市西南位育中学2020-2021学年高一上学期期末数学试题
上海市西南位育中学2020-2021学年高一上学期期末数学试题上海市徐汇中学2021-2022学年高一上学期12月月考数学试题湖北省恩施州咸丰春晖学校2022-2023学年高一上学期11月月考数学试题(已下线)4.2 指数函数的图像与性质(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高一数学精品教学课件(沪教版2020必修第一册)
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4 . 若集合A具有以下性质:①
,
;②若x、
,则
,且
时,
.则称集合A是“好集”.
(1)分别判断集合
是否是“好集”,并说明理由;
(2)设集合A是“好集”,求证:若x、
,则
;
(3)对任意的一个“好集”A,证明:若x、
,则必有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2faf3937abcb6a59071c17bc6bb10f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a2410ce34b36954ed4923e600d42f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46de01c5104b9112a688df37eadb000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd77104cc745d1e0e262122da34482d.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc51474b54120493b300a14e566cbc0e.png)
(2)设集合A是“好集”,求证:若x、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957d41dbe52b49c3a7339e3519a3fe84.png)
(3)对任意的一个“好集”A,证明:若x、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63c91626ffa91e590925e6f206c3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09db4828342fb0a79e0ea8d132b76e6f.png)
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解题方法
5 . (1)已知函数
,
,若对于任意实数
,
,都有
,求证:
为偶函数.
(2)若函数
的定义域为
(
),证明:
是偶函数,
是奇函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.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/333cf846facfab1283527ebe48961a95.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/90c3cfb21d60dc4bea0083dbbba146c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d7211f5ae635028cb349a8580a587d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1836fe79a57e10d585d267c50d67d421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8625e475c73bdfd992254680dc7d6b7f.png)
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2021-11-26更新
|
335次组卷
|
4卷引用:苏教版(2019) 必修第一册 过关检测 第5章 5.4 函数的奇偶性
苏教版(2019) 必修第一册 过关检测 第5章 5.4 函数的奇偶性北师大版(2019) 必修第一册 数学奇书 学业评价(二十二)函数的奇偶性(已下线)专题3-6 抽象函数性质综合归类(2) - 【巅峰课堂】题型归纳与培优练(已下线)第14讲 函数的奇偶性十大题型归类总结(1)-【同步题型讲义】(人教A版2019必修第一册)
名校
6 . 设函数
.
(1)求
的值;
(2)判断函数
的奇偶性并证明;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa6886b6b9df83a5942cdb0c7017539.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0a99715731d8dccd5fd0c77abbd9e3.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6853d01dfa3c24c7a5bf9ad0b026567d.png)
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2021-11-16更新
|
200次组卷
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2卷引用:广东省广州市番禺区实验中学2021-2022学年高一上学期期中数学试题
7 . 若对于任意
,
,使得
,都有
,则称
是W陪伴的.
(1)判断
是否为
陪伴的,并证明;
(2)若
是
陪伴的,求a的取值范围;
(3)若
是
陪伴的,且是
陪伴的,求证:
是
陪伴的.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ba8542fbe02e78cf3948c9abea9855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5c93e9660a396fa4480011de15077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daef57e451456c817f2f64cffe42a73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c124b1e1e7241cc507a351bcd1f273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e70124e83e169692d19cc8d3c2e924ea.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c6c52b42a8404031b97d71ed6a1b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e70124e83e169692d19cc8d3c2e924ea.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b378c027964a5f51a6b004bae5b2d0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce700a387c89497f5c98889881a735c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f0d82308db0868690c7d65935b79ae.png)
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2020高一·上海·专题练习
解题方法
8 . 求证:
是非奇非偶函数,证明如下:
,这种证法正确吗?若正确,说明理由;若不正确,请给出正确的证法.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c395237799431ccbd691c17d5c78ac3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca396931119b281c453a851379538961.png)
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9 . 对于给定的抛物线
,使得实数p、q满足
.
(1)若
,求证:抛物线
与x轴有交点.
(2)证明:抛物线
的最大值大于等于抛物线
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d972cf8c74b5218298b60908716a8d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c059fce1db054ebb94902a84d25fcd43.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e864b9d4b6a0aa76416348778b26d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2630d6cf14b3e8c82ee7080799901b8d.png)
(2)证明:抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bee92cd110cd46e04633e18c17c4b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188f03bd3b6ee375cbc88926cfbcd774.png)
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10 . 证明:已知函数
是二次函数,且
,
.
(1)求
的解析式;
(2)求证
在区间
上是减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b178d7a6c9e31c319407708df1cbce42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2647808a86e7d83b56d7efcdac8a33f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dcdd87d593df4a5c5e98d47fe1cfa6.png)
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