解题方法
1 . 设
,
.
(1)当
时,求满足
的
的取值范围;
(2)求证:函数
在区间
上是严格增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29af63fe493f0dc8f2a608139cfaff1e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cc25a7cf28ed096549fbae97fce40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2372f424431ce7b547a66b7d61d75421.png)
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2 . 用数学归纳法证明
对任意
的自然数都成立,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9b58e5ec64283a9083bff4700d5aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cb5aa6da1c6f69d1d95c47e4bd510b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.1 | B.2 | C.3 | D.4 |
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2020高一·上海·专题练习
3 .
的定义域为
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)求证:
;
(2)
在
最小值为
,求
的解析式;
(3)在(2)的条件下,设
表示不超过
的最大整数,求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c207c772848becff65515cff91879823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf204e8357b7b74b7056c17aba7d4d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a915c1a8a9304aeb307d130faaeb15.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f834919ae05f160dfedc4305851c1c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032e3d25c9f38a3cf745fed1ce3297be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fab6009ffb15a88bd843a1c2b8d7770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56940904b01a6b66a0f8feb551962b69.png)
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4 . 若实数x,y,m满足
,则称x比y接近m,
(1)若
比3接近1,求x的取值范围;
(2)证明:“x比y接近m”是“
”的必要不充分条件;
(3)证明:对于任意两个不相等的正数a、b,必有
比
接近
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4efe2bd1a70890686b5301836e3ab9f7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d8f793466e8e5d1c04ac4d2b61fce3.png)
(2)证明:“x比y接近m”是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac759fcccff5268aa820cc539c06196a.png)
(3)证明:对于任意两个不相等的正数a、b,必有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a977414a3ad65caf5eee28e0cd175de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe2b05214c8b22507f0c36b110593d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c717d2811d58b258ce0b08ff602c027.png)
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2020-12-03更新
|
1850次组卷
|
12卷引用:上海市华东师范大学第一附属中学2020-2021学年高一上学期期中数学试题
上海市华东师范大学第一附属中学2020-2021学年高一上学期期中数学试题(已下线)3.2 基本不等式(2)应用与难点(课堂培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)(已下线)第1课时 课后 等式与不等式性质(已下线)专题2.1 基本不等式的应用技巧-《聚能闯关》2021-2022学年高一数学提优闯关训练(人教A版2019必修第一册)(已下线)第04练 等式性质与不等式性质、基本不等式-2022年【寒假分层作业】高一数学(人教A版2019选择性必修第一册)(已下线)第3章《不等式》 培优测试卷(一)-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)(已下线)3.2 基本不等式福建省福州市长乐第一中学2022-2023学年高一上学期第一次月考数学试题(已下线)第1课时 课后 等式与不等式性质(完成)(已下线)高一上学期期中考试解答题压轴题50题专练-举一反三系列(已下线)专题03 不等式与不等关系压轴题-【常考压轴题】(已下线)专题04 基本不等式压轴题-【常考压轴题】
名校
5 . 已知函数
(
),
(1)求函数
的反函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
(2)判断
的单调性并证明
(3)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a2299ba8b37e81821f1a2dcfaba653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
(3)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c379b552bb751ee121b7fad8202d527.png)
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6 . 已知等差数列
的首项为p,公差为
,对于不同的自然数
,直线
与
轴和指数函数
的图象分别交于点
与
(如图所示),记
的坐标为
,直角梯形
、
的面积分别为
和
,一般地记直角梯形
的面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/adc837fc-8ef6-409e-aa53-fff996a246e8.png?resizew=226)
(1)求证:数列
是公比绝对值小于1的等比数列;
(2)设
的公差
,是否存在这样的正整数
,构成以
,
,
为边长的三角形?并请说明理由;
(3)设
的公差
为已知常数,是否存在这样的实数p使得(1)中无穷等比数列
各项的和
?并请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe9369621149328a9e5629bc5314604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119c3668df6b58ab9c1b446d5cc03f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a462f40a65837da43de04d8b7630f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54adcc408f0836e287a673d04897c691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693358ba8c2bbc11a5964d53d5353322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84866cf313ae21784d3bffc3a73ac6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84866cf313ae21784d3bffc3a73ac6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aebadfbe0d52ea3bbdf6c7497460cb0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9906f38977b8f1245e408d06b3dd762a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6ad57bc4ede4c8a8e144bfd8e59e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d43eb0b274e00cbbc4a210da4165042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530f5b63e797195906285c0c03eb9276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3cb27281079a09332b1d1ce540ee28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f18f2c2ec67b5e59e4b3d28795d125.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/adc837fc-8ef6-409e-aa53-fff996a246e8.png?resizew=226)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519af3f19dde038fab2e68b5e2a5387.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3012337aa392709349731fb1eef5b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95931effbd59c43e8ed1ea09962b84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a61a13583a33aea4b957969b35f858f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2cadd8dd1bb57eef105921197682f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519af3f19dde038fab2e68b5e2a5387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edb7bb97d8cb697434858f1697fefd.png)
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