1 . 已知函数
,函数
.
(1)判断函数
在其定义域上的单调性(不需要证明);
(2)对任意的实数
,都有
.
①求证:
;
②若存在a的两个取值
,
,使得
(c为常数),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b21c310a00732a9eda5489e225bd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df06bdef1d4a203b4174851bc270cfe5.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40295c491170bcf632abafc92eecc33f.png)
(2)对任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fab2aa2162c65b3f30d2b9f4be1226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d682fefb826126ec14c09099eb329e3.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee246607e97330c07187ea9d748d6332.png)
②若存在a的两个取值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54eab256e011759f28bf281b74f52d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f074582e866194b78c3299d4796f418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d52943e3995bdda062b3f7930265682.png)
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2022-02-08更新
|
179次组卷
|
2卷引用:江苏省百校大联考2021-2022学年高一上学期12月阶段测试数学试题
解题方法
2 . 设函数
.
(1)证明:函数
为奇函数;
(2)求函数
的零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cccec29967a0cc5177dd0dfe24df74.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1e29db502e6c1e85a1d07898b96d62.png)
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名校
3 .
技术的价值和意义在自动驾驶、物联网等领域得到极大的体现.其数学原理之一是香农公式:
,其中:
(单位:
)是信道容量或者叫信道支持的最大速度,
单位;
)是信道的带宽,
单位:
)是平均信号功率,
(单位:
)是平均噪声功率,
叫做信噪比.
(1)根据香农公式,如果不改变带宽
,那么将信噪比
从1023提升到多少时,信道容量
能提升![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1078cd967972b58c8eb2783d8b7a41f5.png)
(2)已知信号功率
,证明:
;
(3)现有3个并行的信道
,它们的信号功率分别为
,这3个信道上已经有一些相同的噪声或者信号功率.根据(2)中结论,如果再有一小份信号功率,把它分配到哪个信道上能获得最大的信道容量?(只需写出结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47248d88a8876e1177cbd3ba43b11bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70215f90c7b8bd048aeab814ffcb1075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0594324ac79e120d87761d147159f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53801bf39bf5de59f2853caeac6f8784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bc766cbead9ec6fb613abe669b0be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bfbd55ad2a343daee3194b30a4cca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca586d4c35ce52dec4b545cf13ee0721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca586d4c35ce52dec4b545cf13ee0721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848c6dc59f47173493581489dde138df.png)
(1)根据香农公式,如果不改变带宽
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848c6dc59f47173493581489dde138df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1078cd967972b58c8eb2783d8b7a41f5.png)
(2)已知信号功率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d654dec2ae3a0f1dda3420b354d38b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0116640668a4da68b97f4f7809a95a7.png)
(3)现有3个并行的信道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b0ea548b200fd74a2412d13c00e077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e717353515a0c6f3423dd25b42509006.png)
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2023-03-16更新
|
266次组卷
|
6卷引用:北京市丰台区普通高中2020-2021学年数学合格性调研试卷
北京市丰台区普通高中2020-2021学年数学合格性调研试卷(已下线)第12课时 课后 函数的应用(已下线)专题9.2 期中押题检测卷(考试范围:第1-4章)2(中)-【满分计划】2021-2022学年高一数学阶段性复习测试卷(苏教版2019必修第一册)福建省福鼎市第六中学2022-2023学年高三上学期12月月考试数学试题湖南省名校联合体2022-2023学年高一下学期第一次联考数学试题福建省厦门市第一中学2023-2024学年高一上学期期末模拟数学试题
4 . 设a、b、c是直角三角形的三边长,其中c为斜边长,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f940e491269e04ab4680ee10714ba88c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb20698f97b29da22b1454cac302de3.png)
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2021-11-19更新
|
144次组卷
|
2卷引用:沪教版(2020) 必修第一册 达标检测 第三章 章测试
20-21高一·江苏·课后作业
5 . 设x,y为正数,满足
,求证:
(
,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae36628b71837cfb0420169ced632d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb3f7ad7aa434f11a9b78a8320be783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
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6 . (1)已知
且
,求证:
.
(2)已知a,b,
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f104c7ae45b165b39509371875faecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25fe085f704295ab2ee95ca0d03d9fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764d7cd8de118936bdf093afb8305b8c.png)
(2)已知a,b,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8310f387f5f28b11eb4669e666f3290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d0f56d4ededd1d347317cfe890b7f2.png)
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7 . (1)计算:
;
(2)判断函数
的奇偶性并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021682cc437deb7b5436bb4d1a174b6b.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47b2d73a4858fe5a169a0964c7e878e.png)
您最近一年使用:0次
8 . 已知函数
.
(1)证明:
是偶函数;
(2)设函数
,
,是否存在实数
,使得
的最小值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866bb509e1e15881a6f2651e015fc0fe.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51346a3ced6384ea453ac1f4f0854d0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef3a1198de433b651a0fd1e9a629422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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9 . 已知函数
;
(1)判断函数的奇偶性,并加以证明;
(2)若
,求
的值;
(3)若方程
在
上有解,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae15b037abd9cf52ebc598c3ead7621.png)
(1)判断函数的奇偶性,并加以证明;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7a6957adee99cb743526a1737f0feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd86fbbc5261317ea71eeb6dfbd4541.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf13d0de1e85fd846c39374250c8890.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab18412113c332df6716847f2c97c9a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021-11-29更新
|
694次组卷
|
2卷引用:四川省绵阳中学实验学校2021-2022学年高一上学期期中数学试题
10 . 已知函数
,若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e863ea4f1e8af63d06ad88a235a48f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba934874cc9f2ab272fdff67ea23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d05399ef814325fd8c5a86e52e0bb0.png)
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