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1 . 已知定义在R上的函数
同时满足以下两个条件:
①对任意
,都有
;
②对任意
且
,都有
.
则不等式
的解集为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c519963392bec12711230e02f86c990.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e32125207addc3fdb92ceb0ec80ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef42ef19c30c038b75f1710278ad0c76.png)
则不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cecc6ea0f5a7861bad48939000ab668e.png)
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2 . 函数
对任意的
,有
,设函数
,且
在区间
上单调递减,若
,则实数t的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d146764ebc4321ee4ceda890c342fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2736f4a78fa5e3ba33463ca70a9995a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972a386ca60f230db2f5ca21468090.png)
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解题方法
3 . 同学们,你们是否注意到,自然下垂的铁链;空旷的田野上,两根电线杆之间的电线;峡谷的上空,横跨深洞的观光索道的钢索.这些现象中都有相似的曲线形态.事实上,这些曲线在数学上常常被称为悬链线.悬链线的相关理论在工程、航海、光学等方面有广泛的应用.在恰当的坐标系中,这类函数的表达式可以为
(其中
,
是非零常数,无理数
),对于函数
以下结论正确的是______ .(填序号)
①
是函数
为偶函数的充分不必要条件;②
是函数
为奇函数的充要条件;
③如果
,那么
为单调函数;④如果
,那么函数
存在极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82f925291f499caf267036053060609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2beb22b735da7cb8054dd722450632f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9cdea1e995c59e5d3225acad8b4d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed37ee7432002cd0e0978b2012e184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5f0d374837655cc286d326305da36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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4 . 设函数
为奇函数,当
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba6f464aa447524ec2e4183abb6e64f.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4efa8a11b0c3ab7f965a1b0cdf45b3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba6f464aa447524ec2e4183abb6e64f.png)
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