1 . ⑴求证:对于任意实数x、y、z都有
.
⑵是否存在实数
,使得对于任意实数x、y、z有
恒成立?试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621d907ae622e786d2a56890cea2ad14.png)
⑵是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50eca09b66237488f8b9d9ed9737c406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c9299f308bb04438f647d975c20580.png)
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2 . 已知
,
,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2769ff2378bec4f25ca04fdee23d257b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6511214bd933fe06dc4a44c5f8d0fe.png)
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3 . 已知函数
,数列
、
满足
,
,
,
,
.
(1)求
的取值范围,使得对任意的正整数
,都有
;
(2)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fbd56fe7b6b14439638211d79f79eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d765033fa3e470b4b4bae90a28514587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc5ac1542da56851d19240e723a1530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca42e7cd03df12843de137eb8843f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e713f441cb0f03cf7ca5d7f4cd157f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2798e1dcab1f7f0fe3b8a94b3cd6a88.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b72ddd7de598464a37b10f03f67b904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb774169e51010958807547268ca0430.png)
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4 . 某县位于沙漠地带,人与自然长期进行顽强的斗争,到1998年底全县的绿化率已达到30%.从1999年开始,每年将出现这样的局面,即原有沙漠面积的16%将被绿化,与此同时,由于各种原因,原有绿化面积的4%又被沙化.
(1)设全县面积为1,1998年底绿化总面积为
,经过n年后绿化总面积为
,求证:
.
(2)至少需要多少年的努力,才能使全县的绿化率超过60%?(年取整数,lg2=0.3010)
(1)设全县面积为1,1998年底绿化总面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f48a6e89f0a530b996c8e1a9c0c2e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0976f5e4d3a3ee1ab85f76ceb8ae638b.png)
(2)至少需要多少年的努力,才能使全县的绿化率超过60%?(年取整数,lg2=0.3010)
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5 . 已知
. ①
(1)若存在正数a、b、c使不等式①成立,证明:
;
(2)存在正数a、b、c使不等式①成立,且凡使不等式①成立的任意一组正数a、b、c均为某三角形的三边长,求满足条件的整数k.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da35a5fbce7f381e3631979d089336d.png)
(1)若存在正数a、b、c使不等式①成立,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca42ff2e3224281f0074bb1b5dd4e61.png)
(2)存在正数a、b、c使不等式①成立,且凡使不等式①成立的任意一组正数a、b、c均为某三角形的三边长,求满足条件的整数k.
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