2011高三·陕西·竞赛
1 . 设函数
,其中,
,
.已知当
时,
取得最大值.
(1)求
的值;
(2)设
,求函数
在
上的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecd2dc5603478be1d2818a176f9e4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcadd1781ee9177e9bc76ce48afdd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f56a20bc5fce6b02217627b42249854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97a1894f18b2b4b21e00166046a208f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a1d9a86dac105a6136ab2452b35b2.png)
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2009高三·陕西·竞赛
2 . 设
,
.若对任意的
,都有
恒成立,试求
、
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eeae4e4940d654f083f1073ba872504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23241b8f108df2ebb858c6ab622db460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d868a70648e7bcb20b453c911aec687e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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3 . 设函数
的最大值为
, 最小正周期为
.
(1)求
的值 ,并写出函数
的单调递增区间;
(2)若10个互不相等的正数
满足
, 且
, 求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c215c27ee7f51edcfb0bbba343e1a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8df5cb10e04ae048e67f3b5d2cf276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若10个互不相等的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23707e062bbdc42a260524be0931dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babcd88dfcc0c1155e41815c7a45219f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40bbaf184597390081392a2e39f3beff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d081a4fefbad6b7728cdb03e17e08e4d.png)
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