1 . 计算:
=_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8091f751a15fb454b064699a641c9883.png)
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2 . 若函数
的反函数为
,且
,则满足
的最小正整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c09c5c89b0c2a92f8c4b70e69b0eada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87acb883fe6dd6cb459c033bf9bdb71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed00705daf66f852b389b7610d31bc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8321dab9d32a7adeb315561309d1d8cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
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3 . 方程
的解集为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a9609fa1a1b815015f389ddbeeb37a.png)
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4 . 已知多项式
,其中,
为实数.证明:对任意的实数
,方程
总有一个相同的实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60028d1fc0110b1f1033f1c2369e7084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
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5 . 已知
为实数,且
,对
的子集
,定义
.其中,规定
,问:从
个这样的和中至多可以选出多少个,使得其中任何两个的差的绝对值都小于1?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45632e466a5b812cb07d1028354e9b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5901081b7e6663fa5cfb8e78c296b07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d249b8be9430336508cc335a7ec5365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33606a9773ac6e863372e92af397f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ce378226efe14e225f544e038c49c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5a006b512874cd327a55ad103e13a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b250e4276bf3f328b03a66765541f6.png)
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解题方法
6 . 已知
,存在实数
,使得当
时,
恒成立.则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6646ee1281b3b22e6a6ded9da1f9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2425497f56c3bdc9a8d7cde18e41d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfc7d3c0bbc528e156df4d81c68cd7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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7 . 设
定义在
上,其值域
,且对任意
,都有
,及
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b5f048601c517976d3d0aed0d69a9c.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77a223051a000f12f4aa1782f9168b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3958d0c5011d5ec0fecece58364caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e4525be9d715134956094f1f7c9b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8296abd12e85b7eccd1090e8852c93a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b5f048601c517976d3d0aed0d69a9c.png)
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8 . 已知
,一元二次方程
有重根.则
的值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b59d4aaaf7530f9bd32f8908ffe8fd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8322821f14f589c356fca9039015e274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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9 . 试求所有的正整数
及实数
,使得
与
均为有理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4c713b7949a2d1d135d7de6e79a5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e672b083e78026f5a07f9d90a443b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c932450b050a8b7b1ec8dd2891e4abc.png)
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10 . 使得方程
①只有整数解的实数
的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd5fe667935a08f278f0b74c66832cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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