名校
1 . (1) 设
都是正数,试证明不等式:
;
(2)对一切正整数
,不等式
恒成立,求实数
的取值范围构成的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d66530037e9ad08b11dfe515571f41.png)
(2)对一切正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c6489fd62b55ca837e35a3224c44c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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解题方法
2 . 已知正实数a,b,c满足
.
(1)求
的最小值;
(2)证明:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/863e12c8a6da6c4c76f474cce0792d4a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae24688d4c45aad43e9af0b7bbfda6b.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994b2afd35bd3642b1cdde7d6016c2f6.png)
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解题方法
3 . (1)设
为实数,比较
与
的值的大小.;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49da63bbdd503faeea1ff9d2df57f83f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353a0504082335c98b71653317beabbe.png)
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解题方法
4 . 选用恰当的证明方法;解决下列问题.
(1)
为实数,且
,证明:两个一元二次方程
,
中至少有一个方程有两个不相等的实数根.
(2)已知:
,且
,求证:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1476efe1fd8970d815af8a6e62d454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341f6b48e2c616585ed9bd7dbb9c8728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3ce04492780c4d40fab17aa28d3755.png)
(2)已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c96a416540d6d2c2570c7106f5e0492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03f1c0c0618a585e86afc523bd523e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356bc29ee1bc3f046d9a7b2804c77cf9.png)
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2023-10-14更新
|
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2卷引用:江西省上饶市广丰中学2023-2024学年高一上学期10月月考数学试题
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5 . 已知集合
的子集个数为
.
(1)求
的值;
(2)若
的三边长为
,证明:
为等边三角形的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ce22a79915802052a731ea4eb70a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8858e7b26a1860f4c4e0da7da33bbada.png)
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2023-10-13更新
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6 . 已知
都是正数,且
,证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96795f9bc0252bb5fbc8ad92d4c267b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07804f1adb6446f7a2337b4d9800452.png)
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7 . 已知
.
(1)求
的取值范围;
(2)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c713535cdad706e60b91f752d99e2f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(2)若
![](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/97e188ac2faddbfc1af5ccc789c7cae3.png)
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2023·全国·模拟预测
名校
8 . 已知x,y均为正实数,且
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b8d3564d7ae5687f69b64b150c4b35.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知函数
,对于任意
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1638740ba651b56d0c833fe93d9995e4.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
10 . 已知
,
,且
.
(1)证明:
;
(2)若
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec307143b4bf45106369f256a796d61.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbdd54c04a50fa1c6d7a54a5775cc02e.png)
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2023-02-09更新
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