名校
解题方法
1 . 证明下列不等式:
(1)若
,求证:
;
(2)若
,
,
,求证:
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75e17b53ee815ef4853237102ba053e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e271b6e63206285461a7552d11efd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89dbe5f997bd1b79c750c89ac7c87b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e79fa168ab3bc754a4fdd4deea38246.png)
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解题方法
2 . (1)已知
,
,用作差法证明:
;
(2)已知
,
都是正数,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c79de030dea51c5e80e233b44788de.png)
(2)已知
![](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/cc98f6e2b1d41bc552c083979f53a83d.png)
您最近一年使用:0次
名校
解题方法
3 . (1)设
,证明:
.
(2)已知正实数
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ada798eeba5bd19d497bfd0741afd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6320fbdc13c4ab88cf8f577cce4001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e14cc5eb8fc0c17058e33ae8e3765f.png)
您最近一年使用:0次
名校
解题方法
4 . 已知
,
,且
,证明:
(1)
;
(2)
.
![](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/4a7dbc702617c765a573961953cc0901.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ba449a8e384c9696b21ec11f19e256.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef22557e767d36c91571675e964825e4.png)
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解题方法
5 . 已知
.
(1)若
,求证:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75807858b7804a1ad2039c41f323a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288420f0b137ec90d963e6b5db65fe30.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753bc7b46730ab08df9ee4488ce34986.png)
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解题方法
6 . (1)已知
,求
的取值范围;
(2)已知
,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa4ae5deebd70f636979c67ddeb6dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24fb6244f7eb128adbe4515e88aa9e53.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fed98a219097783e0ca2f41483cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4032f478968290363b0f6488610e123.png)
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名校
7 . 基本不等式是高中数学的重要内容之一,我们可以应用其解决数学中的最值问题.
(1)已知
,
R,证明
;
(2)已知
,
,
,
R,证明
,并指出等号成立的条件;
(3)已知
,
,
,
,证明:
,并指出等号成立的条件.
(4)应用(2)(3)两个结论解决以下两个问题:
①已知
,证明:
;
②已知
,
,且
,求
的最小值.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1f5facca1d0db44613d7c690bc90aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267cd7062303bbe8d8a4bd8dd48fef2e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7701d084d2b153bbea08cfbf63413a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61d582437402db050313612348dfa27.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d51126fd77ba262607809563550b48f.png)
(4)应用(2)(3)两个结论解决以下两个问题:
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5acd1467c10c7ff14caca53feea7a540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d49468bf449d201b533f5f8f9e9add1.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983154ee44321cef8eb8213bd862c70d.png)
您最近一年使用:0次
2024-02-10更新
|
137次组卷
|
2卷引用:云南省昆明市官渡区第五中学2023-2024学年高一上学期期中测试数学试卷
名校
解题方法
8 . 比较下列各组中
与
的大小,并给出证明.
(1)
与
;
(2)
与
,(其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b5bc4aacc85a270b2cf47c59ab0f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c512ead5eebabcf7d2ca3b49dfd17b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4004aac9b2a4373a20e8ebcd0b80a7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e21529984fbaa0c964a0bf7cd8d97f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de80056c578b7bd0078af765b41e51b.png)
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2023-10-11更新
|
136次组卷
|
2卷引用:云南省大理白族自治州民族中学2023-2024学年高一上学期10月月考数学试题
名校
9 . (1)设
,
,求
,
,
的范围;
(2)已知
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e70bbafca5c73383459c37fe7ea35f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b2d527e76722fc897e2b8b29df89c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3910a0f217d8109b9467f740fc84a73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754826457671db8939098215943e656a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be94bcdd073e5e6c8137caa90e41b9a.png)
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2023-01-05更新
|
370次组卷
|
2卷引用:云南省曲靖市第一中学2022-2023学年高一上学期第一次阶段性测验数学试题
名校
解题方法
10 . (1)用作差法比较多项式
与
的大小;
(2)已知
,
,判断
与
的大小关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6933572874f9bf5d1e2dae8b147fc651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6b0d68ad09663edca4afe718479200.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a070d6518b58512d61fcb24e889a75.png)
您最近一年使用:0次