解题方法
1 . 已知实数a,b,c满足
,且
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2 . 已知
两城市的距离是
、根据交通法规,两城市之间的公路车速应限制在
,假设油价是6元
,以
的速度行驶时,汽车的耗油率为
,其它费用是36元
.为了这次行车的总费用最少,那么最经济的车速是______
(精确到
,参考数据
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5a1095f11a367fc0bfdd114211fab3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63485ebe83696b2cafc4def229a72a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4f28d7d8a7d65eb5975c0ce63c0f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c374e788e84cbfee7e2ed8e736dc73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46606b6a3216fe6602234651c295a893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba775247f1c1878457d8a1617138b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ca55c030e7d88040525c4fb9a278f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e35c9a7ad2892527103ef7e0c0f01ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4231756409476912148b5094ce0701fb.png)
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2023-06-18更新
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5卷引用:广西南宁市武鸣区武鸣高级中学2024届高三上学期开学调研测试数学试题
解题方法
3 . 已知a,b均为正实数,且
,证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8335f6dfc2728f7d24d84ebd3554733.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3623ba729fc8c79ac64041467904a981.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e6c9f5a5aa49b8c7c892d7968c61c1.png)
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2023-05-26更新
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2卷引用:广西邕衡金卷2023届高三第三次适应性考试数学(理)试题
4 . 已知实数
,
都为正数,且函数
.
(1)若
,解不等式
.
(2)若
,且函数
的最小值为
,证明:
.
![](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/d4490503c29b1743ca34b05e900d8730.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4d6744a7fceeb92b8d49099cd69f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab989f85a681b41c29465d4be74b789f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3138c30b73a9ebdc65a55cf008eb36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b66865276c9d141213df6858413bd41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e41caf7d9fe70feb99f10b5c9dc423.png)
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5 . 已知
.
(1)求不等式
的解集;
(2)若不等式
的解集为
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d9ef2a3f27e25140d8fe8384f40f84.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665dc334a37e61c356b636604eb0f8c3.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00506b3c9d91ce3d0348de1f6115a97f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
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2023-05-12更新
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6卷引用:广西南宁市第三中学2023届高三一模测试数学(理)试题
广西南宁市第三中学2023届高三一模测试数学(理)试题广西南宁市第三中学邕衡金卷2023 届高三校一模数学(文)试题四川省广元市宝轮中学2023届高三仿真考试(二)数学(理)试题四川省广元市宝轮中学2023届高三仿真考试(二)数学(文)试题(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(十一)(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(十一)
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解题方法
6 . 已知
.
(1)解关于
的不等式:
;
(2)若
的最小值为
,且正数
,
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffc77a665e9cb7aabc960cf97e4261e.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665dc334a37e61c356b636604eb0f8c3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/034a0f4d3755f5f4934e5f11b1296c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64381a97a9a98b979eb2fc4a4cd979d.png)
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2023-05-10更新
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681次组卷
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5卷引用:广西2023届高三毕业班高考模拟测试数学(理)试题
解题方法
7 . 已知函数
.
(1)解关于
的不等式
;
(2)若
的最小值为
,且正数
,
满足
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae283490f6e021b1129b85d0b313419.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5229bf257fabd4342f0e46d0260fd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/c6e0a2cafbf15afb2672ddc89b0059a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0113fd4c7d157757571f9a009e02af.png)
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2023-05-07更新
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303次组卷
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2卷引用:广西桂林市、北海市2023届高三联合模拟考试数学(文)试题
解题方法
8 . 已知
,
,
,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/7ca90d00a0366dbbc3d5e0a4f4a2af61.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4702d88db943970c356b93c5b5292db7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bd367cea975718cd3eba1e114e3086.png)
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2023-05-03更新
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178次组卷
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2卷引用:广西邕衡金卷2023届高三一轮复习诊断性联考数学(理)试题
9 . 若设
为曼哈顿扩张距离,它由
个绝对值之和组成,其中
为正整数.如:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133a79588fde7dc67b916e1e5001d83e.png)
(1)若
,求
的取值范围;
(2)若
对一切实数
恒成立,设
,
,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e033b17895fb89d9b210d2dd2950ae20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133a79588fde7dc67b916e1e5001d83e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcc7cb0ace077a0368e1059e0379b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec74d91bdc05dcedf66bb785d1db45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](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/b111ba21bcdb0e1823a9b0fa4305b289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0113fd4c7d157757571f9a009e02af.png)
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解题方法
10 . 已知函数
,
.
(1)若
,求不等式
的解集;
(2)已知
,若对任意
,都存在
,
使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8012e58e45911358c52e27e367a8182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995ec593baa4ef50b6d87c78380953d7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f88a356f9697e432b397a78b60f262.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e067be545a0178382625422a2e67621d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be16eac83515fc9e60720be12f1f558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-04-26更新
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725次组卷
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7卷引用:广西玉林市北流市2023届高三年级教学质量检测数学(理)试题