2024高三·全国·专题练习
解题方法
1 . 求下列函数的值域.
(1)
;
(2)
;
(3)
;
(4)
;
(5)
;
(6)
;
(7)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e38400e4767456abc2b6f54a598c7e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8354f8b093d8dc6d0cfcab3b9446237e.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8069ed40669ef8a87db48630351eb.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96283383edbce2e5731389b0b494fd57.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b159024997558d17d9557028021c08c5.png)
(6)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729c9998600fb4d05930bd13f85274a5.png)
(7)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d166622df6621861e3910251de70eb44.png)
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2024高三·全国·专题练习
2 . 已知实数x,y满足
,则
的最小值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392c3594f2692b415bc7f71c25a15171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d6df06a5b85848dc4fa33327f8e07.png)
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3 . 已知
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661a1f0149c4aa4961553bb9023d882e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
A.1 | B.![]() | C.![]() | D.0 |
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解题方法
4 . 已知
的值域为
.
(1)求实数
的值;
(2)判断函数
在
上的单调性,并给出证明;
(3)若
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be8c296dba4a6442f262437f6671c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a475fec8ded321e10a6697319fb975.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f3966052d4a779b6247fdf12f97cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb85ae535f90b3c125d86b439ab2562.png)
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解题方法
5 . 已知
,
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b40b1544e62be8b9e9f4dc9f2c0c74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404c3be5eb6a7c2d3c6011c58cd2056f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 冷链物流是指以冷冻工艺为基础、制冷技术为手段,使冷链物品从生产、流通、销售到消费者的各个环节始终处于规定的温度环境下,以减少冷链物品损耗的物流活动.随着人民食品安全意识的提高及线上消费需求的增加,冷链物流市场规模也在稳步扩大.某冷链物流企业准备扩大规模,决定在2024年初及2025年初两次共投资4百万元,经预测,每年初投资的
百万元在第
(
,且
)年产生的利润(单位:百万元)
,记这4百万元投资从2024年开始的第
年产生的利润之和为
.
(1)比较
与
的大小;
(2)求两次投资在2027年产生的利润之和的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e689c77944a79ca81903eb62395017c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7905fd422e78a1d22ff6f11950bc5cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028e5487544a976e62faac4718f6142d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
(1)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde5436f3334064823c8c4ca49aa3a45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d268e3666b7c4de889fd22649d65a20.png)
(2)求两次投资在2027年产生的利润之和的最大值.
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名校
解题方法
7 .
是等腰直角三角形,∠A=90°,
,点D满足
,点E是BD所在直线上一点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee284488e3112e1b450a8be8af85319.png)
______ ;向量
在向量
上的投影向量记为
,则实数m的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359984a59a2867394a9e3a82fa0a6286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3739867311814d91dadacafb107e303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee284488e3112e1b450a8be8af85319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbaeae7045ad94158cdf5ae97073bc17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0735144f6e24b6b32028ff14c17c1cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263f41034e2af4b9b088ce31d96d7cd3.png)
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解题方法
8 . 已知
是定义在
上的奇函数,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f40ec0ee837e68321b17497674e3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求
、
的值;
(2)请用函数单调性的定义说明:
在区间
上的单调性;
(3)求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74dd0b174d40b163469782299211b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d028846b8614318fbf90387d13c75b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f40ec0ee837e68321b17497674e3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)请用函数单调性的定义说明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
9 . 求下列函数的值域:
(1)
;
(2)
;
(3)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8682d2391af7562e3636daeafed9d784.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729c9998600fb4d05930bd13f85274a5.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d166622df6621861e3910251de70eb44.png)
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名校
10 . 已知函数
,其中
.
(1)当
,求函数
的值域;
(2)
,求
区间
上的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae228cd67ccf328a832ad84640eb2f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4108ab700913ff2de435cb0750e973c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
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