23-24高一上·广东·期末
1 . 记
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864a6f0337ffea0d2a0461b75900373b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39864c8569fa9baf0ade8ce49ba2f683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864a6f0337ffea0d2a0461b75900373b.png)
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2 . 已知
,则
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b951adb0efff962d44cf1075074706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9155b2f084a37d04703e2013b5813dc2.png)
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解题方法
3 .
,且
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238182ab55a63ea62b42ec61d5ac9bb5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca62e37fc045990208dc68bcc7ee690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1377f2a513fc287a4a3d6ca384b4f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238182ab55a63ea62b42ec61d5ac9bb5.png)
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4 . 计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daaed1ef2c0c2f8e0fbd90738c98bfee.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daaed1ef2c0c2f8e0fbd90738c98bfee.png)
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5 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4aead27873528ef19d2b24128780b9.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4aead27873528ef19d2b24128780b9.png)
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6 . 牛顿冷却定律描述一个物体在常温环境下的温度变化:如果物体初始温度为
,则经过一定时间
(单位:分钟)后的温度
满足
,其中
是环境温度,
为常数,现有一杯
的热水用来泡茶,研究表明,此茶的最佳饮用口感会出现在
.经测量室温为
,茶水降至
大约用时一分钟,那么为了获得最佳饮用口感,从泡茶开始大约需要等待__________ 分钟.
(参考数据:
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635ccd929471d564cc9d2d96266b34d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb61026150c337abe58a4d6f62b32d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212baa7c3eed6574b6edae95538a7765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e846d9a95f5d9b356478882da78625e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ecafb66dca8b751f9e51bbc43160f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1ea1c0b768f231430b1ae0836a4e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/849ca1e01ff86bdd86ddd4693da05100.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e210b9c6d7eee8142ead1ff1a57680e.png)
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2024-01-16更新
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418次组卷
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2卷引用:江苏省南通市海安高级中学2023-2024学年高一上学期12月月考数学试题
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7 . 已知
,
,则
可以用a、b表示为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a08a2a5540efcdb5a77aa4ea3049884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57115371320bf8c2b5cde136392696c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd649840fc303c4ec0b93b083af31b7d.png)
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8 . 函数
,
,其中
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94b13d581ac8ed4fa8bc5ce8e2869d2.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3207530ec55d0cdcd1de7c0bceef58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3b5fd6afc3d3e117f70e2dd5d7cb4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4182ae07de1768d488892ba0233e94e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94b13d581ac8ed4fa8bc5ce8e2869d2.png)
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9 . 在沪教版教材必修第一册第四章的章首语中有这样一段话:“通过固定等式
中的三个量
中的一个量,研究另两个量的相互关系和变化规律,定义三种基本而应用广泛的函数——幂函数、指数函数和对数函数”.若令
(
是自然对数的底数),将
视为自变量
,则
为
的函数,记作
,若不等式
对任意的
恒成立,则实数
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fcfe7bb3f607ac047d70fea54a21aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab376b03a96dabdc021bb47323e01169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2e0e091cbd0daf2d9ab9abe8e5e78e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e01ac769555d2c50f1be41f649de89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5af8e5480a8f4247b8661a841124faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c40beaf3b21a8d7d06b46d473e99d1c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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10 . 计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e8f617e2747a775448d4f40304027c4.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e8f617e2747a775448d4f40304027c4.png)
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2024-01-10更新
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693次组卷
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3卷引用:重庆市第七中学校2023-2024学年高一上学期12月月考数学试题
重庆市第七中学校2023-2024学年高一上学期12月月考数学试题安徽省安庆市第二中学2023-2024学年高一上学期第二次月考(12月)数学试题(已下线)专题15对数-【倍速学习法】(人教A版2019必修第一册)