名校
1 . 某种绿茶泡茶的最佳水温为85℃,饮茶的最佳温度为60℃.在标准大气压下,水沸腾的温度为100℃.把水煮沸后,在其冷却的过程中,只需要在最佳温度对应的时间泡茶、饮茶,就能喝到一杯好茶.根据牛顿冷却定律,一个物体温度的变化速度与这一物体的温度和所在介质温度的差值成比例,物体温度
与时间
的函数关系式为
,其中
为介质温度,
为物体初始温度.为了估计函数中参数
的值,某试验小组在介质温度
和标准大气压下,收集了一组数据,同时求出对应参数
的值,如下表,
现取其平均值作为参数
的估计值,假设在该试验条件下,水沸腾的时刻为0,则泡茶和饮茶的最佳时间分别是( )(结果精确到个位数)
参考数据:
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5617528c9a89334f4e647cb61ac8d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a7e0e5238148676a584b1748e04d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635ccd929471d564cc9d2d96266b34d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9a78dd4908c74a64f2f8e3c8ad0b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
时间/min | 0 | 1 | 2 | 3 | 4 | 5 |
茶温/℃ | 85.0 | 79.2 | 74.8 | 71.3 | 68.3 | 65.9 |
![]() | —— | 0.9045 | 0.9122 | 0.9183 | 0.9227 | 0.9273 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d842673d79eb00f15152551900d2d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5613d22f9ada8d6ba67259ed64da3092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64544e4844d1b0b7ba069359f4c30c8e.png)
A.3min,9min | B.3min,8min |
C.2min,8min | D.2min,9min |
您最近一年使用:0次
2022-11-10更新
|
511次组卷
|
4卷引用:山东省济南市章丘区2022-2023学年高三上学期诊断性测试数学试题
2 . 若
,N叫a的b次幂,其中a叫做_____ ,b叫做_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e754c3b33a300dedff3c0f1a01e7da8.png)
您最近一年使用:0次
解题方法
3 . 对于两个均不等于1的正数
,定义:
,则
的值是______ ;设
均为小于1的正数,且
,则
的值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de39b9540397fa8e532e891473d77812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8002eed9a73235a5dea08e59854ef262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74418f44da81745fd01b55720b17799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a12e8ffb83ea93fb542a5ffe94316140.png)
您最近一年使用:0次
解题方法
4 . 已知实数
,
,
,满足
.
(1)若
,求实数
的值;
(2)若
,求证:
.
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98ea2f945ef1bfe060d334f6046091b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7eca46642891f6b8e3e30edd9b37dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404f19c00441f801d250ae698fbfcb2f.png)
您最近一年使用:0次
2022-07-18更新
|
352次组卷
|
2卷引用:山东省滨州市2021-2022学年高二下学期期末数学试题
5 . 定义域是复数集的子集的函数称为复变函数,
就是一个多项式复变函数.给定多项式复变函数
之后,对任意一个复数
,通过计算公式
,
,可以得到一列值
,
,
,
,
,
.若
,
,当
时,
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd1b0f6b19f0e80f4157644e6cb8794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c01e03a93ade8659780af659f12e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcc78b50e4eb2ef6076b0ef4fab732d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ddd911777ff68a15267547fa66e1f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcc78b50e4eb2ef6076b0ef4fab732d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd1b0f6b19f0e80f4157644e6cb8794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c16699fdf07ca29eafe7425c695732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627b638fb28fc4c202acfbdeee2176c1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
6 . 已知定义在
上的偶函数
,满足
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b773f3cf95d0a28183eb5e0e7c9288c3.png)
A.![]() ![]() |
B.![]() |
C.若函数![]() ![]() ![]() ![]() |
D.若函数![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-05-31更新
|
2157次组卷
|
7卷引用:山东省淄博市2022届高三三模数学试题
山东省淄博市2022届高三三模数学试题辽宁省沈阳市辽中区第二高级中学2021-2022学年高二下学期期末考试数学试题(已下线)考向06 函数的奇偶性与周期性、对称性(重点)(已下线)第08练 对数与对数函数江苏省南通市海安市实验中学2022-2023学年高一下学期第一次学情检测数学试题江苏省南通市海安市实验中学2022-2023学年高一下学期3月月考数学试题重庆市铜梁一中等三校2024届高三上学期10月联考数学试题
名校
7 . 著名的伯努利(Bemoulli)不等式为:
,其中实数
同号,且均大于-1.特别地,当
,且
时,有
.已知伯努利不等式还可以推广为:设x,
,若
,且
,则
.设a,b为实数,则下列结论正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94a236cac214e5c2b56ca013f62ccca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/361386446d504a14471b9fd89130f1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5026dc5ead3b5adf0e5f4b3e7c4eca1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b280948494849391f9bef054c32c30f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f42a14246a32b61933b220938aa841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac6892e2785afa831608337a3064803.png)
A.任意![]() ![]() ![]() |
B.任意![]() ![]() ![]() |
C.任意![]() ![]() ![]() |
D.任意![]() ![]() ![]() ![]() |
您最近一年使用:0次
8 . 已知函数
,
.若实数a,b(a,b均大于1)满足
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae91b63cb74b91b7b6dce1b9c9d48fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e781c3e1d8fc4a3d4a2db5fc08251d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6ff9984c9c3a725c7a6e7779daf2ff.png)
A.函数![]() |
B.函数![]() ![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
名校
9 . 已知
,
,其中
且
,
且
,若
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4086d4cead9b18a84c8d91ce22ca46fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f8767ca1ef7303b6941cb86beff0c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e7930731eddbcfac592b808e9b698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1252b3493b8854fd86c1618a1d5a6097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f86f62bf3f047627f53d0c882bea23a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
A.![]() | B.![]() | C.2 | D.3 |
您最近一年使用:0次
2022-05-17更新
|
1330次组卷
|
5卷引用:山东省肥城市2022届高三下学期高考适应性训练数学试题(二)
山东省肥城市2022届高三下学期高考适应性训练数学试题(二)天津市实验中学2022-2023学年高三上学期第二阶段学习质量检测数学试题(已下线)专题10 对数与对数函数(已下线)考向07 指数、对数函数(重点)(已下线)专题10 对数与对数函数-3
解题方法
10 . 已知函数
在
上先增后减,函数
在
上先增后减.若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b2f172a130018ca20ac6d3208ee946.png)
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba38169c5dad9d1bc24335d98ae6a574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1a810ac408df0fd5133acb8f345f74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b2f172a130018ca20ac6d3208ee946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5b8e57ddb4dd1dc7262134e74cef3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f039ed23f419ab33c3caea5697f67de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f4f8f5d8cb78c285ff8eb9c616c131.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-05-12更新
|
2039次组卷
|
5卷引用:2022届山东省泰安市高考全真模拟数学试题
2022届山东省泰安市高考全真模拟数学试题河北省保定市2022届高三下学期二模数学试题(已下线)第11讲:第二章 函数与基本初等函数(测)(提高卷)-2023年高考数学一轮复习讲练测(新教材新高考)(已下线)专题03 函数(已下线)专题10 对数与对数函数-2