1 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7c9589a8b6d2937b54aaecf2bd3f3b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6842c57bbbf2e0632c16b1b8ca2e9386.png)
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2023-10-08更新
|
209次组卷
|
3卷引用:习题 3-2
2 . 已知
,求下列各式的值:
(1)
;
(2)
;
(3)
;
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26ca8ee9449dcbece448515c5bf086c.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11afbd452f2fcd40ae32c26055a68ec1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d916d946c56061f3a4b04ecf40682c.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303f67f6d5a3f50d5a54839815c4a1fd.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c764d5f18623010915adb4241c7b6b6.png)
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3 . 化简(式中的字母均为正实数):
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b722c00135498bf4181d670bac8399b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03eb439922ebde61a2b31800a3573881.png)
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4 . 已知
,
,把下面的数写成底数是10的幂的形式:
(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5904a4d0f9b6c1b3acb3facbe886d380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69ddd3a69063bd5a4fd3d3e50b8faea.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31da7291140e430a11e2a10cc6cdefbb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6620729a37129c16cfd61cd59500bfe1.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
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23-24高二上·上海·课后作业
解题方法
5 . 利用导数研究下列函数的单调性,并说明结果与你之前的认识是否一致:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57d371bb05b2c168a29ff17b10f88b2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b005b15adfc48e1ab5f1eebbaeff230.png)
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23-24高二上·上海·课后作业
6 . 已知数列
是等差数列,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79f232288a6d4b336e06153d81c41fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17038e6f33d6ea7070b0d18c619a7dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4962ef726d9ae4dae2ca030411fb5ddd.png)
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23-24高二上·上海·课后作业
7 . 已知
是等比数列,当
时,其中
、
、
、
均为正整数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6fb1dbeaaa23449ccfec570b9433ec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bd839754cc26795de089abcbb0820c.png)
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23-24高二上·上海·课后作业
8 . 某种放射性物质不断衰变为其他物质,设每经过一年剩留的这种放射性物质是年初的84%,这种放射性物质的半衰期为多长?(精确到1年)参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776bb60901cb1b3b8c1ce226a7dcbb5c.png)
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23-24高二上·上海·课后作业
解题方法
9 . (1)已知
,
,
成等差数列,其公差为
.求证:
,
,
成等比数列.
(2)已知正实数
,
,
成等比数列,其公比为
.求证:
,
,
成等差数列.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ef024c58becb626b823dfd3ee99c1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec9a109b4ff41dc4d7716fa776f450f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f2d6b743b57500fb4ba695ec160f27.png)
(2)已知正实数
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24106d94bf13cac0501cdb695b9972c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489ac3f68848980d53033dbd65a0a622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba73c0fc1d96654151175cc84b792c7.png)
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23-24高二上·全国·课后作业
10 . (1)在自然界,死亡生物体中的
有持续稳定的衰变现象.已知
的半衰期为5730年,设
的衰变率为q,试建立一个用
确定生物体死亡时间的模型.
(2)考古学家发现一个古人猿的颅骨,测得该颅骨仅残留原
含量的
,那么古人猿的颅骨已存在了大约多少年?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c595ab427191084b4c94aec0ab67fb2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c595ab427191084b4c94aec0ab67fb2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c595ab427191084b4c94aec0ab67fb2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c595ab427191084b4c94aec0ab67fb2d.png)
(2)考古学家发现一个古人猿的颅骨,测得该颅骨仅残留原
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c595ab427191084b4c94aec0ab67fb2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589d984db8887148c0283bc11e8d27ca.png)
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