1 . 已知函数
.
(1)求函数
的单调区间;
(2)若
,求函数
在区间
上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b527fccc73edf11c0282eb2a67918dc.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d85e1973130da5abb1461be6b3690550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0dfcda9ae3994fc00ad787935d8475.png)
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2 . 曲线
上有相异三点到点
的距离相同,则t的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa0bf168ca4cdfd46585a858fcd58a2b.png)
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3 . 已知函数
有且只有两个零点,则a的范围____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee76255706039aa778ff3add3f71a38.png)
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4 . 已知函数
.
(1)讨论
的单调性;
(2)若
,讨论
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1992673f2428acad25b02245ce76d589.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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5 . 若函数
存在零点
,函数
存在零点
,使得
,则称
与
互为亲密函数.
(1)判断函数
与
是否为亲密函数,并说明理由;
(2)若
与
互为亲密函数,求
的取值范围.
附:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35b13df9d8831bb4368e7036488675d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db18e638db2fb367cfe10bfaee37229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e60075f5d53066c03f106346dada26.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe2f63cdc7606986d6250facf20ad1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfd7245d512a98d9105f843c094c7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c292239a48d1475428eeb9863d5dceb.png)
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2024-06-16更新
|
229次组卷
|
5卷引用:江西省部分学校2023-2024学年高二下学期第二次月考(5月联考)数学试题
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6 . 已知函数
,其中
.
(1)当
时,
,求a的取值范围.
(2)若
,证明:
有三个零点
,
,
(
),且
,
,
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d8543507212b830a2a03d4a8f6d139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301605e86e5a5e61a65c91cd3dd8b77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
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7 . 函数
的零点个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72ca98362bdc5a93d50607227924d3e.png)
A.1 | B.2 | C.3 | D.4 |
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8 . 若数列
的各项均为正数,且对任意的相邻三项
,都满足
,则称该数列为“对数性凸数列”,若对任意的相邻三项
,都满足
则称该数列为“凸数列”.
(1)已知正项数列
是一个“凸数列”,且
,(其中
为自然常数,
),证明:数列
是一个“对数性凸数列”,且有
;
(2)若关于
的函数
有三个零点,其中
.证明:数列
是一个“对数性凸数列”:
(3)设正项数列
是一个“对数性凸数列”,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5323231f6376db726f6fba9dd53b97a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345367d7aac000974ce1e3cf4ce1b15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5323231f6376db726f6fba9dd53b97a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870910beaaf7bd60242701ad7ddaf06b.png)
(1)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a11176eb502db16e19c38278b77e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1e49907ec00414cee66b1d082183fb.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fe507c4d73de71c69ede4cfbdc7fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02ab7609f5b06fc564e8e588f378870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a447e5baee4f7518706498d4aca7553b.png)
(3)设正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5330adb65f6c8bd64d0cad579ad2910c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca2b0946db9bbcbce5f19507f5c485e.png)
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解题方法
9 . 已知函数
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b647867d91de52884cea8c492fb0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b29e5cc1e369f351eb1b505919f6ab.png)
A.函数![]() ![]() ![]() |
B.令![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() |
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2024-06-16更新
|
309次组卷
|
2卷引用:广东省深圳市光明区光明中学2023-2024学年高二下学期期中考试数学试题
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10 . 已知函数
,其中
是自然对数的底数.
(1)当
时,求曲线
在点
处的切线的斜截式方程;
(2)当
时,求出函数
的所有零点;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e13355778854f8c54090201ba91bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c94550573090575b08e641d69980610.png)
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