1 . 设函数
,
有唯一极值点
.
(1)证明:
;
(2)若
,求
的取值范围;
(3)若
的图象上不存在关于直线
对称的两点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be31d79dcf1ba2248c8fd8532e2e727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2367b48e8f6dbbfe3dd14f6eab8238a5.png)
![](https://img.xkw.com/dksih/QBM/2024/3/28/3463519110799360/3467824765468672/STEM/4236e158880542c4b9d3318290fe1b8b.png?resizew=8)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529aaddc617f821a66bfffb1a41303ab.png)
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2 . 相传古希腊毕达哥拉斯学派的数学家常用小石子在沙滩上摆成各种形状来研究数,并根据小石子所排列的形状把数分成许多类.现有三角形数表按如图的方式构成,其中项数
:第一行是以1为首项,2为公差的等差数列.从第二行起,每一个数是其肩上两个数的和,例如:
;
为数表中第
行的第
个数.
和
;
(2)一般地,证明一个与正整数
有关的命题,可按下列步骤进行:①证明当
时命题成立;②以“当
时命题成立”为条件,推出“当
时命题也成立.”完成这两个步骤就可以断定命题对
开始的所有正整数
都成立,这种方法即数学归纳法.请证明:数表中除最后2行外每一行的数都依次成等差数列,并求
关于
的表达式;
(3)若
,
,试求一个等比数列
,使得
,且对于任意的
,均存在实数
,当
时,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5d0a73f50b3e4583f1c1b6d6bf0d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008c3c308a9a18f5a3bad6c67cacf113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdab9718ae9ad2732585fa25b760a956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242d5f694c3c7c9530f5ef0cd1447b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1192d0aa416fc19f7f4b842cf6717808.png)
(2)一般地,证明一个与正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2636b1b9ad69adc8b268d3513a59b7ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469410cf8d7cd28620a58363cb5cbb6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d85b80a9c97bd7106dcbfb34199b1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f1ae8e6654806b02cd359fb484ea4e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e789526ee5eab677295edf78fefb00f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a92d4463e0a56109a13d60b640e0a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2995a87642de38c4a7c79c133fb2d1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c83f7e578f082cbba0e39cff3c2c5da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc83e348654e938962f3fd0c04e023f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe9dbc75f393b682c8a90fe7277ab4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afaaa196735c0c02f05f97fda5534a4.png)
您最近一年使用:0次
2024-03-06更新
|
348次组卷
|
2卷引用:广东省汕尾市陆河县河田中学2023-2024学年高二下学期4月第一次阶段测试数学试题
3 . 已知数列
满足
(
且
),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec805491b68bcd47219f79e69e26b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
A.![]() ![]() |
B.若数列![]() ![]() |
C.数列![]() ![]() ![]() |
D.当n是奇数时,![]() |
您最近一年使用:0次
2023-07-08更新
|
1059次组卷
|
6卷引用:广东省汕尾市2022-2023学年高二下学期期末数学试题
广东省汕尾市2022-2023学年高二下学期期末数学试题福建省宁德第一中学2020-2021学年高二上学期开学检测数学试题云南省昆明市第一中学2024届高三新课标第四次一轮复习检测数学试题江西省宜春市铜鼓中学2023届高三上学期第三次阶段性测试数学试题(已下线)专题2 数列的奇偶项问题【讲】(高二期末压轴专项)(已下线)重组3 高二期末真题重组卷(广东卷)B提升卷
名校
解题方法
4 . 已知函数
.
(1)讨论
的单调性;
(2)已知
,
,且
,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bf0cbbfef914a970d8ae44bdd4f928.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eae9ba258299eb489b490594397e23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5122fe5d167302f3f9f057fb2bbb8d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ecda7bfb0a2043306bf7707a136ad0.png)
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2021-11-16更新
|
595次组卷
|
3卷引用:广东省汕尾市华大实验学校2022-2023学年高二下学期3月月考数学试题
5 . 已知函数
.
(1)若对任意的
,不等
恒成立,求实数a的取值范围;
(2)讨论函数
零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cd96de5449a1bd6c2b2dc1698754eef.png)
(1)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6074e41127276e888e5d9aa8ac767edf.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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