名校
1 . 已知函数
,在原点
处切线的斜率为
,数列
满足
为常数且
,
.
(1)求
的解析式;
(2)计算
,并由此猜想出数列
的通项公式;
(3)用数学归纳法证明你的猜想.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c40e368e4337fd5893c24d05cc23177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eced2ac28495d53e5b9b92548d4b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585da375ce6600e92b1cc516b626f259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fc260207971b4e0f6c76802dc91831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafec6be6c2f54b0164cd0e410da3cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826753109a00d2383a7fc4e5feb2e8fa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
(2)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47de41d36313d2de3d76a9381bdad57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
(3)用数学归纳法证明你的猜想.
您最近一年使用:0次
2018-04-14更新
|
719次组卷
|
3卷引用:湖南省张家界市2017-2018年高二期末联考理科数学试题
解题方法
2 . 已知函数
,
.
(1)证明:
为奇函数,并求
的单调区间;
(2)分别计算
和
,并概括出涉及函数
和
对所有不为0的实数
都成立的一个等式,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c18e8294aea776c11fac9ef8c29925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672801e5775fa1dd78538178397d5481.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)分别计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d6bd1f1247031f6e55e131241a7d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142e1c0fdc64a2a99cbd9361df7aa374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
3 . 对于命题
:存在一个常数
,使得不等式
对任意正数
,
恒成立.
(1)试给出这个常数
的值;
(2)在(1)所得结论的条件下证明命题
;
(3)对于上述命题,某同学正确地猜想了命题
:“存在一个常数
,使得不等式
对任意正数
,
,
恒成立.”观察命题
与命题
的规律,请猜想与正数
,
,
,
相关的命题.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7c4bc85a8f4ce17887cc89bad774a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)试给出这个常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)在(1)所得结论的条件下证明命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)对于上述命题,某同学正确地猜想了命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e636bd36d433adcc1860e9174aa6a6.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](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)
您最近一年使用:0次
2017-07-09更新
|
587次组卷
|
3卷引用:广东省中山市2016-2017学年高二下学期期末统一考试数学(文)试题
4 . 已知点列
,
,其中
,
(
),
是线段
的中点,
是线段
的中点,…
是线段
的中点,…
(Ⅰ)写出
与
、
之间的关系式(
);
(Ⅱ)设
,计算
、
、
,由此推测数列
的通项公式,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee6ab09715b2211b4c30c0a66b82bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b6ab454199d2738ea1b5cefb133d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad71bbef310726e8799208cdacf358f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11603c89c66f064b263af841dae023f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a4f2bafc3346d14a8967ce2546157d.png)
(Ⅰ)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c6cc1e8086c67bed8f50f2bbb19c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d816bd1ec64514db59b1cfa84fa838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c775fc62e7696028a9184e5212f0446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
您最近一年使用:0次
2017-04-23更新
|
730次组卷
|
4卷引用:2012届大纲版高三上学期单元测试(3)数学试卷
(已下线)2012届大纲版高三上学期单元测试(3)数学试卷2016-2017学年安徽省池州市第一中学高二下学期期中考试数学(理)试卷上海市嘉定区封浜高级中学2018-2019学年高二上学期期中数学试题山西省长治市潞城区第一中学2020-2021学年高二下学期第一次月考数学(文)试题
真题
解题方法
5 . 已知集合
,
,![](https://img.xkw.com/dksih/QBM/2015/6/24/1572144820469760/1572144826089472/STEM/c7de27294bca40a4a9e2d6ca7ccbb303.png)
,令
表示集合
所含元素的个数.
(1)写出
的值;
(2)当
时,写出
的表达式,并用数学归纳法证明.
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572144820469760/1572144826089472/STEM/a23d6454560e4573b5dd53b390b1efa0.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572144820469760/1572144826089472/STEM/32a34f704dd0466bb0c0f0fe614fd9aa.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572144820469760/1572144826089472/STEM/c7de27294bca40a4a9e2d6ca7ccbb303.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572144820469760/1572144826089472/STEM/c951020daaf4456d84a3ca1c8662e168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc3f52cd9edf88e49e2409f050108d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8656cb8f5a2b576edf99cf13944707b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
您最近一年使用:0次
2016-12-03更新
|
2275次组卷
|
3卷引用:2015年全国普通高等学校招生统一考试数学(江苏卷)
11-12高三上·江苏泰州·期中
6 . (Ⅰ)试比较
的大小;
(Ⅱ)试比较nn+1与(n+1)n(n∈N+)的大小,根据(Ⅰ)的结果猜测一个一般性结论,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/badb98545fb91dbd88cb37bcba9744a9.png)
(Ⅱ)试比较nn+1与(n+1)n(n∈N+)的大小,根据(Ⅰ)的结果猜测一个一般性结论,并加以证明.
您最近一年使用:0次
2014·上海静安·一模
7 . 已知数列
满足
(
为常数,
)
(1)当
时,求
;
(2)当
时,求
的值;
(3)问:使
恒成立的常数
是否存在?并证明你的结论.
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/0d9480d920674a39b018d2ef9dc20b08.png?resizew=33)
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/8280b8fd052545cf8c60d36e15526bf8.png?resizew=170)
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/3174c6ae47fd4e67894e0461c4ea1d8c.png?resizew=12)
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/7a3882326d58465ab97227562217e756.png?resizew=53)
(1)当
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/27aa41d37fae4772af07fd1650cf2769.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/dea8d83a42f644e7934bbb678d5c78b2.png?resizew=19)
(2)当
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/60ae0bb4d989440ba877087d223174eb.png?resizew=34)
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/a4c8fa98c61a4966b4de232beb5f8e0c.png?resizew=33)
(3)问:使
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/17c923db0a8f4678a0ad777f1e43ea78.png?resizew=62)
![](https://img.xkw.com/dksih/QBM/2014/6/17/1571779815956480/1571779821707264/STEM/3174c6ae47fd4e67894e0461c4ea1d8c.png?resizew=12)
您最近一年使用:0次