真题
1 .
为圆周率,
为自然对数的底数.
(1)求函数
的单调区间;
(2)求
,
,
,
,
,
这6个数中的最大数与最小数;
(3)将
,
,
,
,
,
这6个数按从小到大的顺序排列,并证明你的结论.
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/0bf3fe716ef145c6b81b426dcfe02853.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/3b67feb885254dd68f85f6f85d7ccc77.png)
(1)求函数
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/236ea42229ac4216b0a83eeae49a1cce.png)
(2)求
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/0553709f25134b6483481ded9f3f7f2f.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/dc9f74543779496f86b9049e03efaa35.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/b3c9a5a609cb4a14bca89120433daee3.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/ae10b12900ba471bbed9fe072e0ccdd4.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/51e171bc3c7d4d22b6bc42f72aff6011.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/b068011bfdc7493494f5f1415724f2c7.png)
(3)将
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/0553709f25134b6483481ded9f3f7f2f.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/dc9f74543779496f86b9049e03efaa35.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/b3c9a5a609cb4a14bca89120433daee3.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/ae10b12900ba471bbed9fe072e0ccdd4.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/51e171bc3c7d4d22b6bc42f72aff6011.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571785559441408/1571785565421568/STEM/b068011bfdc7493494f5f1415724f2c7.png)
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2019-01-30更新
|
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2卷引用:2014年全国普通高等学校招生统一考试理科数学(湖北卷)
真题
2 . 已知数列
的各项均为正数,
,
为自然对数的底数.
(Ⅰ)求函数
的单调区间,并比较
与
的大小;
(Ⅱ)计算
,
,
,由此推测计算
的公式,并给出证明;
(Ⅲ)令
,数列
,
的前
项和分别记为
,
, 证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c73e3f1f5c7b7ff2f59d9c22f436200.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046600704/STEM/7bb4a6b2614143e687465abe961d2098.png)
(Ⅰ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca7856da98d03a82c6e6f73b97ecaad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753daa25630fa6e903e252f3f84bcb91.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046600704/STEM/7bb4a6b2614143e687465abe961d2098.png)
(Ⅱ)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42d92e582d2401ed0c8e69faea6d97f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1779f08ea146dfc266375d42b0555a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809ddc61ffc79ff7fb54e3adf406678d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d39e50faa6fa0f927496cdd613ad0f7.png)
(Ⅲ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ebe482242d456a006b0db816e2a25b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c522c1c881528ab6f9708f6bdd4c4db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://img.xkw.com/dksih/QBM/2015/6/24/1572139040808960/1572139046600704/STEM/31e0dadd5fb141f2b905e7e29bc9a75a.png)
您最近一年使用:0次
2016-12-03更新
|
4057次组卷
|
9卷引用:2015年全国普通高等学校招生统一考试理科数学(湖北卷)
2015年全国普通高等学校招生统一考试理科数学(湖北卷)(已下线)专题6.6 数学归纳法 (练)-浙江版《2020年高考一轮复习讲练测》(已下线)专题12.3 数学归纳法及其应用(练)【理】-《2020年高考一轮复习讲练测》(已下线)专题33 算法、复数、推理与证明-十年(2011-2020)高考真题数学分项(八)(已下线)专题7.6 数学归纳法(练)-2021年新高考数学一轮复习讲练测(已下线)专题7.6 数学归纳法(练)- 2022年高考数学一轮复习讲练测(新教材新高考)(已下线)第二篇 函数与导数专题1 重要极限(逼近、放缩)(已下线)专题22 导数解答题(理科)-3专题35导数及其应用解答题(第二部分)
3 . 已知函数
的图象在点
处的切线方程为
.
(I)用
表示出
;
(II)若
在
上恒成立,求
的取值范围;
(III)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b198677e91defa3ffba5e1865eb387c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
(I)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a475fec8ded321e10a6697319fb975.png)
(II)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f890eb5d86a7484141a8aa9d946552df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(III)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aac55d3e280c5629d97e619bf074430.png)
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8卷引用:2010年普通高等学校招生全国统一考试(湖北卷)数学(理科)
2010年普通高等学校招生全国统一考试(湖北卷)数学(理科)(已下线)2010年高考试题分项版理科数学之专题十三 导数(已下线)2011-2012学年广东新兴县惠能中学高二下学期期中理科数学试卷2015-2016学年江西吉安一中高二下第一次段考理科数学卷天津市耀华中学2018届高三上学期第一次月考数学(文)试题2天津市耀华中学2018-2019学年高二下学期期中考试数学试题广东省珠海市第二中学2021-2022学年高二下学期期中数学试题(已下线)专题15 数列不等式的证明 微点5 函数放缩法证明数列不等式