真题
名校
1 . 请先阅读:
在等式
(
)的两边求导,得:
,由求导法则,得
,化简得等式:
.
(1)利用上题的想法(或其他方法),结合等式
(
,正整数
),证明:
.
(2)对于正整数
,求证:
(i)
; (ii)
; (iii)
.
在等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32eac4b7f177c041219fab18de973c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc1e9d6c038e98eb3ced183bb6dcc53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0035911136a83c7915137c3438e055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ba7e0c985c673fbb513b4a97d93746.png)
(1)利用上题的想法(或其他方法),结合等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9641914b1dcb9c0097550aebead97810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910adb8a80fceb7949c3526087947220.png)
(2)对于正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5c659f6e87ab7327ef8c3b3368ab23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe3f70202a3b38d077fe431a6e63099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a002cedddac1e750b5e3f204974078.png)
您最近一年使用:0次
2016-11-30更新
|
2395次组卷
|
4卷引用:2008年普通高等学校招生全国统一考试数学试题(江苏卷)
2 . 我们知道通过牛顿莱布尼兹公式,可以求曲线梯形(如图1所示阴影部分)的面积
,其中
,
.如果平面图形由两条曲线围成(如图2所示阴影部分),曲线
可以表示为
,曲线
可以表示为
,那么阴影区域的面积
,其中
.
在区间
与
的图形分别为直径为1的上、下半圆周,在区间
与
的图形分别为直径为2的下、上半圆周,设
.求
的值;
上某一个点处作切线,便之与曲线和x轴所围成的面积为
,求切线方程;
(3)正项数列
是以公差为d(d为常数,
)的等差数列,
,两条抛物线
,
记它们交点的横坐标的绝对值为
,两条抛物线围成的封闭图形的面积为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f102cb4c683b01f1cd728f543f703f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924840404483fbdef9af58e844c001ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babadc15694ea4139b1bb919a7d49b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bc1742d6a5f52c750720b3f099c3fcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfbd9b2c33ae11831377f140b728ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b668edb1a8974b1e882f78178b265c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8d35b10249abb8a2d50677f56db638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac9833eb592cadc3503eebc041aab21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376cd70523564eb2a9b8509ca5fec6ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bc5c4dc60dacc4d88d0e929574c0f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2cc4cd1e8bcb4b75b6e799156736e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f76d4f2878eb5a4879b74719b8a69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c3b46e63249a782f911667bbd68e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61f3ad8e800d5fde4f5e48567509a074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d7abf02717d6e59d8a64a65a87c412.png)
(3)正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0c92880b4a88b78d0324564628be0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c5c0257094e981bec043dfa99a6373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9929daf4497eb9657b95b17b212a0886.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87500c37fe72a39bab426214083e0dbd.png)
.
(1)若
在
处有极值,问是否存在实数m,使得不等式
对任意
及
恒成立?若存在,求出m的取值范围;若不存在,请说明理由.
;
(2)若
,设
.
①求证:当
时,
;
②设
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87500c37fe72a39bab426214083e0dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1466e5ee63d3c3b94e40b35fb879d5e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab764788b299582009afd9fc613a59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff71c87ed2ae102fbacedaac36ff2bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8326eccb6fccce4cad9ff889bf0febbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6514519af132d4ae3c6aa03ed8c9f1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdab28f21cd89c17dfaebb3fdb701498.png)
①求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3c2088213b0ee376d1c41a637eb0ec.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4473e6a3eab1230911921fe2b5345e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5300e0c6410241ac66517c3e4b1cb55.png)
您最近一年使用:0次
2020-05-23更新
|
418次组卷
|
4卷引用:江西省宜春市奉新县第一中学2019-2020学年高二下学期第一次月考数学(理)试题
江西省宜春市奉新县第一中学2019-2020学年高二下学期第一次月考数学(理)试题宁夏回族自治区银川一中2023届高三二模数学(理)试题宁夏回族自治区银川一中2023届高三二模数学(理)试题(已下线)专题10 数列不等式的放缩问题 (练习)