名校
1 . 如果函数
的导数
,可记为
.若
,则
表示曲线
,直线
以及
轴围成的“曲边梯形”的面积.
(1)若
,且
,求
;
(2)已知
,证明:
,并解释其几何意义;
(3)证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d4d758bac9a7272c1d40a5ea4176c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd8f5b33be6db5be0833f1801bd7a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6a5e6776e205fb09d8a689e1638947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436ff3cf58de28b55f7605675a47d818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ed0afb829f4d5c61ce89a556376d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0dc2a031743126b8b4fabb843a55bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc282dae4ac9132196ac5d13f63b901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c38abf9dbef1c45d9fd8143798fa0ea.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59176a49cf2e21c94cf550888de88c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
您最近一年使用:0次
2024-02-20更新
|
2430次组卷
|
7卷引用:压轴题函数与导数新定义题(九省联考第19题模式)练
(已下线)压轴题函数与导数新定义题(九省联考第19题模式)练(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编湖北省黄冈市浠水县第一中学2024届高三下学期第三次高考模拟数学试题(已下线)第5套 新高考全真模拟卷(二模重组)(已下线)压轴题01集合新定义、函数与导数13题型汇总-2重庆市第八中学校2023-2024学年高三下学期入学适应性考试数学试题湖北省十一校2024届高三联考考后提升数学模拟训练一
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)
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2023高三·全国·专题练习
3 . 若4次方程
有4个不同的实根,证明:
的所有根皆为实根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5afe0f1d91d69e4a7f0bee645f39d26f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2bd199b361b791e6effd564b733007.png)
您最近一年使用:0次
4 . (1)已知
,求
;
(2)求证:椭圆
的面积为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203f1c9654642f78af74fd1d75d01651.png)
(2)求证:椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3218d9fbe87452c00739ca1883d6060e.png)
您最近一年使用:0次
名校
解题方法
5 . 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: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)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
6 . 求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8369bbcd598a0d9a6ac5549904838f4.png)
您最近一年使用:0次