名校
解题方法
1 . 罗尔定理是高等代数中微积分的三大定理之一,它与导数和函数的零点有关,是由法国数学家米歇尔·罗尔于1691年提出的.它的表达如下:如果函数
满足在闭区间
连续,在开区间
内可导,且
,那么在区间
内至少存在一点
,使得
.
(1)运用罗尔定理证明:若函数
在区间
连续,在区间
上可导,则存在
,使得
.
(2)已知函数
,若对于区间
内任意两个不相等的实数
,都有
成立,求实数
的取值范围.
(3)证明:当
时,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94345694d4215284c41f87146795ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e655794426cb48ec8f537baae3dd07d0.png)
(1)运用罗尔定理证明:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1486d2ae6c7e7904ab47b909039ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2982ec308d84c83d538a58dae3ff1569.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee44b0f79b66f04bde9b696c393eb47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafa44c4a404f62f54460dbcd7b8a0fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1837cd091231e2ea18571efa5d60403c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c3786a1c3167a200c9d1c8f0e6184a.png)
您最近一年使用:0次
2024-04-06更新
|
1496次组卷
|
2卷引用:四川省眉山市仁寿第一中学校南校区2023-2024学年高二下学期4月数学滚动检测卷
名校
解题方法
2 . 在
中,点P为
所在平面内一点.
(1)若点P在边BC上,且
,用
,
表示
;
(2)若点P是
的重心.
①求证:
;
②若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)若点P在边BC上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac077c25a98e791e4a81b1c48c09015d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
(2)若点P是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699b82be749af3fa36f1fed5122591a9.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f4aa4e839e8104005fe94eaf81f503e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3acf551f38311eccdcc325c0d283473.png)
您最近一年使用:0次
2023-07-05更新
|
432次组卷
|
5卷引用:四川省眉山市2022-2023学年高一下学期期末数学试题
名校
3 . 世界上有许多由旋转或对称构成的物体,呈现出各种美.譬如纸飞机、蝴蝶的翅膀等.在
中,
.将
绕着
旋转到
的位置,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/988d1a8e-5371-4dac-b5fe-ca36ad4ba5ff.png?resizew=418)
(1)求证:
;
(2)当三棱锥
的体积最大时,求平面
和平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e239f048f2b3a121fa40d16a6fd3c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0005e1ef60f6ddc5f9a83e3de1ef3b2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/988d1a8e-5371-4dac-b5fe-ca36ad4ba5ff.png?resizew=418)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d72a007e3c4a134956b0e3fbde5f46.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4739afd7311501e948aa4e1e5c1cb17.png)
您最近一年使用:0次
2023-02-25更新
|
863次组卷
|
3卷引用:四川省眉山市仁寿第一中学校(北校区)2023-2024年高二上学期期末数学试题
解题方法
4 . 将①
,
,②
,③
,
之一填入空格中(只填番号),并完成该题.
已知
是数列
前n项和,___________.
(1)求
的通项公式;
(2)证明:对一切
,
能被3整除.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbb03e9f93969580c6f07667c209779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b109fa86a3b571445e5352e89e0af67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3db132af8f7366d6b98f8c5609756a7.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:对一切
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235ed1dfea3ec3bc0c2d81a3cf66c202.png)
您最近一年使用:0次
2022-05-10更新
|
768次组卷
|
7卷引用:四川省眉山市2022届高中第三次诊断性考试数学(文史类)试题
四川省眉山市2022届高中第三次诊断性考试数学(文史类)试题四川省乐山市2022届高三下学期第三次调查研究考试数学(文)试题(已下线)数学归纳法(已下线)4.4 数学归纳法(1)1.4 数学归纳法(同步练习提高版)1.5 数学归纳法7种常见考法归类(1)(已下线)4.4数学归纳法——课后作业(巩固版)