1 . 已知一扇形的圆心角为
(
为正角),周长为
,面积为
,所在圆的半径为
.
(1)若
,
,求扇形的弧长;
(2)若
,求
的最大值及此时扇形的半径和圆心角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa57d7c189fcfd360247063053fc2f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210e4cc913c2b111e67f1e033b69824a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786cb3b718223d49726e1ad5cbd12b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2024高三·全国·专题练习
解题方法
2 . 已知函数
.
(1)若函数
有三个零点分别为
,
,
,且
,
,求函数
的单调区间;
(2)若
,
,证明:函数
在区间
内一定有极值点;
(3)在(2)的条件下,若函数
的两个极值点之间的距离不小于
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077315c5a7b12294497294e536831d77.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f5cd91996571c9da95e6f26bc80661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23292eca257af6a97309ee40ce6cbf9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37f19a2ad8f24cf63bff68be15faa67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799f6009a476fa056e1af71f26dd2fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
(3)在(2)的条件下,若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)若曲线
在点
处的切线方程为
,求
和
的值;
(2)讨论
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f73397c4d12734a677d025078bbb72e.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9bd144e0e96e4236a14523e0729cacb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
昨日更新
|
335次组卷
|
3卷引用:核心考点2 导数几何意义和函数的单调性、极值 专题讲解 B提升卷 (高二期末考试必考的10大核心考点)
(已下线)核心考点2 导数几何意义和函数的单调性、极值 专题讲解 B提升卷 (高二期末考试必考的10大核心考点)河北省邢台市名校联盟2023-2024学年高二下学期第三次月考(6月)数学试题吉林省部分名校2023-2024学年高二下学期联合考试数学试题
4 . 已知无穷数列
,构造新数列
满足
,
满足
,
,
满足
,若
为常数数列,则称
为
阶等差数列;同理令
,
,
,
,若
为常数数列,则称
为
阶等比数列.
(1)已知
为二阶等差数列,且
,
,
,求
的通项公式;
(2)若
为
阶等差数列,
为一阶等比数列,证明:
为
阶等比数列;
(3)已知
,令
的前
项和为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22e75bf99dcb0fe32f66fa90a74f9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc06ff2f65c456efb6a114e67b62cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d16e3ca4fb65342b0e9a0594d661ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf623a6dd661f87cf64ea150072fd78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcbdf91bb5a49f293f9b52ac8dcfa35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ab5abd104649f9a3c231df9a55813a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69c653f3a05dd25f6affdba7baeab38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0606df3b6fbc6fcf863f9c59e0e54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab214e5f34d976717284bed52c645e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e796a0144ff9b3329c7064a01c5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a4b318fa151fab14b3857942ed3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07418f1fa0f6569b50944b5a13ffa021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7778648d93a10ed66ddd99672d3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.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/a2a5a414f3f5d724058a2e887f3d1c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3fec47d2dd2b8099d86c87b6e57de8.png)
您最近一年使用:0次
解题方法
5 . 已知数列
满足
,
,数列
的前
项和为
,且
.
(1)求
,
的通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc37f810989be7ef62d15b5bc9f51d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/52340b43114618ed02b59cd6085d6c69.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52c9237cb0b4acc568d4afb12997186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
6 . 已知函数
.
(1)讨论
的单调性;
(2)若
,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e240a5e97a7c1b55cf69946c4dc553.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d197dd0adef956d012dc96f8dc0846d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
昨日更新
|
801次组卷
|
8卷引用:期末模拟卷-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(天津专用)
(已下线)期末模拟卷-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(天津专用)(已下线)核心考点3 导数的应用(恒成立,不等式,零点) B提升卷 (高二期末考试必考的10大核心考点)内蒙古名校联盟2023-2024学年高二下学期教学质量检测数学试题河北省保定市部分学校2023-2024学年高二下学期5月期中考试数学试题河北省秦皇岛市卢龙县2023-2024学年高二下学期5月考试数学试题内蒙古开鲁县第一中学、和林格尔县第三中学等2023-2024学年高二下学期5月月考数学试题(已下线)专题09 导数与零点、不等式综合常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)江西省部分学校2023-2024学年高二下学期第二次月考(5月联考)数学试题
7 . 已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62559d143b4a977be9990eebcbec539e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79699156efecc21a555e63da6456031a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a551a88ac426439803f564a3bbee04a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
昨日更新
|
7071次组卷
|
5卷引用:2024年高考数学真题完全解读(新高考Ⅰ卷)
(已下线)2024年高考数学真题完全解读(新高考Ⅰ卷)专题03导数及其应用(已下线)2024年新课标全国Ⅰ卷数学真题变式题16-192024年新课标全国Ⅰ卷数学真题湖北省黄冈市浠水县第一中学2023-2024学年高二下学期期末质量检测数学试题
解题方法
8 . 已知数列
满足
,
.
(1)证明:数列
是等差数列;
(2)若
,
,求
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e4e9a12482be70c189ddd6b4b29a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110f419f979c0dc47a8576de41102fc4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bf75e900509aa73771677aeb81cb14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/007b1ce7e388273fde9715af3e6d89fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
名校
9 . 如图,已知四边形
为矩形,
,
,E为
的中点,将
沿
进行翻折,使点D与点P重合,且
.
;
(2)设
,
的延长线交于点N,则线段
上是否存在点Q,使得平面
与平面
所成角的余弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58bbc02479917ad761a24eaae0dbfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985905ab3559ed7ec54e745a493629af.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24daf297c1d4e669a05623e8dde92de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,已知四棱台
的上、下底面分别是边长为2和4的正方形,平面
平面ABCD,
,点P是棱
的中点,点Q在棱BC上.
,证明:
平面
;
(2)若二面角
的正切值为5,求BQ的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a45953045e613b97eeee15ac188ae2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b90595662af9a1936e1e703462cb69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99fea37dbf4145c3b311bcec0fc25ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e866091156cbd7beea724fbbdb25082.png)
您最近一年使用:0次