名校
解题方法
1 . 已知数列
的前
项积为
,且
.
(1)求证:数列
是等差数列;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3406df6552d66166d04a3d22e2f86929.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a40442811c08c432ec613102e4502c0.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031efafb3886a33f3ac39fc85eab869d.png)
您最近一年使用:0次
2023-10-13更新
|
1988次组卷
|
4卷引用:江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题
江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题江苏省连云港市部分学校2023-2024学年高三上学期10月第二次学情检测数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期教学质量调研(一)数学试题江苏省南京市江宁区东山高级中学三校联考2023-2024学年高三上学期期中调研考试数学试题
2 . 已知函数
和
,它们的图像分别为曲线
和
.
(1)求函数
的单调区间;
(2)证明:曲线
和
有唯一交点;
(3)设直线
与两条曲线
共有三个不同交点,并且从左到右的三个交点的横坐标依次为
,求证:
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86161d12df385eb4cfec8a8a38277fc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8da208132c56cf53ce7f4d0985582c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e632de0a4a7142242b1c4310b0a6f185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
您最近一年使用:0次
2022-12-26更新
|
577次组卷
|
3卷引用:江苏省连云港市灌南高级中学2024届高三上学期期中数学试题
名校
解题方法
3 . 如图,在四棱锥
中,底面
是矩形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/fdb48697-d46f-452c-85a1-a75595d32731.png?resizew=199)
(1)设
为
上靠近
的三等分点,
为
上靠近
的三等分点.求证:
平面
.
(2)设
是
上靠近点
的一个三等分点,试问:在
上是否存在一点
,使
平面
成立?若存在,请予以证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/fdb48697-d46f-452c-85a1-a75595d32731.png?resizew=199)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
您最近一年使用:0次
2021-05-08更新
|
2328次组卷
|
4卷引用:江苏省连云港市赣榆第一中学2020-2021学年高一下学期第二次月考数学试题
江苏省连云港市赣榆第一中学2020-2021学年高一下学期第二次月考数学试题吉林省东北师大附属中学2020-2021学年高一下学期期中考试数学试题(已下线)专题23 立体几何中平行的存在性问题-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)(已下线)第03讲 空间直线、平面的平行 (高频考点—精练)
名校
解题方法
4 . 已知五面体
中,四边形
为矩形.
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261553512448/2542432970964992/STEM/3d7768ff89c248cd9855d5c3fa13639c.png?resizew=201)
(1)证明:
平面
;
(2)若
,求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261553512448/2542432970964992/STEM/3d7768ff89c248cd9855d5c3fa13639c.png?resizew=201)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
5 . 正项数列
满足
.
(1)求
;
(2)猜想数列
的通项公式,并给予证明;
(3)若
,求证:
是无理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624f10fb877734018a18b280e4efa7ba.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
(2)猜想数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ccfa38896c6ac193fbab372f963dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
您最近一年使用:0次
6 . 分析法或综合法证明:
(1)求证:
;
(2)已知
为正数,求证:
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add637eef4cd8802b4eb211aa4f6e572.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391db0f4a44538e1fc16316bfc82bb7a.png)
您最近一年使用:0次
7 . 用分析法或综合法证明:
(1)求证:
;
(2)设
,求证:
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add637eef4cd8802b4eb211aa4f6e572.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1caa2030ac2f57deccc5b24e940facc9.png)
您最近一年使用:0次
解题方法
8 . 如图,在棱长为2的正方体
中,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/10/e9af847d-61f0-4147-9a77-e1678a87bfd5.png?resizew=156)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/10/e9af847d-61f0-4147-9a77-e1678a87bfd5.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c376fe379602e2b4d4085ac5b71c6f8.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea84e9242d2667cd6a0f7436425ad418.png)
您最近一年使用:0次
名校
9 . 在
中,AD是
的角平分线,AE是边BC上的中线,点D、E在边BC上.
(1)用正弦定理证明
;
(2)若
,求DE的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3322a2ad9a95bdc9fc576a7a158d4d.png)
(1)用正弦定理证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c6ba1dce1e32a78ea2f3a85a3c8962.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95d54823e4a9895941d5b88b802670c.png)
您最近一年使用:0次
2024·江苏连云港·模拟预测
10 . 已知A,B是抛物线E:
上不同的两点,点P在x轴下方,PA,PB与抛物线E分别交于C,D两点,C,D恰好为PA,PB的中点.设AB,CD的中点分别为点M,N.
(1)证明:
轴;
(2)若点P为半椭圆
上的动点,求四边形ABDC面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52cbeb9b1c1d637b903cf3e5c7f730f6.png)
(2)若点P为半椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdf37f8de66bafa4d1c4e3b217a82aa.png)
您最近一年使用:0次