名校
解题方法
1 . 如图所示,在四棱锥
中,底面
为直角梯形,
∥
、
、
、
,
、
分别为
、
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/8372c1fd-7a2e-46d0-82d4-828a5e99b5da.png?resizew=184)
(1)证明:平面
平面
;
(2)若
与
所成角为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ff6d7dd48b57f03d82d2c522ee9b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639bec6242a4b3f7bfb4b7033a67328c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9829fc6685b59fdc609f32f30ebd9e6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/8372c1fd-7a2e-46d0-82d4-828a5e99b5da.png?resizew=184)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a590bdfe296689fc138d8995deae2026.png)
您最近一年使用:0次
2023-11-05更新
|
2813次组卷
|
13卷引用:新疆克拉玛依市2022届高三下学期第三次模拟检测数学(理)试题
新疆克拉玛依市2022届高三下学期第三次模拟检测数学(理)试题广东省广州市奥林匹克中学2021-2022学年高二下学期6月月考数学试题辽宁省铁岭市昌图县第一高级中学2021-2022学年高一下学期期末数学试题(已下线)1.2.4 二面角(已下线)第07讲 空间向量的应用 (2)重庆市北碚区缙云教育联盟2024届高考零诊数学试题新疆维吾尔自治区阿克苏地库车市第二中学2023-2024学年高二上学期第二次月考(12月)数学(已下线)第4讲 空间向量的应用 (3)山西省运城市稷山县稷山中学2023-2024学年高二上学期11月月考数学试题(已下线)四川省成都市第七中学2023-2024学年高二上学期12月月考数学试题北京市丰台区2023-2024学年高二上学期期末模拟数学试题江西省上饶市广丰区南山中学2023-2024学年高二上学期期末模拟数学试题河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(三)
解题方法
2 . 若函数
是奇函数,函数
,若
恒成立,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcaf22c518cf410a4fcd862ea3648dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d99c9ed5a71bf65749eedfbba6db9f18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811893a2f837045f345a1e2c79527962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 已知椭圆
,椭圆
的焦点在y轴上.经过点
且与椭圆
有相同的离心率.
(1)求椭圆
的方程;
(2)设A为椭圆
的上顶点,点P是椭圆
上在第一象限内的一点,点Q与点P关于原点对称,直线
与椭圆
的另一个交点分别为M,N两点,设
与
的面积分别为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be052f0deaa8c6de37c57ad17edd32a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd80b108b9a6cf2ef20bab203674831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设A为椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
解题方法
4 . 已知
.
(1)当
时,求曲线
在
处的切线l的方程,并证明
的图像在直线l的上方(切点除外);
(2)若
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6326bb588482f5ca6a42232401605968.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a508720957af1de8fe9d03829fb3cde.png)
您最近一年使用:0次
解题方法
5 . 四棱锥P-ABCD各顶点都在球心为O的球面上,且PA⊥平面ABCD,底面ABCD为矩形.
,
,则球O的半径是__________ ;设M、N分别是PD、CD的中点,则平面AMN截球O所得截面的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2753753faf2cb9a0003aa8e3945159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedd51383f8f047f565191b128cec637.png)
您最近一年使用:0次
解题方法
6 . 已知
.
(1)若
,求
的最小值;
(2)当
时,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce69636147b723e958a64e5dbe18cfe5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
7 . 已知函数
的图象在原点处的切线方程为
.
(1)求函数
的解析式;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d90fcd223cc53e9fd75759b530d9f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a9b769d70cb6f29e965c800921c8ea.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6096dcd8029361d0734ce9382291d02b.png)
您最近一年使用:0次
2022-05-13更新
|
420次组卷
|
3卷引用:新疆维吾尔自治区普通高考2022届高三第三次适应性检测数学(文)试题
名校
解题方法
8 . 对于正实数
有基本不等式:
,其中
,为
的算术平均数,
,为
的几何平均数.现定义
的对数平均数:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b454c722316d2e530e935987adcb81.png)
(1)设
,求证:
:
(2)①证明不等式:
:
②若不等式
对于任意的正实数
恒成立,求正实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1f53d48a9ad9f88f4b3c14f2637d3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0bcbf744c3da99e6488f8e66cb8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee128ea692363f9a7b0cf0958e5f74e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b9514b5e245327b05261ac9a946063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b454c722316d2e530e935987adcb81.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855eaf612ac4e4505948ee0a1c3c080e.png)
(2)①证明不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8188a2ffd328c07a359ea9be8102a70.png)
②若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0a551c4d6741cae6d513122166db90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff93e03b22c6053550486ea4e911c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2022-05-11更新
|
493次组卷
|
6卷引用:新疆昌吉州2022届高三第二次诊断性测试数学(理)试题
9 . 已知
,
.
(1)讨论
的单调性;
(2)当
时,若
存在两个极值点
,
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6675a76c7e622bc80d7da02e842777da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619e5bb980013cd2dc109a4cce18a3d9.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21872d5d768a8041ab7bb57aa212ba0d.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/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0fbf3a9d9ca515a9216a6395d472e7.png)
您最近一年使用:0次
名校
解题方法
10 . 半正多面体亦称“阿基米德多面体”,是由边数不全相同的正多边形围成的多面体,体现了数学的对称美,以正方体每条棱的中点为顶点构造一个半正多面体,如图,它由八个正三角形和六个正方形构成,它的所有棱长都为2,则该半正多面体外接球的表面积为___________ ;若该半正多面体可以在一个正四面体内任意转动,则该正四面体体积最小值为___________ .
![](https://img.xkw.com/dksih/QBM/2022/5/10/2976570010050560/2977093207187456/STEM/8f99dff4-7d25-4248-86ba-34c13f457e8f.png?resizew=153)
您最近一年使用:0次
2022-05-11更新
|
364次组卷
|
3卷引用:新疆维吾尔自治区2022届高三下学期第三次适应性检测数学(理)试题