1 . 已知数列
和
,设
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f56e14765e0275bd98aedd8f021975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638baab21fc1218c89671cb871af4648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f926978fad9cdc89916a5272479d17.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2 . 已知函数
(
,
为自然对数的底数).
(1)若不等式
对于一切
恒成立,求
的最小值;
(2)若对任意的
,在
上总存在两个不同的
,使
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba790bfc7240d9f86fea1f9367a4cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46ecf935049473045cdebae68415657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd9add1ab2b4a7baf1396c57bb2e05df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20082e474b757273b4b83b13f16ddb61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281106d1eb0462759ab01d17ba958a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/214618dca74e79067bc27a47ea178ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 将边长为
,锐角为
的菱形沿较长的对角线折叠成大小为
的二面角,若该菱形折叠后所得到的三棱锥内接于表面积为
的球,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81eed0e1eecdfd4a22f099b5c927324f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fdc0f7fca676bc059a7955ea9088643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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4 . 已知函数
,
.
(1)求
的单调区间;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc1e1eda1e062dc9c898622072f0495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1610bcd07b02c4ed7184ad586b88f373.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375d897a1f137d6c6704d24f9b4b0948.png)
您最近一年使用:0次
2023-11-15更新
|
385次组卷
|
5卷引用:辽宁省铁岭市一般高中协作校2023-2024学年高三上学期期中考试数学试题
名校
解题方法
5 . 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
|
2827次组卷
|
13卷引用: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
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(已下线)1.2.4 二面角(已下线)第4讲 空间向量的应用 (3)(已下线)第07讲 空间向量的应用 (2)山西省运城市稷山县稷山中学2023-2024学年高二上学期11月月考数学试题重庆市北碚区缙云教育联盟2024届高考零诊数学试题(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)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
名校
6 . 已知函数
的定义域为R,对任意实数x,y满足:
,且
,当
时,
,给出以下结论,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a9899e7d63283051092fa4f7f7c73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8dfda35f1dc37e92b20d67219aa91e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6fa27b49d26e8e9e878128915676d8.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2023-11-01更新
|
814次组卷
|
4卷引用:辽宁省铁岭市西丰县第二高级中学2023-2024学年高一上学期期中考试数学试题
名校
7 . 下列不等关系中正确的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
8 . 已知函数
.
(1)求
的图象在点
处的切线方程;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001c91ca71305c4d2968b40ad643895b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e4cc4c1ee692c8a691b2b032b72ab5.png)
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名校
解题方法
9 . 在
中,角
所对的边分别为
.
(1)求
;
(2)若
,过
作
垂直于
交
于点
为
上一点,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142df6aa468d536b5c31c2ede01ef4da.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f46ef99700d9160d32d9c29f4a3948b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429d4830ab93100e6bcaffd39c039632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
2023-07-16更新
|
1062次组卷
|
4卷引用:辽宁省铁岭市昌图县第一高级中学2022-2023学年高一下学期期末数学试题
辽宁省铁岭市昌图县第一高级中学2022-2023学年高一下学期期末数学试题云南省楚雄州2022-2023学年高一下学期期末考试数学试题(已下线)广东省佛山市第一中学2024届高三上学期第二次调研数学试题变式题17-22(已下线)湖南省长沙市雅礼中学2023-2024学年高一下学期期中考试数学试题变式题16-19
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10 . 已知函数
,
.
(1)若不等式
恒成立,求a的取值范围;
(2)若
时,存在4个不同实数
满足
.证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7525c9480d4b7ac129996dbd7b1cb7cb.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9699d5af88ccdcccc1fd0cdce6018ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4a18c09f0055baa3e0abcbc75a84ed.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa939782348f031b9aba60c05fb13187.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908bfb759e6375da922bbb1d1a028ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7525c9480d4b7ac129996dbd7b1cb7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377df1441214a18e60de35e5df609cfe.png)
您最近一年使用:0次
2023-05-25更新
|
402次组卷
|
2卷引用:辽宁省铁岭市昌图县第一高级中学2022-2023学年高二下学期6月月考数学试题