14-15高一上·湖南张家界·期末
解题方法
1 . 设函数
满足
且
.
(1)求证
,并求
的取值范围;
(2)证明函数
在
内至少有一个零点;
(3)设
是函数
的两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d0b83762279e1e6d818d3999201fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39675659305a1b59862e5f222083f6f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a1f987b14c075c1ca923de99be51449.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
(2)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbfd0c7caacb8f926dbc857f913a6dd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be837b55c392129d22e35a0b97921c5.png)
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名校
2 . 如图①,在矩形
中,
为边
的中点.将
沿
翻折至
,连接
,得到四棱锥
(如图②),
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/79d34a5a-2936-4062-8ffa-c34b6c19cdab.png?resizew=317)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
面
,并求
的长;
(2)若
,棱
上存在动点
(除端点外),求直线
与面
所成角的正弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfdcde01d0b8d46415f598db47a27b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/dbe40405cd7bd60d69dd535d6da85c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c3cc1f331dbb2248b0829039df7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efeadd146662b5d8fe14a424138ef751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/79d34a5a-2936-4062-8ffa-c34b6c19cdab.png?resizew=317)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58bbc02479917ad761a24eaae0dbfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
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解题方法
3 . 如图,沈阳东塔桥是沈阳唯一一座“双塔钢结构自锚式悬索桥”,悬索的形状是平面几何中的悬链线,悬链线方程为
(
为参数,
),当
时,该方程就是双曲余弦函数
,类似的有双曲正弦函数
.
;
(2)当
时,求
的最小值
;
(3)设
,证明:
有唯一的正零点
,并比较
和
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcee592f27561a08c5382ae859f1895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b7ca7aa39924a7b0e9553eb841cadd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174887c6a781255eb8eda6f5c92c438e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd11c9bd4cb5ac688ea801dec1b0153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a59cab56922cffd14358d2f48d1e00.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25fc54e432fbe61c86401a76b4f1fe8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50eeae6b06ff0f6cb7caabefdee109f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb708adff55a5bda517c3f570f06584c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7598b54c2ae46e8d8397ad3ef12e4b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c5690823d3da4dfdb815576ca0a5d4.png)
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名校
4 . 已知函数
是定义域为
的奇函数,且
.
(1)求
的值,并判断
在
上的单调性(不必证明);
(2)已知
为实数,函数
,若对于任意
,总存在
,使得
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8717af5b57ca8eb3402b17118fec7a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f69d0e3fecdd5be1f979e896be0713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a3163cc2d37e7b7fe450f6e8bf8500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12165378c124c0a17ed6b7dbe253412c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
5 . 已知函数
.
(1)用定义证明
是
上的增函数.
(2)是否存在m,使得对任意的
恒成立?若存在,求出m的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b586d5da50edf2b5d624b1f3368570eb.png)
(1)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)是否存在m,使得对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce5e41c8ad37efd3b0f1d07423a7ea9c.png)
您最近一年使用:0次
2023-11-28更新
|
669次组卷
|
3卷引用:辽宁省葫芦岛市协作校2023-2024学年高一上学期第二次考试数学试题
名校
6 . 如图所示,在△ABC中,点D是边BC的中点,点E是线段上靠近A的一个三等分点,过点E的直线与边AB,AC分别交于点P,Q.设
,
,其中
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ce10d13e84bc67c1a12f0acd35d9d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/a39fda62-9563-45f7-b5dc-c1e1bc04ea7a.png?resizew=128)
(1)求证:
为定值,并求此定值;
(2)设△APQ的面积为
,△ABC的面积为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a96f93c74e45318dab2ef44893ad687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e20b752572a7e0ab2e32e4a93a8c8f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ce10d13e84bc67c1a12f0acd35d9d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/a39fda62-9563-45f7-b5dc-c1e1bc04ea7a.png?resizew=128)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(2)设△APQ的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
2022-10-29更新
|
654次组卷
|
2卷引用:辽宁省沈阳市东北育才学校2022-2023学年高三上学期联合考试数学试题
解题方法
7 . 已知
,
为常数,函数
.
(1)当
时,求关于
的不等式
的解集;
(2)对于给定的
,
,且
,
,证明:关于
的方程
在区间
内有一个实根;
(3)若
为偶函数,且
,设
,若对任意
,
均成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ad38aec9b8b5c741a9e83943809967.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f359fbd7bb48389efebb8787398478a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)对于给定的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33890c6b0bf167514d44139d9dca0154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7ecd5cee1dce002ba2356bc164c56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f803a468e5d66004e57372a5bf2c5e1b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc20d351d51723c9b0a07a20ac14114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35821eae71dfea3b136fe7ee19944a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3c81a19a9adcdb16b2327c77917166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b767854aade97dc70a9b32e99be19eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-11-17更新
|
342次组卷
|
3卷引用:辽宁省协作校2022-2023学年高一上学期期中考试数学试题
名校
解题方法
8 . 设函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/92cae942-5c13-4214-8f9d-c15ecc6c3045.png?resizew=168)
(1)当
时,在平面直角坐标系中作出函数
的大致图象,并写出
的单调区间(无需证明);
(2)若
,求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afdd9c055d2a0a01199692a2dfbee330.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/92cae942-5c13-4214-8f9d-c15ecc6c3045.png?resizew=168)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2bb00228e4e58363598fe3dd6efa945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2022-10-28更新
|
111次组卷
|
2卷引用:辽宁省朝阳市建平县实验中学2022-2023学年高一上学期期中数学试题
9 . 已知函数
(
).
(1)求
在区间
上的最小值
;
(2)设函数
,用定义证明:
在
上是减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbdaff297141813399af6f71b8803e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a7b7c834d06f3e28a339db94690172.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3109a3db9931922fda8851ab5875b915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
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10-11高一上·安徽蚌埠·期中
名校
10 . 已知函数
对一切实数
都有
成立,且
.
(1)求
的值;
(2)求
的解析式,并用定义法证明
在
单调递增;
(3)已知
,设P:
,不等式
恒成立,Q:
时,
是单调函数.如果满足P成立的
的集合记为A,满足Q成立的
集合记为B,求
(R为全集).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43664f69478dfae1918764cb626f197a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196be101149acfb6a6c4ceca7fc96828.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e700b05548ed94c2bb28fc3c9a0c715e.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7511e6ce72a5232820b7007f976be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de838da88f9592272c32eaec3eb18c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75bde2e500fd5386e355db9040a1946d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92806f646c860991ed47556ffd1169a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba8578787a6b9068b5957d40e8925d9.png)
您最近一年使用:0次
2019-10-13更新
|
1818次组卷
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23卷引用:【区级联考】辽宁省大连市旅顺口区2018-2019学年高一上学期期中考试数学试题
【区级联考】辽宁省大连市旅顺口区2018-2019学年高一上学期期中考试数学试题(已下线)2010年安徽省蚌埠二中高一第一学期期中考试理科数学卷(已下线)2011-2012学年江西省新余一中高一第一次月考数学试卷(已下线)2011年安徽省师大附中高一第一学期期中考试数学(已下线)2011-2012学年天津市天津一中高一上学期期中考试数学(已下线)2014-2015学年广东省揭阳三中高一上学期第一次阶段考试数学试卷2014-2015学年安徽省蚌埠市五河县高中高一上学期期中考试数学试卷2014-2015学年江西省南昌市八一中学高一文理分科考试数学试卷2015-2016学年山东省郯城县一中高一12月月考数学试卷2015-2016学年宁夏石嘴山三中高二下期中文科数学试卷12015-2016学年宁夏石嘴山三中高二下期中文科数学试卷22016-2017学年河北定州中学高二上周练7.8数学试卷河北辛集中学高一上学期数学限时训练试卷广西贺州市桂梧高中2017-2018学年高二上学期第一次月考数学(A卷)试题河南省商丘市九校2017-2018学年高一上学期期中联考数学试题福建省清流县第一中学2017-2018学年高一上学期第二阶段(期中)考试数学试题天津市耀华中学2017-2018学年高一上学期期中考试数学试题【校级联考】福建省宁德宁市-同心顺-六校联盟2017-2018学年高一上学期期中考试数学试题【全国百强校】福建省厦门市双十中学2018-2019学年高一上期中考试数学试题青海师大二附中2016-2017学年高一上学期月考数学试题广西壮族自治区宾阳县宾阳中学2019-2020学年高一9月月考数学试题人教A版(2019) 必修第一册 突围者 第三章 综合拓展(已下线)第五章 函数概念与性质(选拔卷)-【单元测试】2021-2022学年高一数学尖子生选拔卷(苏教版2019必修第一册)