名校
1 . 已知:函数
,
.
(1)若
的定义域为
,求
的取值范围;
(2)设函数
,若
,对于任意
总成立.求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc90719c0078d2a9dd6590b9ba55bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fda90490b6b98cb1f0878b0cace041.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a20457d180264f78d611dc7893d735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989f8bd34cd1acecae079e1bc244d64b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ea6baecc58836834dff78b68bf09cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-05-08更新
|
769次组卷
|
3卷引用:江西省都昌蔡岭慈济中学2019-2020学年下学期高三5月月考文科数学试题
名校
2 . 已知函数
.
(1)求函数
的定义域;
(2)设
,若函数
在
上有且仅有一个零点,求实数
的取值范围;
(3)设
,是否存在正实数
,使得函数
在
内的最小值为4?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c7082ad32db40f04008553b1d366b9.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a79534888449d1d808fb981bbed56ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be3ad3dd6803d92df6ff8a80cd35095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6b2aa084c5878f18ad0642a5c9b4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67333949e76ee3da8b17c9f9d4a97fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-05-05更新
|
2796次组卷
|
10卷引用:天津市宝坻区第一中学2020-2021学年高三上学期第四次月考数学试题
天津市宝坻区第一中学2020-2021学年高三上学期第四次月考数学试题湖南省长沙市长郡中学2018-2019学年高二下学期期中数学试题湖南省常德市石门县第六中学2019-2020学年高一下学期期末数学试题广东省深圳市南头中学2020-2021学年高一下学期期末数学试题(已下线)第4章 指数函数与对数函数 章末测试(提升)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第一册)天津市西青区杨柳青第一中学2021-2022学年高二实验班下学期期末适应性测试数学试题山东省青岛市莱西市第一中学2022-2023学年高一上学期12月月考数学试题江西省吉安市永丰县永丰中学2022-2023学年高一上学期期末考试数学试题(B)新疆生产建设兵团第一师第二高级中学等2校2022-2023学年高一下学期2月月考数学试题福建省闽江学院附属中学2022-2023学年高一上学期期中考试数学试题
真题
解题方法
3 . 已知
,
,
试比较
与
的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a357693afa2cb64082bde4ed5227f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0d3e5a7cab453ae9821ac5a26ad1cd.png)
您最近一年使用:0次
2020-04-17更新
|
646次组卷
|
2卷引用:1982 年普通高等学校招生考试数学(理)试题(全国卷)
名校
4 . 设函数
(
)的最小值为
.
(1)求
的值;
(2)若
,
,
为正实数,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57530a487367697c920f4bb2df591599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861ec3a6c3c6fd17393f625d32940dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80656b731580035f2d5f137a0a97cbb7.png)
您最近一年使用:0次
2020-03-28更新
|
883次组卷
|
9卷引用:2020届五岳湖南、河南、江西高三3月线上联考理科数学试题
名校
5 . 如图,河的两岸分别有生活小区
和
,其中
,
三点共线,
与
的延长线交于点
,测得
,
,
,
,
,若以
所在直线分别为
轴建立平面直角坐标系
则河岸
可看成是曲线
(其中
是常数)的一部分,河岸
可看成是直线
(其中
为常数)的一部分.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/92f83a74-2e60-4940-8684-5a047ca5fe88.png?resizew=201)
(1)求
的值.
(2)现准备建一座桥
,其中
分别在
上,且
,
的横坐标为
.写出桥
的长
关于
的函数关系式
,并标明定义域;当
为何值时,
取到最小值?最小值是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b697cfa31f6809017ad35b95b45ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6e8312671b97cd11a49682f394f463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ceb34ba50edb6400ea587d4b90ec5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43196011f26ecba93218f51226c23e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b136f3841ab4b4aa30fa89d6b1ba52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d05eb22f985b471366ef41afe34530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b82c8e05dde6af83ecb42aee5fd46e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dceafe558f74a53631f42ca3c3d489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bd32133d04a42aff675da13e8645c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef3e9eb0c4bd9c899886668229c4c947.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/92f83a74-2e60-4940-8684-5a047ca5fe88.png?resizew=201)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e70f7d639ea16f49eb4d5df6d288a9.png)
(2)现准备建一座桥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d26633cc499d15d86afb2f54a492cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66fae8e33cd86fa8dab72704eaafe1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7807b0ac88dc2f8e3491e76aa2e45857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-03-25更新
|
610次组卷
|
11卷引用:2020届江苏省盐城中学高三(尖子生班)下学期3月调研考试数学试题
2020届江苏省盐城中学高三(尖子生班)下学期3月调研考试数学试题2020届江苏省新海高中、昆山中学、梁丰高中高三下学期5月高考模拟数学试题江苏省南通市2020届高三(3月份)尖子生班高考数学模拟试题(一)(已下线)预测08 不等式、推理与证明-【临门一脚】2020年高考数学三轮冲刺过关(江苏专用)江苏省无锡一中2019-2020学年高三上学期12月考数学试题(已下线)福建省厦门市2019-2020学年高一上学期质量检测期末考试数学试题湖南省岳阳市2019-2020学年高二下学期期末数学试题(已下线)【南昌新东方】江西省南昌市外国语学校2020-2021年高二上学期10月月考数学试题江西省南昌外国语学校2019-2020学年高二10月月考数学试题河南省信阳市2020-2021学年高二上学期期末数学(理科)试题(已下线)第02讲 函数与数学模型(教师版)-【帮课堂】2021-2022学年高一数学同步精品讲义(苏教版2019必修第一册)
2012·陕西·三模
名校
6 . 若
,且
,
(
且
),
(1)求
的最小值及相应
的值;
(2)若
且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0ae6796e21d422342799b6155343f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c47d9504f274be4c53cbb56b093ad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dac3fa4d10b586514f751ffb532f858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b22587c4fcd78f4b64296e9a1116fccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d6d161e8eb824b07162c57528dac46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6544c32c90da1c9e5fcaab67cb740e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2020-03-19更新
|
444次组卷
|
8卷引用:2012届陕西省交大附中高三第三次诊断理科数学试卷
(已下线)2012届陕西省交大附中高三第三次诊断理科数学试卷2017届江西南昌新课标高三一轮复习训练三数学试卷(已下线)专题12 基本初等函数综合练习-2021年高考一轮数学(文)单元复习一遍过(已下线)专题12 基本初等函数综合练习-2021年高考一轮数学(理)单元复习一遍过(已下线)专题12 基本初等函数综合练习-2021年高考一轮数学单元复习一遍过(新高考地区专用)山西省河津市第二中学2019-2020学年高一上学期12月月考数学试题2016-2017学年辽宁省庄河市高级中学高一下学期开学考试数学(理)试卷江西省景德镇一中2020-2021学年高一(2班)上学期期末考试数学试题
名校
解题方法
7 . 已知函数f(x)
,g(x)
1.
(1)若f(a)=2,求实数a的值;
(2)判断f(x)的单调性,并证明;
(3)设函数h(x)=g(x)
(x>0),若h(2t)+mh(t)+4>0对任意的正实数t恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a63905c821ad3119a793ea3bc755ea53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/144f6637aabd3be93fe6647b99d01e2f.png)
(1)若f(a)=2,求实数a的值;
(2)判断f(x)的单调性,并证明;
(3)设函数h(x)=g(x)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0482af1f0d226806475d78b02af9921.png)
您最近一年使用:0次
2020-03-18更新
|
1013次组卷
|
3卷引用:2020届河南省中原名校高三上学期第三次质量考评数学(文)试题
名校
8 . 已知函数
,
(1)若存在
,使得不等式
有解,求实数
的取值范围;
(2)若函数
满足
,若对任意
且
,不等式
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbd9e52b79fb84c320dc522e13d4f0b.png)
(1)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd0f1e3e3b41948f1b3d287c4b0cb44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfda93888e67df317e8b59b9fa8c79da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfe3e041b26dd1024a6ca08c7f1f4c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe55610b65b7bb3ec6defa8aa4fa73e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-03-15更新
|
685次组卷
|
3卷引用:2020届江苏省淮安市涟水中学高三上学期期中数学(理)试题
名校
解题方法
9 . 定义:给定整数i,如果非空集合满足如下3个条件:
①
;②
;③
,若
,则
.
则称集合A为“减i集”
(1)
是否为“减0集”?是否为“减1集”?
(2)证明:不存在“减2集”;
(3)是否存在“减1集”?如果存在,求出所有“减1集”;如果不存在,说明理由.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc7338b2a8a4a7d06acd6eb1b446564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebabd7323bae39388835a33e09046c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669926e4732ba3eca48e018aaebe7079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957d41dbe52b49c3a7339e3519a3fe84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45251c3475305d50c946539a1bd6a5f8.png)
则称集合A为“减i集”
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ed72c5ada5b4d689310406b7cef32f.png)
(2)证明:不存在“减2集”;
(3)是否存在“减1集”?如果存在,求出所有“减1集”;如果不存在,说明理由.
您最近一年使用:0次
2020-03-14更新
|
1147次组卷
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7卷引用:2020届北京市中国人民大学附属中学高三开学复习质量检测数学试题
2020届北京市中国人民大学附属中学高三开学复习质量检测数学试题北京市海淀区中国人民大学附属中学2023届高三下学期开学摸底练习数学试题北京市人大附中2023届高三下学期2月开学考数学试题(已下线)专题03 集合的运算压轴题型-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)高一上学期期中【压轴60题考点专练】(必修一前三章)-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)北京市海淀区宏志中学2023-2024学年高一上学期期中考试数学试卷重庆市西南大学附属中学校2023-2024学年2023-2024学年高二下学期3月测试数学试题
解题方法
10 . 如图,某市建有贯穿东西和南北的两条垂直公路
,
,在它们交叉路口点
处的东北方向建有一个荷花池,荷花池的外围是一条环形公路,荷花池中的固定观景台
位于两条垂直公路的角平分线
上,
与环形公路的交点记作
.游客游览荷花池时,需沿公路
先到达环形公路
处.为了分流游客,方便游客游览荷花池,计划从靠近公路
,
的环形公路上选
,
两处(
,
关于直线
对称)修建直达观景台
的玻璃栈道
,
.以
,
所在的直线为
,
轴建立平面直角坐标系
,靠近公路
,
的环形公路可用曲线
近似表示,曲线
符合函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/6dada63c-d9e0-422a-9af9-e9f0179900fe.png?resizew=170)
(1)若
百米,点
到
的垂直距离为1百米,求玻璃栈道
的总长度;
(2)若要使得玻璃栈道
的总长度最小为
百米,求观景台
的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95df8aa0fabb9ff4594fbda756fe40e8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/6dada63c-d9e0-422a-9af9-e9f0179900fe.png?resizew=170)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcd4286cd044729071fb7ff9117a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac656ec89607f52b5353dba400fab6.png)
(2)若要使得玻璃栈道
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac656ec89607f52b5353dba400fab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2793aa39b517d1a5e7ca2d8243710c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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