1 . 集合论在离散数学中有着非常重要的地位.对于非空集合
和
,定义和集
,用符号
表示和集
内的元素个数.
(1)已知集合
,
,
,若
,求
的值;
(2)记集合
,
,
,
为
中所有元素之和,
,求证:
;
(3)若
与
都是由
个整数构成的集合,且
,证明:若按一定顺序排列,集合
与
中的元素是两个公差相等的等差数列.
![](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/88c7a43079a55f6a53b1307b2b04b55e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf60f60fedb84bb62a0c00276908ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce69cd33d105ce280170f0cd0513026.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed0081de4e04574dd0884c4e6077fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d651573ff643d295dcceafdb6f1249d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42500dfa5011086d43ef7e6dac58271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b27c12cad9040ae9698895e43903747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c9e547b17582b99e548037172eeff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f7f9dc32fa86d097de2b7d78b6b487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594e60168219fdebb98b45493de0128a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc9ec58912d76aabf278faa7bf06e45.png)
(3)若
![](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/ef96e432405a1037b5aea7514715e52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa740177330d445b0d506f3b53f9ad2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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2 . 如图所示,四边形
为梯形,
,
,
,以
为一条边作矩形
,且
,平面
平面
.
;
(2)甲同学研究发现并证明了这样一个结论:如果两个平面所成的二面角为
,其中一个平面内的图形
在另一个平面上的正投影为
,它们的面积分别记为
和
,则
.乙同学利用甲的这个结论,发现在线段
上存在点
,使得
.请你对乙同学发现的结论进行证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a75b1354b8b783a65ee5e3bc596a976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3362a45b72536c714c5107b0ae94f1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0db1f4f666a9be9ede868065a50997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31025539da369c563e8633f375146593.png)
(2)甲同学研究发现并证明了这样一个结论:如果两个平面所成的二面角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5a434a89f3f689db2a4623efbc74a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81722445de00f3cfcc3cb97e45b0d8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27e50f80b7bf7025a049692b17abcd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbce6d96030ceae48cfef1634085c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3effb95a6c4422798440cd8a2a110636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8c820f511d3b23ffebae3822f19589.png)
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3 . 已知动圆
过定点
且与直线
相切,记圆心
的轨迹为曲线
.
(1)已知
、
两点的坐标分别为
、
,直线
、
的斜率分别为
、
,证明:
;
(2)若点
、
是轨迹
上的两个动点且
,设线段
的中点为
,圆
与动点
的轨迹
交于不同于
的三点
、
、
,求证:
的重心的横坐标为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5421a28dc3675ae20190d6090793246e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)已知
![](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/879a4007beef22e009248112d664f7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf209717d3bde602ab96c53d6a43a811.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb2356a3833defed220ee1fa481aad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaecf08a22124a457128fb04c9c02bb.png)
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4 . 在平面直角坐标系
中,P,Q是抛物线
上两点(异于点O),过点P且与C相切的直线l交x轴于点M,且直线
与l的斜率乘积为
.
(1)求证:直线
过定点,并求此定点D的坐标;
(2)过M作l的垂线交椭圆
于A,B两点,过D作l的平行线交直线
于H,记
的面积为S,
的面积为T.
①当
取最大值时,求点P的纵坐标;
②证明:存在定点G,使
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb9603390e28948abd2e3cd96e1720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)过M作l的垂线交椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895f5fcb1cebfc09dc14ab6efad03437.png)
②证明:存在定点G,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac90c4158636c076ef1d0d45df68be88.png)
您最近一年使用:0次
2023-05-08更新
|
942次组卷
|
5卷引用:湖南省株洲市第二中学2022届高三下学期第三次月考数学试题
湖南省株洲市第二中学2022届高三下学期第三次月考数学试题山东省烟台市2023届高考适应性练习(一)数学试题山东省枣庄市2023届高三三模数学试题(已下线)高二上学期期中复习【第三章 圆锥曲线的方程】十二大题型归纳(拔尖篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)通关练17 抛物线8考点精练(3)
名校
解题方法
5 . 已知函数
与
的定义域为R,若对任意区间
,存在
且
,使
,则
是
的生成函数.
(1)求证:
是
的生成函数;
(2)若
是
的生成函数,判断并证明
的单调性;
(3)若
是
的生成函数,实数
,求
的一个生成函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71717fb069fa0f5a1d196b6484618351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c035964f2f9d1c84a91cc651fb5e4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b23eea271d1b00e358ca6dc048e8134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fad236fddf9598b319a1acd223a9269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d761c4444f5eac17133caaf19d6b9ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f4b87b2b2d6297cb330a6aa6a96c95.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c18e7d848da79e20188ed6a0225a0c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aed37e8318fb8ca63e19e06dbcdd791.png)
您最近一年使用:0次
2023-05-05更新
|
572次组卷
|
4卷引用:湖南省长沙市明德中学2022-2023学年高一下学期5月月考数学试题
湖南省长沙市明德中学2022-2023学年高一下学期5月月考数学试题上海交通大学附属中学2022-2023学年高一下学期期中数学试题(已下线)第3课时 课后 函数的单调性(完成)(已下线)5.2.2 函数的单调性-数学同步精品课堂(沪教版2020必修第一册)
6 . 如图,在
中,
为
边上一点,
与
分别为
和
的平分线.
![](https://img.xkw.com/dksih/QBM/2022/8/24/3051581032407040/3054416256311296/STEM/432c6f09ddd742e0800436bc37acdea7.png?resizew=265)
(1)判断
是什么三角形,并证明你的结论;
(2)比较
与
的大小;
(3)以
为直径的
交
于点
,连接
与
交于
,若
,
,求证:
,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c42b59b76eafbbe36f13b2daa60132c.png)
![](https://img.xkw.com/dksih/QBM/2022/8/24/3051581032407040/3054416256311296/STEM/432c6f09ddd742e0800436bc37acdea7.png?resizew=265)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(3)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.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/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29224be6a2381b38bc64b144d26dad26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f364bf9d8b0bfc299e51097b3ca512f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b092922acd073edfc3a3887822af40.png)
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21-22高二·湖南·课后作业
7 . 阅读“多知道一点:平面方程”,并解答下列问题:
(1)建立空间直角坐标系,已知
,
,
三点,而
是空间任意一点,求A,B,C,P四点共面的充要条件.
(2)试求过点
,
,
的平面ABC的方程,其中a,b,c都不等于0.
(3)已知平面
有法向量
,并且经过点
,求平面
的方程.
(4)已知平面
的方程为
,证明:
是平面
的法向量.
(5)①求点
到平面
的距离;
②求证:点
到平面
的距离
,并将这个公式与“平面解析几何初步”中介绍的点到直线的距离公式进行比较.
(1)建立空间直角坐标系,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b5103a4c35ab0c395c68690a300023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f6f9d8550d619061ab0ba1105ec6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf322f683d50ecd3c7d4d5996122726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b82ad92798b264062c062f4a9a1a5c.png)
(2)试求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3ea554707fa3fc12fc9de51c94e4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5622d4be6bba8c7a6851dc082ef34fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1f4b53c90e4c31dd35b4bb548c5193.png)
(3)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b163c34a920cb649829c376e7870007a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b5103a4c35ab0c395c68690a300023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(4)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e0ae1c14104ee9985e3ba31c604531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(5)①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae715c996c1a6b5e35a3807c671bd6e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
②求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e874a5821372c21a768cd1f5e20536d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c828e62664e7373ed1f6dde8aa9653c.png)
您最近一年使用:0次
21-22高一·湖南·课后作业
解题方法
8 . 证明不等式:
(1)若
,
,
,
都是正数,求证:
;
(2)若
,
,
是非负实数,则
;
(3)若
,
是非负实数,则
;
(4)若
,
,则
.
(1)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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e7387a3fbab6508695365955f55258.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/b2d92a6b95fdfdedb405447340293bdc.png)
(3)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/727ff3ac24b506706045956c16336f94.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f58b9bc974b789928f6490acb43fb3.png)
您最近一年使用:0次
名校
解题方法
9 . 悬索桥(如图)的外观大漂亮,悬索的形状是平面几何中的悬链线.
年莱布尼兹和伯努利推导出某链线的方程为
,其中
为参数.当
时,该方程就是双曲余弦函数
,类似的我们有双曲正弦函数
.
![](https://img.xkw.com/dksih/QBM/2022/1/23/2900721970536448/2907279254913024/STEM/8a914e2499134cf68207c8add767fe65.png?resizew=325)
(1)从下列三个结论中选择一个进行证明,并求函数
的最小值;
①
;
②
;
③
.
(2)求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046db679c09a10434e81f7a01c55e243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad2f5a11d7437f506adab0996961269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099b9b80ed478824fa95677ebe9d5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3321510a9eb73909a36c084a8630e89.png)
![](https://img.xkw.com/dksih/QBM/2022/1/23/2900721970536448/2907279254913024/STEM/8a914e2499134cf68207c8add767fe65.png?resizew=325)
(1)从下列三个结论中选择一个进行证明,并求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634cf0ca04b381dec8fcfee8805bdac.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff61bdd9ed784248cfdcc965ce06db0.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40ff30f6f7fca28159dedeff7168c74.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c3de984177769fa426e10eb14cd82c.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0645c3c42e19271f86a10b1fe9dbb0f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b39ee39c38f49390a03be161109a2b4.png)
您最近一年使用:0次
2022-02-01更新
|
1295次组卷
|
7卷引用:湖南省株洲市第二中学2021-2022学年高一下学期“同济大学”杯数理化联赛数学试题
湖南省株洲市第二中学2021-2022学年高一下学期“同济大学”杯数理化联赛数学试题湖南省株洲市南方中学2022-2023学年高一下学期期末数学试题江苏省苏州市2021-2022学年高一上学期期末数学试题重庆市2023届高三下学期3月月度质量检测数学试题(已下线)重难点突破02 函数的综合应用(九大题型)(已下线)压轴题函数与导数新定义题(九省联考第19题模式)讲(已下线)压轴题三角函数新定义题(九省联考第19题模式)讲
名校
解题方法
10 . 记
.
(1)若
,求
和
;
(2)若
,求证:对于任意
,都有
,且存在
,使得
.
(3)已知定义在
上
有最小值,求证“
是偶函数”的充要条件是“对于任意正实数
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d80225e12934cd8d4ffc73d5fad815d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04beea76c59a6c5b096d8c5a3b77f8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1b9f62690647a1597f4000ad5a64b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c8381377b90826897eb4bf16cb3bae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28034dcafe542a98d95d4504ad7d8a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4def7108b0a2338f07a0143b00b48271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3761d7ab4d00c91177fdbde67af36089.png)
(3)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625e9d3c298a595678933b59583632c2.png)
您最近一年使用:0次