名校
1 . 定理(三角不等式),对于任意的
、
,恒有
.定义:已知
且
,对于有序数组
、
、
、
,称
为有序数组
、
、
、
的波动距离,记作
,即
,请根据上述俼息解决以下几个问题:
(1)求函数
的最小值,并指出函数取到最小值时
的取值范围;
(2)①求有序数组
、
、
、
的波动距离
;
②求证:若
、
、
、
且
,则
;题(注:该命题无需证明,需要时可直接使用).设两两不相等的四个实数
、
、
、
,求有序数组
、
、
、
的波动距离
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49506c61cf5c61605f1cf90a440348cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec475a4298eab592d6589aab8915276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef141315bf951ddcd300f0743a16897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7cfd590897d8d908066c781c63a812d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3b887215cd1514d3e2e79063729a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)①求有序数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7330e52932883877de428cfe91962b96.png)
②求证: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/7a876ecb804eb0553c246e5fcc40b708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effb89a4bffb74028211ecfe671b79d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46944e1594eec140cacd7b454342561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc0ce632fa217dc77f6c92afd311815.png)
您最近一年使用:0次
2022-08-22更新
|
417次组卷
|
7卷引用:上海市控江中学2021-2022学年高一上学期期中数学试题
上海市控江中学2021-2022学年高一上学期期中数学试题(已下线)专题02 等式与不等式(练习)-2上海市高桥中学2022-2023学年高一上学期期中数学试题(已下线)期中模拟预测卷03(测试范围:前三章)-2022-2023学年高一数学上学期期中期末考点大串讲(沪教版2020必修第一册)(已下线)上海高一上学期期中【压轴42题专练】(2)(已下线)第二章 等式与不等式(压轴题专练)-速记·巧练(沪教版2020必修第一册)上海市吴淞中学2023-2024学年高一上学期期中数学试题
名校
2 . 已知函数
.
(1)若函数
的解集为
,求函数
的解集;
(2)若
,
,
,试证明:对于任意
,有
;
(3)若
时,有
,求证:当
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d7ed6f4b0e08cd887d2fdc2a5e37e4.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd089f65fb0afc3e31275ca01bd158d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008da60eb4dd38b35c5799fd5f7e0e97.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c8cef5386fbe3367564f9ebbc811cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897f9f5f44fe210d22abe4cbe719847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de87cccecadfae19f11358010521f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a6bea084567e3055f0e58499398a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0950253f473515ab175867f8fc5b5a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a6bea084567e3055f0e58499398a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366839b25310cb3168d411b1d5f73b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a6bea084567e3055f0e58499398a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d781166b65da7a054727f5503591e984.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)若
,求
在点
处的切线方程;
(2)令
,判断
在
上极值点的个数,并加以证明;
(3)令
,定义数列
. 当
且
时,求证:对于任意的
,恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb46a163897842c1fe507d8fca253bc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa80a12751a326ffabe3115ff779983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0138235d884d203490107787ea2e2830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff61248b4e57f4f9f5b2d9ab74a82ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06b9066e5f16f7a4c2ccc88d48fbea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fee9e71a4c714607f4b7af44337c411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad94568bce23439be8ded967d870c98.png)
您最近一年使用:0次
12-13高一上·北京·期中
4 . 定义在
上的函数
,如果满足:对任意
,存在常数
,都有
成立,则称
是
上的有界函数,其中
称为函数
的上界.
(1)判断函数
是否是有界函数,请写出详细判断过程;
(2)试证明:设
,若
在
上分别以
为上界,求证:函数
在
上以
为上界;
(3)若函数
在
上是以
为上界的有界函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea232de27d21a2646fd4520ea0726bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ee2d6f5c82efb89f3ebe7857bbe19.png)
(2)试证明:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7bba058b2e191718d59debbe97a73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aae37cac299cbe3ccac181b2175287f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae0f8520349250a31be6d58542ef2d9.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a18264722215b39ab53a098fd18bded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
5 . 设函数
.
(1)当
时,解不等式
;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcdf060d4d385cb9a30d19d6e88e28d4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24904df8527b7bfc0b8c39ffec7adbe0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376a50211c8df09ec2762b996d5c33d5.png)
您最近一年使用:0次
名校
解题方法
6 . 对于空间向量
,定义
,其中
表示x,y,z这三个数的最大值.
(1)已知
,
.
①直接写出
和
(用含
的式子表示);
②当
,写出
的最小值及此时
的值;
(2)设
,
,求证:
;
(3)在空间直角坐标系
中,
,
,
,点Q是
内部的动点,直接写出
的最小值(无需解答过程).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b303ef66609858e8ab234b6dabccba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e382f70d741ee01c165391ce980155d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4461408813c1476a8a8073c83b8989.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23056c429159c0198f865ff11972d8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e17d2355419564f6d9737295412b58c.png)
①直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9873960d64934875139754efbdfe951d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af5f843689a63bc176c2d2171b6a1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53168695826b0a33a23067b76173c7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780ef5119f58f853ce9dd2b9176ffdde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778ae4468d857c229073875e0ee0ce31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6772fa3937b97d9ec3aec1ea2ea143b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95086cc97ef93f5166489b3bc47e1911.png)
(3)在空间直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b32ab04dd852329d5918b177c199eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee736aec4313d04a5921ed7e5800b3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d04a00e46c1ffb335f73506041c66dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084fc7655647b596d07e80269d086e5a.png)
您最近一年使用:0次
解题方法
7 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302cd6e850c45a8917edb18140d37f6e.png)
(1)当
时.解不等式
;
(2)记
表示实数
中的较大者.任意的
,是否有
恒成立?若是,请证明:否则,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb92bdb11a3d3f436891b4343b4d1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302cd6e850c45a8917edb18140d37f6e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558e11d700481dc414d5d073b4b88a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfe74dd3d0e67b768c83c41be7ab155.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03049a2f3be286f52c971144a37781c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee66828ed2d01defc1008d146d54728.png)
您最近一年使用:0次
8 . 根据三角不等式我们可以证明:
,当且仅当
,
,
时等号成立.若等式
对任意x,y,
都成立,则符合要求的有序数组
数量为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e63a54f1a49e7d84cb064ac80e13dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eacd0a48a993d1cd82054d55d80b4b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8d7c76b84ff78f9333046f71761b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba383b25120365f4778dc858489199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafeb20c434b2a9002a1f9700b5bee25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a89495c19be4f58ee3f60940f9765f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a57d1215099fab4a97db12b2fa8f14.png)
A.有且仅有6组 | B.有且仅有12组 |
C.大于12组,但为有限多组 | D.无穷多组 |
您最近一年使用:0次
解题方法
9 . 已知
是任意非零实数.
(1)运用定理“两个实数和的绝对值小于等于它们绝对值的和”证明:
,并指出等号成立的条件;
(2)求
的最小值;
(3)若不等式
恒成立,求实数x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(1)运用定理“两个实数和的绝对值小于等于它们绝对值的和”证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7d1b109311c3f4c63697f98e9000a1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac54056610e9b914091eb83ad5ab35f.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0c7ccef6a693f768a06da80e9872b1.png)
您最近一年使用:0次
解题方法
10 . 已知数列
中
,其前
项和记为
,且满足
.
(1)求数列
的通项公式;
(2)设无穷数列
,
,…
,…对任意自然数
和
,不等式
均成立,证明:数列
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f085575b5c456ae641143d2d430458b0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7121ac4377ec9bcd071cb259678ab071.png)
(2)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402b8223a5be456f2acb45f65648eb34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
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2023-03-16更新
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3卷引用:江苏省南京市中华、东外、镇江三校2022-2023学年高三下学期3月联考数学试题
江苏省南京市中华、东外、镇江三校2022-2023学年高三下学期3月联考数学试题广东省韶关市武江区广东北江实验学校2022-2023学年高二下学期第一次(3月)月考数学试题(已下线)第4章 数列 单元综合检测(重点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)