名校
1 . 已知
.
(1)若
均为正数,证明:
.
(2)若
均为实数,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9c07f0aab98148ab7c89c5d5310f99.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a516fd9b81aa4ca3c81d041dbcff6dc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f51c52793b9aa03155f6595303fcb2.png)
您最近一年使用:0次
2023-10-19更新
|
142次组卷
|
2卷引用:四川省部分名校2023-2024学年高三上学期10月联考文科数学试题
2 . 在平面直角坐标系xOy中,将从点M出发沿纵、横方向到达点N的任一路径称为M到N的一条“L路径”.某地有三个新建的居民区,分别位于平面xOy内三点A(3,20)、B(14,0)、C(-10,0)处.现计划在x轴上方区域(包含x轴)内的某一点
处修建一个文化中心.
(1)写出点P到居民区A的“L路径”长度最小值的表达式(不要求证明);
(2)若以原点O为圆心,半径为1的圆的内部是保护区,“L路径”不能进入保护区,请确定点P的位置,使其到三个居民区的“L路径”长度值和最小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
(1)写出点P到居民区A的“L路径”长度最小值的表达式(不要求证明);
(2)若以原点O为圆心,半径为1的圆的内部是保护区,“L路径”不能进入保护区,请确定点P的位置,使其到三个居民区的“L路径”长度值和最小.
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)求不等式
的解集;
(2)设函数
的最小值为m,正数a,b,c满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb17ac09361f8aadef3f1a49232257d7.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cc25a7cf28ed096549fbae97fce40a.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4608bd040954b318466fbf8c99f609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ee7ffbb52ae9bc3248ac8358fc474b.png)
您最近一年使用:0次
2023-06-03更新
|
316次组卷
|
2卷引用:四川省成都市石室中学2023届高考适应性考试(二)理科数学试题
名校
解题方法
4 . 已知函数
,
.
(1)求函数
的最小值;
(2)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a483b28b0a51697e711e832a5ca3d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0bc6775d59e23a45d1c4357d5ffe228.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfcc567b95a320abcb25509923cd001.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76acc9d0f0f0f6befbb9d9a64c497d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef791a5215dfbde16dea9499dda72a53.png)
您最近一年使用:0次
2023-07-27更新
|
302次组卷
|
8卷引用:河南省商丘市等2地2023届高三三模数学(理)试题
23-24高二上·上海·课后作业
5 . 已知数列:
,
,
,…,
,…,设
为该数列的前
项和.计算
,
,
,
的值;根据计算的结果,猜想
(
为正整数)的表达式,并用数学归纳法加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ed98e34b84285163a8b1b45c6fe403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231fd0fbb933002c6a527dcc4f7186f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4a646b098601ebe77beadf1707deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548714be29a1ee51b484b68904543ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](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/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c1332cd528333b840601948c3eefa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
6 . 已知
、
、
都是正实数.
(1)求证:
;
(2)若
,求证:
.
![](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)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718baee4ebadc334bb21aa4898ee72b9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e4b197a779a73068930151f9bbc5c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c7104c76550301474c1f115958ef8a.png)
您最近一年使用:0次
名校
7 . 已知数列
的前
项和为
,且
,
.
(1)求数列
的通项公式;
(2)令
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/5170584604571b5e1afd5ece941e2e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be29d8f996c54183663d8a954166dc16.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb6b45ecc2d4141fb3c4a9bdd90054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc65fd8233d6c78d4f943ba863713c.png)
您最近一年使用:0次
2023-05-29更新
|
392次组卷
|
3卷引用:河北省唐山市第十中学2023届高三模拟数学试题
8 . 已知
.
(1)求不等式
的解集;
(2)若
的最小值为t,且实数a,b,c满足a(b+c)=t,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e9ee8fb169f54d0e3f401391efc0a6.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a33c8e64e3650140754b22a5596c6c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e8f45b00fed345a17aa57d6f9c7d9b8.png)
您最近一年使用:0次
2023-05-29更新
|
192次组卷
|
2卷引用:甘肃省定西市2023届高三下学期高考模拟考试文科数学试题
名校
解题方法
9 . 设函数
.
(1)当
时,求不等式
的解集;
(2)若
,
,
的最小值为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9928170ed70b7185a19b8b123b749955.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe680e7333cc33b5a799f499fff7c56.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf113499ea01e353379f293cfe79bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f952af1c30f32ee1c94333c16c003d3.png)
您最近一年使用:0次
2023-09-02更新
|
333次组卷
|
5卷引用:百师联盟(陕西省西安市部分学校)2024届高三上学期开学摸底联考理科数学试题(全国卷)
解题方法
10 . 设
,
,
均为正数,且
.证明:
(1)
;
(2)
.
![](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/de51c58cf8ae8b3f1446f5b6959e6f4a.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472780d66203bcc0b887c0b71941a5f3.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd06cc261d1ac490c1a702ad40931ccb.png)
您最近一年使用:0次
2023-09-06更新
|
272次组卷
|
4卷引用:江西省景德镇市2023届高三第三次质量检测理科数学试题
江西省景德镇市2023届高三第三次质量检测理科数学试题江西省景德镇市2023届高三第三次质量检测文科数学试题(已下线)考点7 基本不等式及其应用 --2024届高考数学考点总动员【讲】四川省成都市教育科学研究院附属中学2023-2024学年高三下学期4月综合测试数学(理科)试题