名校
解题方法
1 . 已知函数
.
(1)若函数
在
上是增函数,求正实数
的取值范围;
(2)当
时,求函数
在
上的最大值和最小值;
(3)当
时,对任意的正整数
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac15cac5b3af917dfc947318d968121.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)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/b448fe164c2c2931805e3b3847dcdd75.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5e5ba3a62f61ff22319d3decfdc48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742254b2bd8972eb9d52341ed2ef98f7.png)
您最近一年使用:0次
名校
2 . 若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01cdb4a84f02a75eb447b54f73f7df6.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8302775bd5e16145edfaaf6e95490e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01cdb4a84f02a75eb447b54f73f7df6.png)
您最近一年使用:0次
3 . 已知数列
满足
.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1688ed39612b6f3da8e0a4d7a50547a5.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a2a5d37d6a6eb6074550cb80ab155f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
名校
解题方法
4 . 有4人到甲、乙、丙三所学校去应聘,若每人恰被一所学校录用,每所学校至少录用其中1人,则所有不同的录用情况种数为__________ .(用数字作答)
您最近一年使用:0次
名校
5 . 已知正项数列
是递增的等差数列,
是公比为
的等比数列,且满足
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe0f4e8a80a2840c0f6929a8a6351b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0426eb784f9c387f6a0d2e7e21a11118.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
6 . 已知在等差数列
中,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f110d93bbbcb9e2f3abc60b7388309a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
A.3 | B.4 | C.5 | D.6 |
您最近一年使用:0次
名校
7 . 已知函数
,
是
的极值点.
(1)求实数
的值及函数
的单调区间;
(2)求
在
上的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416fafac369b3d1accfe1892ced99b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d7454ac738bf964b74deca7794e8df.png)
您最近一年使用:0次
名校
8 . 数列
满足:
,
且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d211c5a622d0be3b39931d814f9a683.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c963447bb8637bd5ce56b372555d329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6fbb34d35909ad228ef3123772c752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d211c5a622d0be3b39931d814f9a683.png)
您最近一年使用:0次
名校
解题方法
9 . 在正方形
中,点
,
分别是
,
的中点,则
=______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc81279c0024f1fb93d0eb2f811237ed.png)
您最近一年使用:0次
名校
10 . 对于函数
,若存在非零常数
,使得对任意的
,都有
成立,我们称函数
为“
函数”;对于函数
,若存在非零常数
,使得对任意的
,都有
成立,我们称函数
为“严格
函数”.
(1)若函数
,是“
函数”,求k的取值范围;
(2)对于定义域为
的函数
对任意的正实数
,
均是“严格
函数”,若
,求实数a的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b232cd355157f66f1f0c6b02a03c5e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea657922fae2c5875761f5c3ce4b6ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b232cd355157f66f1f0c6b02a03c5e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0741d41839ae1ee0914daad3c00f9243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951d13b1ddae2726049144b5b21c4b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(2)对于定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb676cb3d49edadeaf419b3038591c4.png)
您最近一年使用:0次