1 . 已知函数
.
(1)讨论函数
在
上的单调性;
(2)当
时,
①判断函数
的零点个数,并证明.
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea8ddadb910710765fb78ca1696c10b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c6b9fa72109ba69163a5c6b7874a2.png)
①判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1350cb142ba647b1a96ed5d7063665.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
.
(1)当
时,直接写出函数
的单调区间(不需证明);
(2)当
时,求
在区间
上的最大值和最小值;
(3)当
时,若函数
在
上既有最大值又有最小值,求证:
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edebc46619f44fc7db7a82b55754ca78.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fab11f38ab8593932082ec4d9c8c91f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a3a7a0d64b9c01ccecd21cc97beb80.png)
您最近一年使用:0次
名校
解题方法
3 . 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)试证明:设
,
,若
,
在
上分别以M,N为上界,求证:函数
在
上以
为上界.
(2)若函数
在
上是以3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/4fe7d5809da02c15a43a0e9a898b9086.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/a0a1c02c533c60949a994212c90fbeda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)试证明:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a891d21bb2c7a11304beaab5054074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfcc567b95a320abcb25509923cd001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae0f8520349250a31be6d58542ef2d9.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d866d4d7f9c7676657aa4ed4dfebd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.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
4 . 已知函数
,
.
(1)当
时,求证:
;
(2)当
时,
恒成立,求实数
的取值范围;
(3)已知
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b1868d9850b7103e1326eb001dfbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9100abe06c208f6742dc75861a33989.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2aa78c96db411c9e1e939ae16de78d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d062874efc06af87693c548b09fbc91.png)
您最近一年使用:0次
2023-11-30更新
|
428次组卷
|
3卷引用:江苏省镇江市扬中高级中学2024届高三上学期十月学情检测数学试题
名校
解题方法
5 . 已知
是定义在
上的奇函数,且
.
(1)求
和
的值;
(2)判断
在
上的单调性,并证明你的结论;
(3)求证:
的值域为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01ae79b7370ecef836c2be4b228db53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0ec616dbf64b0e1bfce4c84afad5b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
您最近一年使用:0次
名校
解题方法
6 . 已知数列
的前
项积为
,且
.
(1)求证:数列
是等差数列;
(2)证明:
.
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3406df6552d66166d04a3d22e2f86929.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a40442811c08c432ec613102e4502c0.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031efafb3886a33f3ac39fc85eab869d.png)
您最近一年使用:0次
2023-10-13更新
|
1988次组卷
|
4卷引用:江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题
江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期教学质量调研(一)数学试题江苏省连云港市部分学校2023-2024学年高三上学期10月第二次学情检测数学试题江苏省南京市江宁区东山高级中学三校联考2023-2024学年高三上学期期中调研考试数学试题
7 . 设
,函数
(e为常数,
).
(1)若
,求证:函数
为奇函数;
(2)若
.
①证明函数
的单调性;
②对任意
,都有
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f5d965c3a2e685e5723323b65fdf18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
①证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bb7883ea87e6275472dbe14ee62357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4788c7e09a775d68647c44a24d9f0c6.png)
您最近一年使用:0次
名校
解题方法
8 . 问题:已知
均为正实数,且
,求证:
.
证明:
,当且仅当
时,等号成立.学习上述解法并解决下列问题:
(1)若实数
满足
,试比较
和
的大小,并说明理由;
(2)求
的最小值,并求出使得
最小的
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1fcc8430f84c56f2dbd81e0c5bb6b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc07ff9c2cb23cfe630c7785ba7ed93b.png)
(1)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2edfccf9159bb4010669e938f788149b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09ffc1644c7029219b88232145abbdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e32a3a39e310fe224a979e0cafce49.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9447fa25fa5be609b960f77971610e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
9 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f912ee8b686b231b3e6ecbcf26250e.png)
(1)判断8,9,10是否属于集合
;
(2)已知集合
,证明:“
”的充分条件是“
”;但“
”不是“
”的必要条件:
(3)记集合
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f912ee8b686b231b3e6ecbcf26250e.png)
(1)判断8,9,10是否属于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765038d98aaa2b44be5bc14b53baf76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a5ab202f3250c69eb834f7399297f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0383768b4c98b3bc57d1abba6c381813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c458592ba2d5ddd559b8720438a8fe.png)
您最近一年使用:0次
名校
10 . 在平面直角坐标系xoy中,已知
,圆C:
与x轴交于O ,B.
(1)证明:在x轴上存在异于点A的定点
,使得对于圆C上任一点P,都有
为定值;
(2)点M为圆C上位于x轴上方的任一点,过(1)中的点
作垂直于x轴的直线l,直线OM与l交于点N,直线AN与直线MB交于点R,求证:点R在椭圆上运动.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6316e0e6da742e9b035d8f2cc91a4dd.png)
(1)证明:在x轴上存在异于点A的定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439e95540157803d4ac3cf61a49f50a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7383714dc2ac9fe164e26a4d1bbd0c.png)
(2)点M为圆C上位于x轴上方的任一点,过(1)中的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439e95540157803d4ac3cf61a49f50a8.png)
您最近一年使用:0次