2024·江苏连云港·模拟预测
名校
解题方法
1 . 已知函数
(
,且
).
(1)若
,求函数
的最小值;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b02f7eb75c4920528be28f08541c276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b06387179d53c1e474fcfcb408b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467ebe7ef361ddf4cfab29baeefc66aa.png)
您最近一年使用:0次
23-24高三上·北京西城·期末
名校
解题方法
2 . 给定正整数
,已知项数为
且无重复项的数对序列
:
满足如下三个性质:①
,且
;②
;③
与
不同时在数对序列
中.
(1)当
,
时,写出所有满足
的数对序列
;
(2)当
时,证明:
;
(3)当
为奇数时,记
的最大值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2477167a02872167b2a3760f09d6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc25d4213ca2eadce49e6d8ba805e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b730e2023809495f2bd7fbf48f07a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca986e62ec3a6e50e4e2cad639aa9201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd869b784314b8278f5d144b2d3a9fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302391681aa37ac20d6f533dbae9e137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a215612787e43d28bfebc840c3903b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241d587c2e6f2f109a4e41b79f1c800f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926c16dd072c9ff8a560b003cfb47053.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4546b12ff89d1599427da82294afc09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4546b12ff89d1599427da82294afc09b.png)
您最近一年使用:0次
2024-01-19更新
|
2113次组卷
|
7卷引用:江苏省连云港高级中学2023-2024学年高二下学期第一次月考数学试卷
江苏省连云港高级中学2023-2024学年高二下学期第一次月考数学试卷(已下线)北京市西城区2024届高三上学期期末数学试题北京市西城区2024届高三上学期期末数学试题(已下线)高三数学开学摸底考 (北京专用)2024年普通高等学校招生全国统一考试数学冲刺卷二(九省联考题型)江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(四)广东省深圳市外国语学校2024届高三教学情况测试(一)数学试题
名校
3 . 设
,函数
.
(1)求证:
存在唯一零点
;
(2)在(1)的结论下,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b3a457ebfd6e86ae30219f4bc45a44.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)在(1)的结论下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fcbdf2921f8918880ed58166039993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0277dc483305886d6a1ce0833634713f.png)
您最近一年使用:0次
2022-12-03更新
|
614次组卷
|
4卷引用:江苏省连云港市赣榆高级中学2022-2023学年高三上学期12月学情检测数学试题
江苏省连云港市赣榆高级中学2022-2023学年高三上学期12月学情检测数学试题江苏省苏州八校联盟2022-2023学年高三上学期第二次适应性检测数学试题(已下线)5.3 导数在研究函数中的应用(练习)-高二数学同步精品课堂(苏教版2019选择性必修第一册)广东省汕头市潮阳实验学校2024届高三上学期元月阶段测试数学试题
名校
4 . 已知函数
.
(1)若
,是否存在a
,使
为偶函数,如果存在,请举例并证明,如果不存在,请说明理由;
(2)若
,判断
在
上的单调性,并用定义证明;
(3)已知
,存在
,对任意
,都有
成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e73422d2197a5a71769436381b7229.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c1fd1da3a9e6465bb3b66894120b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5500ad00466c3f2ff8ba691f2653e6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd456469aaa6dafb1e275183d217435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4438620ff101b83aef035104db1a6e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a1f815b0e0b6516b684a93e1850667.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e424a9e6b2505aad5eb944b00f5222bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76d0c6032c22c5d435968f414e506cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9956260c9412f340df7addda6707f3.png)
您最近一年使用:0次
2022-03-14更新
|
1233次组卷
|
3卷引用:江苏省连云港市灌南高级中学2022-2023学年高一提优班上学期期末数学试题
5 . 1.在平面直角坐标系xOy中,已知点
,点M满足
.记M的轨迹为C.
(1)求C的方程;
(2)点T在直线x=4上,过T的两条直线分别交C于A,B两点和P,Q两点,且|TA|·|TB|=|TP|·|TQ|,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10f5be271d5e18347e2792d348e5411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b549d39d7e273f5ba461f1d508b20dc.png)
(1)求C的方程;
(2)点T在直线x=4上,过T的两条直线分别交C于A,B两点和P,Q两点,且|TA|·|TB|=|TP|·|TQ|,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18cad6ab2dd26fb28da19be0f8358265.png)
您最近一年使用:0次
6 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe71df7eac5e44cba50d2f2a8c26ee51.png)
.
(1)证明:
;
(2)若方程
有两个不等实根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40ab948e5df77b57035f6b2717700858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe71df7eac5e44cba50d2f2a8c26ee51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3e3bcd67cf1a355986c6e3132470c7.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26449970128fa51a694ed908d84a994c.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abf0cdd5f11934878e479ef1abfea64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021-05-29更新
|
591次组卷
|
2卷引用:江苏省连云港市2021届高三下学期3.5模数学试题
7 . 已知数列
各项均为正数,
是数列
的前
项的和,对任意的
,都有
,数列
各项都是正整数,
,
,且数列
,
,
,…,
是等比数列.
(1)求
,
;
(2)证明:数列
是等差数列;
(3)求满足
的最小正整数n.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](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/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786dce700f614ef34e9cf42ddee9022e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab7d59ce066c8f0b346719003f8e28f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fd0f362d2c0560c6207c5634d3732a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec342b0a17f898d4e70f75f04b50fdb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb16f890ca919e5a116f3056d7b04f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f814b537650d7b2ab376a1dbca25d84d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3be18ca37723026c986af0d3e9968f.png)
您最近一年使用:0次
2020-10-11更新
|
790次组卷
|
4卷引用:江苏省连云港市东海县第二中学2020-2021学年高二上学期9月月考数学试题
8 . 如图,已知点
是椭圆
上的任意一点,直线
与椭圆交于
,
两点,直线
,
的斜率都存在.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/d6cfe5eb-5842-4726-8b75-786d7252f716.png?resizew=183)
(1)若直线
过原点,求证:
为定值;
(2)若直线
不过原点,且
,试探究
是否为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/d6cfe5eb-5842-4726-8b75-786d7252f716.png?resizew=183)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5702feefd657c2987d3fe5d9884f2d0.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ec52d0ca60bf71503a639b95b6ccab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5702feefd657c2987d3fe5d9884f2d0.png)
您最近一年使用:0次
9 . 已知
,
.
(1)求
的值;
(2)试猜想
的表达式(用一个组合数表示),并证明你的猜想.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ff73d6ea82e5a173f6a41108282e8a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10aa6134eeec0fc1d2b8f140fb894060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91c6ad898dcf2d229d8c8b264a263188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347bb4ffedcbea2f4c16d047a138d75.png)
(2)试猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
您最近一年使用:0次
2018-01-18更新
|
919次组卷
|
5卷引用:江苏省连云港市锦屏高级中学2017-2018学年高二下学期期中数学(理)试题
江苏省连云港市锦屏高级中学2017-2018学年高二下学期期中数学(理)试题南京市、盐城市2018届高三年级第一次模拟考试数学(理)试题(已下线)二轮复习测试专项 【新课标版理科数学】专题七 排列组合二项式定理(已下线)2018年高考二轮复习测试专项【苏教版】专题九 算法 推理与证明 复数2020届江苏省南通市西亭高级中学高三上学期第一次校内模拟测试数学(理)试题
名校
10 . 已知函数
且
.
(1)设
,讨论
的单调性;
(2)若
且
存在三个零点
.
1)求实数
的取值范围;
2)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f26cc366989b203c047e13db8de54d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47352a6ebe48c4d92e32275a4f32dc4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7803d86067299198e6d14b0c83947f58.png)
您最近一年使用:0次
2022-12-21更新
|
5085次组卷
|
10卷引用:江苏省连云港市赣榆智贤中学2023-2024学年高三上学期9月模拟考试数学试题
江苏省连云港市赣榆智贤中学2023-2024学年高三上学期9月模拟考试数学试题广东省广州市2023届高三一模数学试题河北省衡水市第十三中学2023届高三上学期1月月考数学试题四川省南充高级中学2023届高考模拟检测(七)理科数学试题江苏省南通市海安高级中学2023届高三下学期一模数学试题江苏省盐城市亭湖高级中学2022-2023学年高三上学期期末数学试题天津市蓟州区第一中学2024届高三上学期第三次学情调研数学试题辽宁省辽东十一所重点高中联合教研体2024届高三高考适应性考试模拟数学试题(已下线)(新高考新结构)2024年高考数学模拟卷(三)(已下线)专题3 导数与函数的零点(方程的根)【练】