名校
解题方法
1 . 已知集合
,其中
且
,若对任意的
,都有
,则称集合
具有性质
.
(1)集合
具有性质
,求
的最小值;
(2)已知
具有性质
,求证:
;
(3)已知
具有性质
,求集合
中元素个数的最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd70e76e1780a839fcbff88cd71c2fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac10f1abfec87624afd60003af4eaddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5269913f25626c9615a0851c59c20d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2aa8c7598aa438022d7ff0db9a3de7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e86a882ef57f44f0ad22836079afe1.png)
(1)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f65336695f80a1fe2a7838a3ae17c51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353433462b58fe2eba495f2589b81380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2be2cef8c6e56b2381acca7f3c0cf4.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353433462b58fe2eba495f2589b81380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2023-10-12更新
|
1774次组卷
|
5卷引用:湖南省长沙市第一中学2024届高三数学新改革适应性训练一(九省联考题型)
名校
解题方法
2 . 已知
,且0为
的一个极值点.
(1)求实数
的值;
(2)证明:①函数
在区间
上存在唯一零点;
②
,其中
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aaf8922b1b6e2a4366bbd142ad447b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd531902180b2316d92936e1d1c5219d.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f759e5772fb6972efa066f9d0ea363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
您最近一年使用:0次
2023-03-24更新
|
3416次组卷
|
9卷引用:山东省烟台市2023届高三一模数学试题
山东省烟台市2023届高三一模数学试题山东省德州市2023届高考一模数学试题江苏省南京市临江高级中学2023届高三下学期二模拉练数学试题广东省深圳市福田区红岭中学2023届高三第五次统一考数学试题专题07导数及其应用(解答题)湖北省武汉市武昌区2022-2023学年高二下学期期末数学试题四川省宜宾市叙州区第一中学校2023-2024学年高三上学期10月月考数学(理)试题(已下线)重难点突破09 函数零点问题的综合应用(八大题型)(已下线)第九章 导数与三角函数的联袂 专题四 利用导数证明含三角函数的不等式 微点1 利用导数证明含三角函数的不等式(一)
名校
3 . 设A是由
个实数组成的2行n列的矩阵,满足:每个数的绝对值不大于1,且所有数的和为零.记
为所有这样的矩阵构成的集合.记
为A的第一行各数之和,
为A的第二行各数之和,
为A的第i列各数之和
.记
为
、
、
、
、…、
中的最小值.
(1)若矩阵
,求
;
(2)对所有的矩阵
,求
的最大值;
(3)给定
,对所有的矩阵
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9dbdea32a8f7b9fd4c8982eef6dea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15fc1924d5c54d4f2824f6accc1238b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b68fd1ac04715b65105c0cf40aa84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a2629e9e3b3fcf0c0bdd49c76b95cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a954ad5b391cfc9440f0444cbbfa889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f128d1af43d66e8048295604ef89046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ba5c6f604da3afa5c18d368fb12060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30773f6541752c8d133db5662ccee553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d137142642163af066957fe19218ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260bcd4709ef67852ef6e2de9841e75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af2bb6f225862039961601a07e7d7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9624751c77e7b93a0166bbdc302cdc6.png)
(1)若矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63da318b4a47902b2a7979230e997e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ba5c6f604da3afa5c18d368fb12060.png)
(2)对所有的矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b432f6219d00bd0b2bc483401b9dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ba5c6f604da3afa5c18d368fb12060.png)
(3)给定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18969d9db906a0f002b762113ecf077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01aef0b7f72cd41492cade2785ccc6cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ba5c6f604da3afa5c18d368fb12060.png)
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2022-05-28更新
|
452次组卷
|
3卷引用:上海市2022届高三高考冲刺卷六数学试题
名校
4 . 英国数学家泰勒发现了如下公式:
,其中
,此公式有广泛的用途,例如利用公式得到一些不等式:当
时,
,
.
(1)证明:当
时,
;
(2)设
,若区间
满足当
定义域为
时,值域也为
,则称为
的“和谐区间”.
(i)
时,
是否存在“和谐区间”?若存在,求出
的所有“和谐区间”,若不存在,请说明理由;
(ii)
时,
是否存在“和谐区间”?若存在,求出
的所有“和谐区间”,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c8d6b7790572ee26dac80e0c7fe648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c875ad8fafc41d5c82baf23bb5e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee051a4daa81ab32ef9c153ecf90e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305249d05ecc23ee86ae55f7bf8566e1.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f80e45170c557aed6187a6bd11177d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f95d2a9ba5f50d14cdee5ecda28461a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0db2c49919467a2e14540f2aabd05cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2022-02-22更新
|
1523次组卷
|
5卷引用:2024届高三新改革适应性模拟训练数学试卷七(九省联考题型)
2024届高三新改革适应性模拟训练数学试卷七(九省联考题型)福建省福州第一中学2021-2022学年高一上学期期末考试数学试题(已下线)专题09 导数压轴解答题(证明类)-1辽宁省实验中学2023-2024学年高一下学期第一次月考数学试题(已下线)专题11 利用泰勒展开式证明不等式【练】
2022高三·全国·专题练习
5 . 数列
满足
,
(1)求
的值;
(2)求数列
前
项和
;
(3)令
,
,证明:数列
的前
项和
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d1f5ed8701852d94f1f2bdca27214c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)求数列
![](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)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aaee408bdec05bbdfcd4b841a331e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/170a008facca7caf11cb80765d801399.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/b3e205f31d50e1edbe83af4e088b9533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c5f845194ad77dfb97a15ba4ebfca6.png)
您最近一年使用:0次
6 . 已知正实数列
满足
,当
时,记集合
,且集合
中的最大元素为
.
(1)若
,求数列
的通项公式;
(2)记数列前n项和为
,证明:存在正实数
,对于任意的正实数
与整数n>1,都有
.注:对于任意实数a,b,定义
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10b321b66145a2ed6b30d30b62fd8acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7afe76f3b456f040fef0d89e0f2996f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191a66915ee31c2c7e0a0ace99df4586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列前n项和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bc85af36f64be115dd7c5d88fac6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c0e8564359b3f5bd268ab136314f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478e75f2162f25b93d4c337e2829fc05.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
.
(1)证明:函数
仅有一个极值点;
(2)若不等式
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079a2efb85b43f76fb82668aef36e58c.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a2f37acd5b240fade8f5254d785a5a.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
8 . 已知
为定义在
上的奇函数,且当
时,
取最大值为1.
(1)写出
的解析式.
(2)若
,
,求证
(ⅰ)
;
(ⅱ)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/886d2d7da83c74826a757bffc10183a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195fc747e2fc50cb6df2c844d51e4d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85a01f2a5b003d545aabd58658f430.png)
(ⅰ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/935d2dec00d5584f549d9135df57d4ff.png)
(ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89c48120fe5326e9b1c718d948816d0.png)
您最近一年使用:0次
解题方法
9 . 数列
满足
且
.
(1)证明:
;
(2)证明:
.
![](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/56d7dcf478da9ade18ef22fb21555e01.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88df297a5b7b11083b3e87828c9b97d.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86abd8ce35e5088b91065d206eeb3cf.png)
您最近一年使用:0次
解题方法
10 . 已知数列
中,
,
(n
).
(1)分别比较下列每组中两数的大小:①
和
;②
和
;
(2)当n≥3时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ecf69901899bba130968c7a091790d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473292ef3cbf11a8118cd3afd4512ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010799cc7efae681c6de874fb6e3d053.png)
(1)分别比较下列每组中两数的大小:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bec36481482bb3d094cabbf87c61095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a950be0540f6d8b7f8f9a81d6736d7.png)
(2)当n≥3时,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d8b4c76d90408154490e94e254d33d.png)
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