1 . 已知A,B,C,D,E是空间五个不同的点,若点E在直线BC上,求证:“AC与BD是异面直线”是“AD与BE是异面直线”的充分必要条件.
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2 . 已知函数
,
是自然对数的底数,
,
.
(1)求
的单调区间;
(2)记
:
有两个零点;
:
.求证:
是
的充要条件.要求:先证充分性,再证必要性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656ed69a6c78d2b66f47d08f5913796d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8166e75ef9ebda44ee6c4f23209acca3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81d60b0525a338954e9a4fde52aa643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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2022-03-14更新
|
719次组卷
|
3卷引用:云南省2022届第一次高中毕业生复习统一检测数学(理)试题
名校
解题方法
3 . 若实数数列
满足
,则称数列
为
数列.
(1)请写出一个5项的
数列
,满足
,且各项和大于零;
(2)如果一个
数列
满足:存在正整数
使得
组成首项为1,公比为
的等比数列,求
的最小值;
(3)已知
为
数列,求证:
为
数列且
为
数列”的充要条件是“
是单调数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4cd04c0ff2844105bc4486b5a900ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4da8d81786807287d2101b3fd4699a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)请写出一个5项的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2750dc9a0ad9b327da7a92f524cb90f.png)
(2)如果一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b158dfcb45253a4421f2742ac81cd08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502266dd0d7fc16762e2eea895fb19a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb2eadbfbedd46b5ea213da4d950b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1b84c660a03ac3c99d2f129d6b3bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac6d57306a71e64529ca4b8f2edeb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2a75b4bd3940642d93bda6a99f1b87.png)
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4 . 数列
:
满足
,称
为数列
的指数和.
(1)若
,求
所有可能的取值;
(2)求证:
的充分必要条件是
;
(3)若
,求
的所有可能取值之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a197918d989143a09028897f3a8a773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5e4185d2217f1ae68ad8f62586374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68424226b0d40c09b990f0eca3ff8db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155c5f3a5c55e0c95191c5a893f63062.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0c2b029e1c1d7963c043ca041d82de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7bdaaf8b0adf10bf2ef6c1255b1dc.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047ec104459998bd3cbd339b29eaffc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00136ab4fd69ba9c28b47cd38442dc3a.png)
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名校
5 . 若有穷数列
且
满足
,则称
为M数列.
(1)判断下列数列是否为M数列,并说明理由;
① 1,2,4,3.
② 4,2,8,1.
(2)已知M数列
中各项互不相同. 令
,求证:数列
是等差数列的充分必要条件是数列
是常数列;
(3)已知M数列
是
且
个连续正整数
的一个排列.若
,求
的所有取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc976debe187e9d6162766e99d5beba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04aa91499257c87478609c5987cd60b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8bafccc3590fb8dcce1b717d372d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)判断下列数列是否为M数列,并说明理由;
① 1,2,4,3.
② 4,2,8,1.
(2)已知M数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5cbea2c988187a8508c96e4bc7fe7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
(3)已知M数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4caa2af970b457b1e7ee17132c860b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae12372b9477473e5541f879e13ccc28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6c18eaf2f4309e6a014a1100c2380f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8a0c49920d0d91486915755f7ff6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2022-01-16更新
|
918次组卷
|
4卷引用:北京市丰台区2022届高三上学期数学期末练习试题
北京市丰台区2022届高三上学期数学期末练习试题北京市首都师范大学附属中学2022届高三下学期开学检测数学试题北京市东直门中学2023届高三上学期期中考试数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大题型)(练习)
6 . 记实数
,
中的较大者为
,例如
,
,对于无穷数列
,记
,若对于任意的
,均有
,则称数列
为“趋势递减数列”.
(1)已知数列
的通项公式分别为
,
,判断数列
是否为“趋势递减数列”,并说明理由;
(2)已知首项为
公比为
的等比数列
是“趋势递减数列”,求
的取值范围;
(3)若数列
满足
,
为正实数,且
,求证:
为“趋势递减数列”的充要条件为
的项中没有
.
![](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/f2ff5bb0fe6702b7d57492e82dabc3e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c633c4d52075cb924e6e311d121b829c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c218d14281906e19cfadd586d1f23a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175faa34d8fc79072c97fe2665a0b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d61cf95a6aa06636278be1069888b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e55241a2e145d54849129b8ffd20f.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d789500bdc2144b75c29e4fd28374ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492d0ca5ecaafcb665967f08e1af87aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62f5b4e6d475e233cc30238667b4bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b7716b4e1271cc80c63a38e56446ad.png)
(2)已知首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c84bc401cb7e5a4b0bc1157e5dbd194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4077480b54eb99a86b2bc4fb165b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21098099da24af151a1337ec0754bcd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4077480b54eb99a86b2bc4fb165b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4077480b54eb99a86b2bc4fb165b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
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7 . 已知a、b、c为
的三边长,集合
,
.
(1)若
,求
;
(2)求
的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f230edcaa4a6bc34672332588dfd0c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee85c6468ee8f23539d77901becc8f7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe167384913cab85ad3f56f697588a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f1ba0a1129741502600e47bf058c98.png)
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2022高三·上海·专题练习
8 . 已知无穷数列
的首项为
其前n项和为
且
(
),其中
为常数且
.
(1)设
,求数列
的通项公式,并求
的值;
(2)设
,
,是否存在正整数k使得数列
中的项
成立?若存在,求出满足条件k的所有值;若不存在,请说明理由.
(3)求证:数列
中不同的两项之和仍为此数列中的某一项的充要条件为存在整数m且
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4b9e475158c0c9eef9dd015342221c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7a9511c3d1b6d41d17df1559919880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fade3b62af2d51880b021a075dcd551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://img.xkw.com/dksih/QBM/2021/10/26/2837748827766784/2838709742600192/STEM/7fc32bc6ec324f02b776a2efc3a3b665.png?resizew=13)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7335c79ec0592fc36288f5135e86c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8212a513bceafbdb6e7e617a29079c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c1344592c925b273f2cb9b9e47ebbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6760775a38ed18ab8f346346e25de2ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636f37adeddc68d0830ecd7d1c61ff8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98b2a1269d8cb234c7cc9d49e75196b.png)
(3)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87a9ef1f87936695fb681df932efd10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54680219b440350ffc5f1f43b3b78e0.png)
您最近一年使用:0次
名校
9 . 设
是公比为
的等比数列,若
中任意两项之积仍是该数列中的项,那么称
是封闭数列.
(1)若
,
,判断
是否为封闭数列,并说明理由;
(2)证明
为封闭数列的充要条件是:存在整数
,使
;
(3)记
是数列
的前
项之积,
,若首项
为正整数,公比为
,试问:是否存在这样的封闭数列
,使
,若存在,求
的通项公式;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fde3541708c770e48a06c28f9a3434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f45f5bc7c648c0e8924b4fa7b1ad08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87a9ef1f87936695fb681df932efd10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a265e46cb43d734e304e867683fef530.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb10d4ac17d6a6aa8b6f3df88522143.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/00c854cbba7a54e40677b6d7ce398e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e411db1a07e11f02eae9f8352d74d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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10 . 已知函数
.
(1)若函数
的定义域为R,求a的取值范围.
(2)求关于x的不等式
有正数解的充要条件(a满足的条件).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6518f8835270bd9608d7a4a9676b6682.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35316d622731468e6d9416ccd3151d7b.png)
(2)求关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
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