1 . 已知数列
满足
(
),且
.给出下列四个结论:
①
;
②
;
③
,当
时,
;
④
,
,当
时,
.
其中所有正确结论的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6601304f30b786d0dbc35a3ed07c084a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a95f98737192b55293edb36307ab27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1381f0937c6052ce088e0eaee7df4880.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245874c7590632dbfe943e38b645062e.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279efbf5a2768db8064621fe997d5fe2.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf0d92d11ac8d916de7858529b6b56fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eae51f0310b87cde2e206643e9d25a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6e1ad3cc94c60786612117ca27689b.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b133fe372537a59d8307d805dede37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f616248ea756e33bc9ab439feb199d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f7c8e642529926f31c90ab0ccee9cca.png)
其中所有正确结论的个数为( )
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
2 . 设函数
的极值点为
,且
,则
可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42cd5920c27db7257886fece226833b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28319174975bd87487e49585c65a79a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
3 . 在空间直角坐标系中,已知
,若点
在平面
内,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5767f884a5eedfbb4d850bee9adc8311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dcd81f83699ed945f5bb0d534ab09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c34b0d3df28bc275ca31c02d74865e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
4 . 已知函数
的值域为
,且关于x的不等式
的解集为
.则有如下结论:
①
;
②函数
图像与直线
的两个交点之间的距离等于6;
③若关于x的不等式
的解集为
,则
;
④
的值与
的大小有关.
其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63aaa178677e179fd17fb87877ccb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8acd04f62bbce37e384254b337d24620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a2d1f0df2c0a8fae29b0117bdd7ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba18457e072ac06b381c3f73c90ba9b3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54dd96cd4dd5d6d7dd660c00e443bbaa.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008e80e33ba7b182a6d82862fadc8009.png)
③若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585080b717e145c729881a42b4dd533b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88cadcbd692b0b44dac4bc2bf2bf2759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8503e2b6f81cb4c978a21a71ac5ef840.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
其中所有正确结论的序号是
您最近一年使用:0次
5 . 设数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f1e3715064947e94c0b25f7940b93c.png)
,如果
,且
,
,对于
,
,使
成立,则称数列
为
数列.
(1)分别判断数列
和数列
是否是
数列,并说明理由;
(2)若数列
是
数列,且
,求
的最小值;
(3)若数列
是
数列,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f1e3715064947e94c0b25f7940b93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e815a51d2602a545588c5a1d0fdaebdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b8f5ba01a66cbfd850275b11ecca76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602744ef8bcccfdd9f00bd275e2ece2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85719767bc8b764fcde16731c1ea45c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2ebecf4a0f024b9fcf300196c52493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300b8b745c8f8b5e095cf7dc81d0ecf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152094b2404f8f0f27f56ed43d9eee5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)分别判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63541441d26f277d9ed7816c089c6b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f38ef6812c86a02d00dd485785d7f926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f73eec2bbbfa166f874c39d05accb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae270cb776026e11a9ca10f4d5098da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解题方法
6 . 对于非空有限整数集X,
,定义
,对
现有两个非空有限整数集A,B,已知
且
.
(1)当
时求集合B;
(2)证明:
;
(3)当
且
时,任取
构造函数
问:当a,b取何值时,
的最小值最小?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9451ce4fed053674ea20d5b455b783d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb70a272d3abd0bb156e332e75dc36b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cd3b18a04c9a72a0bf7791bdf56a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9a194c0b9152e11aabc059c8483b93.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba387b457949fde336790c9d05c4f1c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15d281a85375fcf633d2cd86e294028.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eeee50bc500aad281fbb28d465db5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4a0f5fcd7882200fa25b6ee5143f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c41c277675b413bbff28387082c9785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbad171aea431ed7347bcdc7fbef54d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
7 . 在
中,
.
(1)设点
为边
靠近点
的三等分点,
,求
的值;
(2)设点
是线段
的
等分点,其中
,
.
(i)当
时,求
的值;(用含
的式子表示)
(ii)求
的值.(用含
的式子表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a090959162421593f75617a7c8bfcb7.png)
(1)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3235a1c37276b3af572302da1972e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759ded5c4d3bc2ab67bf37a6c376e712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce99690471cb1d86794a4f81017c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed44d30460ef5e6e6baf7201694d0b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804609594d0ee7a777290f97eaf8a76e.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42bb5c0976fbd0ac5eda8217470d894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298e3fa774712113dc508a6abd5e99da.png)
您最近一年使用:0次
解题方法
8 . 某校举办乒乓球团体比赛,该比赛采用
场
胜制,每场均为单打,若某队先胜
场,则比赛结束,要求每队派
名运动员参赛,每名参赛运动员在团体赛中至多参加
场比赛,前
场比赛每名运动员各出场
次,若
场不能决出胜负,则由第
位或第
位出场的运动员参加后续的比赛.
(1)若某队从
名运动员中选
名参加此团体赛,求该队前
场比赛有几种出场情况;
(2)已知某队派甲、乙、丙这
名运动员参加此团体赛.
①若
场决出胜负,列出该队所有可能出场情况;
②若
场或
场决出胜负,求该队共有几种出场情况.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)若某队从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(2)已知某队派甲、乙、丙这
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
您最近一年使用:0次
9 . 某高台跳水运动员在运动过程中的重心相对于水面的高度
(单位:
)与跳起后的时间
(单位:
)存在函数关系
,
的图象如图所示,已知曲线
在
处的切线
平行于
轴,根据图象,给出下列四个结论:
①在
时高度
关于时间
的瞬时变化率为
;
②曲线
在
附近比在
附近下降得慢;
③曲线
在
附近比在
附近上升得快;
④设在
和
时该运动员的瞬时速度分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814f55724f7ee57bd395eb3b95393c68.png)
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602d1b2e4f1ba4784c0030ad379dc914.png)
,则
.
其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65502a7ea4d1ce6d6d8c720845c73e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7a1500e8c55a333fcb40d749ed8088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b36da3b4cc0a0cc408ef324b04c9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b36da3b4cc0a0cc408ef324b04c9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82120861c1c4f7cc1a7a3f169f082a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/22/6b459c44-4032-466a-8702-e1539783ff8a.png?resizew=119)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82120861c1c4f7cc1a7a3f169f082a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b36da3b4cc0a0cc408ef324b04c9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b1e1e25b1b8633d360f0922605ff2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719a627af6b0de19823983b65637cd92.png)
③曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b36da3b4cc0a0cc408ef324b04c9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3628e2583517dddb1148b929642bfdfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bade62c061fc94c754b6a06790ea6a.png)
④设在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b1e1e25b1b8633d360f0922605ff2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bade62c061fc94c754b6a06790ea6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814f55724f7ee57bd395eb3b95393c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abb53d5e68cfdbe0a24471a3a2ac6aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602d1b2e4f1ba4784c0030ad379dc914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abb53d5e68cfdbe0a24471a3a2ac6aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a3645e6aa2d5450d539efa8cf97d66.png)
其中所有正确结论的序号是
您最近一年使用:0次
10 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938b2ae7ed25336d9056cb8e23fb0022.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938b2ae7ed25336d9056cb8e23fb0022.png)
您最近一年使用:0次