1 . 在等比数列
中,
,前
项和为
是
和
的等差中项.
(1)求
的通项公式;
(2)设
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdf53108bee755f5aa9a34ea4d163e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c246a6f84b5345f6786d41e45f192115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ff66d163e1c542742c3ef4b26f38b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2 . 若
满足约束条件
,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce2dce0f3192cda4d14dc5d12adacb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5145885aab26b915ebc9cee8d9ae33b9.png)
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3 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc6092100600070328042adaf76aad3.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9b0c44251cf0ff461bf74f8fcef224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc6092100600070328042adaf76aad3.png)
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2022-05-31更新
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2卷引用:吉林省松原市长岭县第三中学2020-2021学年高三下学期开学摸底检测数学试题
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4 . 已知
为R上的奇函数,且图象关于点
对称,当
时
,则函数
在区间
上的零点个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58427d5aa7deeca47c8789241913f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc04588f4a056855c9a3697554259437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f3c0210ddd6c878dbb2afb9bff7ff2.png)
A.1010 | B.1011 | C.4036 | D.4037 |
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5 . 已知椭圆
)的焦距为2c,F为右焦点,直线
与椭圆C相交于A,B两点,
是等腰直角三角形.若记椭圆C上任一点Q到抛物线
的焦点P的距离最大值为
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157c13923b1faff5d7b672e10d1927bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f344ca38f295f3586bab1d014e32b5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98908c3834d8a95cadda737a9a1997bb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 已知函数
,若
在
上的最大值为4,则
在
上的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193602c99b1fb74956818f849fd26691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50188f84f379b3d0418c54cbade7d7.png)
A.-4 | B.![]() | C.-1 | D.2 |
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3卷引用:吉林省松原市吉林油田高级中学2021-2022学年高三上学期开学调研考试数学(文科)试题
吉林省松原市吉林油田高级中学2021-2022学年高三上学期开学调研考试数学(文科)试题吉林省松原市吉林油田高级中学2021-2022学年高三上学期开学调研考试数学(理科)试题(已下线)第07讲 利用导数研究函数的单调性(核心考点讲与练)-2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)
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解题方法
7 . 已知
为奇函数,若当
时,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7e167a3da7721e6f703aed31fa1614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71599cd707909eb30d2a54be7f8c966.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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8 . 已知函数
.
(1)讨论函数
的单调性;
(2)若函数
存在两个不同的零点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ed947071194c2bea66fb3c1d8c6bc7.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/581b8ef0e4bb6c014a68282ac27a97fe.png)
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9 . 如图,四边形ABCD与四边形BDEF均为菱形,
,
.
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879309076627456/2928155737235456/STEM/2b86be23-4edd-4562-91b3-4289e7903eda.png?resizew=182)
(1)求证:
平面BDEF;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd3ed8807db1250667c70433e1b6f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6b27bd5f1437c638082a7eec033b4c.png)
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879309076627456/2928155737235456/STEM/2b86be23-4edd-4562-91b3-4289e7903eda.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed7a8116d2f02b52c33fb7a49fc0d1ae.png)
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10 . 函数
满足
,且在区间
上,
则
的值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc6f81274395df9c4f37f17b24d89a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf321f6c066105161659ffadbccb45dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859b0ef2fa5253583ab64f195ef41fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3dd44739ef2b255f8f766215a5ee52.png)
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