名校
1 . 如图,已知在
中,
,
是
边上一点,且
,将
沿
进行翻折,使得点
与点
重合,若点
在平面
上的射影在
内部及边界上,则在翻折过程中,动点
的轨迹长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bb0cc36a05dda3725f4b3b03a7feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb08f6a798dc293f3d8de281190f65e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
2 . 若定义在D上的函数
满足:对任意
,存在常数
,都有
成立,则称
是D上的有界函数,其中
称为函数
的上界,最小的M称为函数
的上确界.
(1)求函数
的上确界;
(2)已知函数
,
,证明:2为函数
的一个上界;
(3)已知函数
,
,若3为
的上界,求实数
的取值范围.
参考数据:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea232de27d21a2646fd4520ea0726bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a920c2d27134a9c514f82bf464aed4ee.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066737c8b5ab483d0e853124de99429e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72bd2c5317e503a513881970a9badf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc03b242716eaa6ee3bef9061a63ce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405361d7be3c9e4d462a4e955d8fe3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c0309456de2cd6420ece4fbc5eeddb.png)
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2024-04-30更新
|
220次组卷
|
5卷引用:云南省下关第一中学教育集团2023-2024学年高一下学期段考(二)(6月)数学试题
名校
解题方法
3 . 设O为坐标原点,定义非零向量
的“相伴函数”为
,
称为函数
的“相伴向量”.
(1)设函数
,求函数
的相伴向量
;
(2)记
的“相伴函数”为
,若方程
在区间
上有且仅有四个不同的实数解,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0e4e35cf9b9f97c19e4b72cc2a1b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15530d256df9ecf36c7476381c7ab3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3fa5a2ec0f43acc49c5f7f848f212c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227e04b76330c7bc1f7b62a1756cd5a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b604c6522119e77c1cb16b91532a2c1.png)
您最近一年使用:0次
2024-03-31更新
|
343次组卷
|
2卷引用:云南省下关第一中学2023-2024学年高一下学期5月期中考试数学试题
名校
4 . 已知函数且
图象的相邻两对称轴间的距离为
,则以下说法正确的是( )
A.若![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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5 . 已知函数
的部分图象如图所示,则( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d25ffc739618adc609f7fd95cfeadf.png)
A.函数![]() ![]() |
B.函数![]() ![]() |
C.函数![]() ![]() |
D.![]() |
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2024-02-21更新
|
714次组卷
|
4卷引用:云南省开远市第一中学校2023-2024学年高一下学期开学考试数学试题
解题方法
6 . 已知函数
的部分图象如图所示,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d656979658cafaffdd73bc5075e78e31.png)
A.![]() |
B.函数![]() ![]() |
C.直线![]() ![]() |
D.函数![]() ![]() |
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2024-01-26更新
|
318次组卷
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2卷引用:云南省曲靖市沾益区第一中学2023-2024学年高一下学期开学考试数学试题
解题方法
7 . 如图,公园要在一块圆心角为
,半径为
的扇形草坪
中修建一个内接矩形文化景观区域
,若
,则文化景观区域
面积的最大值为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41d3f7d55fcbaebc4e2450ac63a3dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
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2024-01-26更新
|
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|
3卷引用:云南省昆明市盘龙区2023-2024学年高二上学期期末质量检测数学试题
名校
解题方法
8 . 已知
,
(
为自然对数的底数)
,比较
,
,
的大小( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55ecba0e40ef4feede322fc09fc97ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d3d56a72f49320d7d0be8aa762d8f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa535449dd5d22bdda16b92d0a83187f.png)
![](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/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-01-22更新
|
477次组卷
|
3卷引用:云南省昆明市禄劝彝族苗族自治县第一中学2023-2024学年高二上学期期末教学测评数学试卷
9 . 设函数
,已知
在
单调递增,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2bb7354fb64b7bf5ae232a93747955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff8872f9dff36b373313ebae391728b.png)
A.![]() | B.![]() |
C.若![]() ![]() | D.若![]() ![]() |
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名校
解题方法
10 . 已知函数
(
,
)的图象向右平移
个单位长度后,所得函数在
上至少存在两个最值点,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef983b6fc8108b3e0a99071345f8c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b8c40284d691ad45cae166462cff78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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