1 . 已知函数
,则下面四个结论中:
①函数
在
上单调递减;
②当
或
时,
有一个零点;
③函数
存在最小值;
④当
时,
恒成立.
其中所有正确的结论序号为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b47d4c5d3ddd3ce7f949670d36f974.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75807858b7804a1ad2039c41f323a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63783f2f99cc5d905af8050b34c5e482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a048c77ba546fd52ba4a73db53f092e.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4160810e172570db3367a657605ed7ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c6aeaef586ed4aff1bd3aa93fb728b.png)
其中所有正确的结论序号为
您最近一年使用:0次
名校
解题方法
2 . 定义集合
的“长度”是
,其中a,
R.已如集合
,
,且M,N都是集合
的子集,则集合
的“长度”的最小值是_____ ;若
,集合
的“长度”大于
,则n的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3296f5d3fbd7177849bbd7bd30fbd3a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7701d084d2b153bbea08cfbf63413a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2532b1aa9a6b334d7395fc020bf0a6be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2512da0056b913e36a72419c91a5d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640f4732df2e4b84c5e98b47e37d4e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81919684bc4047d376c7e57dc6c8f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc8032a17aee665217899ed88652375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ae18508906c21d3e1199f231b1a9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
您最近一年使用:0次
解题方法
3 . 已知下列五个函数
,从中选出两个函数分别记为
和
,若
的图象如图所示,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0908ff4409d87277ab3b8583837bd1e.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae6be1c40cb864c38df5dcebf5f2035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870a586e90a7bb79dc44f9451dee19ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0908ff4409d87277ab3b8583837bd1e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/5f92437d-7854-4769-a256-899f9ed1c297.png?resizew=116)
您最近一年使用:0次
2024-03-07更新
|
169次组卷
|
3卷引用:北京市朝阳区2022-2023学年高一上学期数学期末试题
名校
解题方法
4 . 某中学开展“劳动创造美好生活”的劳动主题教育活动,展示劳动实践成果并进行评比,某学生设计的一款如图所示的“心形”工艺品获得了“十佳创意奖”,该“心形”由上、下两部分组成,并用矩形框
虚线
进行镶嵌,上部分是两个半径都为
的半圆,
分别为其直径,且
,下部分是一个“半椭圆”,并把椭圆的离心率叫做“心形”的离心率.
,则当该矩形框面积最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
__________ ;
(2)若
,图中阴影区域的面积为
,则该“心形”的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d578394cd8e4d7a705599269c512960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce072bcd423b56c827e40f0b731de85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9eb8f0efaf6fe8a69150fcdf3c83fc.png)
您最近一年使用:0次
2024-03-03更新
|
281次组卷
|
3卷引用:北京市第二中学2023-2024学年高二上学期12月第二学段考试数学试卷
名校
解题方法
5 . 函数
,给出下列四个结论:
①
的值域是
;
②
且
,使得
;
③任意
且
,都有
;
④规定
,其中
,则
.
其中,所有正确结论的序号是______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e965fb1d3fbadd5769d86c3853e384.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9faf2212b2e789fe72211ad0b85fad24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3ecbbaca8eeb1cfa8f4035f7d5726.png)
③任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9484fcea82180e9886a18d7a947b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb572cf70a40f65fb90f3e93cdc439b.png)
④规定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6bcb585a1ef10a3cf0e178782dec40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5664c8ff0e617bbdff16b4470bd198b2.png)
其中,所有正确结论的序号是
您最近一年使用:0次
2024-03-01更新
|
187次组卷
|
2卷引用:北京市广渠门中学2023-2024学年高一上学期期中考试数学试题
6 . 如图,在长方体
中,
为棱
的中点,点
是侧面
上的动点,满足
,给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/b6c99aeb-145d-4106-9230-1f577e7c4384.png?resizew=183)
①动点
的轨迹是一段圆弧;
②动点
的轨迹长度为
;
③动点
的轨迹与线段
有且只有一个公共点;
④三棱锥
的体积的最大值为
.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c338c277213e4176c9b67e0b9f8be9fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05058f5a119f7b10644bab23e8f3533.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/b6c99aeb-145d-4106-9230-1f577e7c4384.png?resizew=183)
①动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
③动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b03ab10cdcb79af60acfb52b85f910d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c779d5364c9231b1dfab30545ad045.png)
其中所有正确结论的序号是
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7 . 近日北方地区普遍降雪,某幼儿教师手工课上带孩子们做描述雪花形状的图案:从一个正三角形开始,把每条边分成三等份,然后以各边的中间一段为底边分别向外作正三角形,再去掉底边.反复进行这一过程,就得到一条“雪花”状的曲线.设原正三角形(图①)的边长为1,把图①,图②,图③,图④中图形的面积依次记为数列
的前四项,则数列
的通项公式为_____________ ,如果这个作图过程可以一直继续下去,那么“科赫雪花”的面积将趋近于__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/13/da8c63cf-168f-48dd-8a8f-cecaddb69e71.png?resizew=394)
您最近一年使用:0次
2024-01-25更新
|
352次组卷
|
3卷引用:北京市丰台区怡海中学2023-2024学年高二上学期期末模拟练习数学试题(2)
北京市丰台区怡海中学2023-2024学年高二上学期期末模拟练习数学试题(2)河北省石家庄市第二十七中学2024届高三上学期金太阳联考数学试题(已下线)考点11 由实际问题探究递推关系 2024届高考数学考点总动员
8 . 已知椭圆
的两个焦点分别为
和
,短轴的两个端点分别为
和
,点
在椭圆
上,且满足
.当
变化时,给出下列三个命题:
①点
的轨迹关于
轴对称;
②对任意的
使得椭圆
上满足条件的点
都有4个;
③
的最小值为
;
其中,所有正确命题的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5addf5e1f5bdedd13b1c3614583a474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2983259dc4602df3bdcd6441a75cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
②对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcef941284c5a3b3f63585c71b7a1a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae743852e53bb3a32144cfa423d2bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
其中,所有正确命题的序号是
您最近一年使用:0次
解题方法
9 . 关于曲线
,下列结论正确的有__________
①.曲线C关于原点对称
②.曲线C与直线
有四个交点
③.曲线C是封闭图形,且封闭图形的面积大于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
④.曲线C不是封闭图形,且它与圆
无公共点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66eda389249f92eaba886f7c67e05e89.png)
①.曲线C关于原点对称
②.曲线C与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04836ba2906cf6f1e9aecd2a00824aae.png)
③.曲线C是封闭图形,且封闭图形的面积大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
④.曲线C不是封闭图形,且它与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
您最近一年使用:0次
10 . 已知点
在函数
的图象上,点
在函数
的图象上,且
,
,
,给出下列说法:
①当
时,
;
②存在点
在直线
上;
③
,
,使点
和点
为两个函数图象的公共点;
④若点
在函数
的图象上,则函数
的周期是
,
两点间距离的整数倍;
⑤定义满足长度
取最小值时的区间
为最小区间.若
,区间
是满足
的最大区间,则函数
的周期为
.
其中,说法正确的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369e2cc0b7c553969627461819e80229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04129b7390acd7d936fbd204cc111dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6db7130ea4b0ea4da3d316b3070f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7602e4015d02cb188ffb82092ee980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b59c92a868cc6f448e5d92d257401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96d62cdf358f79c7831dd009c26430c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b519531dbeee800a08ba5ce55ff7e51.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d387a4f4ed6f48afd7fc75ff68ae026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75ff0c325ddcac48cf1c233f033c2c7.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67de794bd1d73ebe1e7fca6622579587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677ad4c4ea0722f0ee064f44624c585f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96d62cdf358f79c7831dd009c26430c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369e2cc0b7c553969627461819e80229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6db7130ea4b0ea4da3d316b3070f46.png)
④若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6db7130ea4b0ea4da3d316b3070f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e59bc063c88b1add34184da82283251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e59bc063c88b1add34184da82283251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
⑤定义满足长度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31d1c786e88987bb3bc7c54b7b66819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63313f7ac7402fcb5a9a840db64c6f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85cbdee531d4b394d674d90adda132b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b83fe99c90a7bf139a7e6e537820c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00feb80debaf63029240652a21b4b38f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04129b7390acd7d936fbd204cc111dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
其中,说法正确的序号是
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