名校
1 . 已知函数
,
为
的导数
(1)讨论
的单调性;
(2)若
是
的极大值点,求
的取值范围;
(3)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0405779583ded3b24cfa5479851dbf20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5caabda288fc01cc168938846eec5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a901b3cb6a4b5201add46eb26a0d8c2.png)
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2024-06-08更新
|
1365次组卷
|
6卷引用:山东省济南市2024届高三下学期5月适应性考试(三模)数学试题
(已下线)山东省济南市2024届高三下学期5月适应性考试(三模)数学试题(已下线)专题9 利用放缩法证明不等式【练】湖北省武汉市汉铁高级中学2024届高考数学考前临门一脚试卷江苏省扬州市扬州中学2023-2024学年高二下学期5月月考数学试题山东省枣庄市2024届高三三调数学试题山东省青岛市2024届高三下学期第二次适应性检测数学试题
2 . 在不大于
的正整数中,所有既不能被2整除也不能被3整除的个数记为
.
(1)求
,
的值;
(2)对于
,
,是否存在m,n,p,使得
?若存在,求出m,n,p的值;若不存在,请说明理由;
(3)记
表示不超过
的最大整数,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc1e9444e6cbbcccfb19bef934fda45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c581f06adc031bd163f98c461300d862.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0f3595c506dd94a3399da87f0b33ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985ea7ad3004613e28dd691829437c11.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5510ef06b326f131933224473550d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf45fc1d20ec9adb3b25794ac938855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80b43936d042aae836465212e716964.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bbe68c798af91a4f5fbf939c4ed315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a3651b3fedba1f0e9998fa88acefd08.png)
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2024-06-07更新
|
464次组卷
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3卷引用:情境10 存在性探索命题
名校
3 . 对于定义在
上的函数
,如果存在一组常数
,
,…,
(
为正整数,且
),使得
,
,则称函数
为“
阶零和函数”.
(1)若函数
,
,请直接写出
,
是否为“2阶零和函数”;
(2)判断“
为2阶零和函数”是“
为周期函数”的什么条件(用“充分不必要条件”“必要不充分条件”“充要条件”或“既不充分也不必要”回答),并证明你的结论;
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f4cc0837a4e6dcd0072887e4e2704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe6d9f54a34762aadfdf8e2bac977cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892519541cfba6f2763cd29159bf1b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329fb959f16f82835aa68fca9d3f08f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcda6a21da79726f8fb3ba6235b9010f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebef85c05f6d84ceb67d92abf77ba2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ace630100e64ed290d82936ad249c8.png)
(2)判断“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab7da79b2400cf8125ef040cd056b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321b15db96dc89f136a7421e09fc9814.png)
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2024高三·全国·专题练习
4 . 已知
满足
,则函数
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416d5e42afc12ecde0820b68b45911e2.png)
您最近一年使用:0次
名校
5 . 在平面内有三个互不相交的圆,三个圆的半径互不相等.三个圆的方程分别为
.其中圆
与圆
的两条外公切线相交于点
,圆
与圆
的两条外公切线相交于点
,圆
与圆
的两条外公切线相交于点
,
表示直线AB的斜率,
表示直线AC的斜率,
表示直线BC的斜率.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298d4f4782916ab6c13f27ac0d024054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
A.存在![]() ![]() |
B.对任意![]() ![]() |
C.存在点![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知抛物线
上的动点到其焦点的距离的最小值为
.
(1)求抛物线的方程;
(2)过抛物线上一点
作抛物线的切线,分别交
轴于点
,交
轴于点
.点
在抛物线上,点
在线段
上,满足能
;点
在线段
上,满足
,且
,线段
与
交于点
,当点
在抛物线上移动时,求点
的轨迹方程
.
(3)将
向左平移
个单位,得到
,已知
,
,过点
作直线
交
于
.设
,求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea1ce7588f88b39746159233be9cd82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
(1)求抛物线的方程;
(2)过抛物线上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3524943b0e75d20ddf258aa058323918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b033c1899f43a66a56ba34ba6cef82db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ff37d05b92697213a56a24238d7bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a85ea4968343b0d94ed2fe01b535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(3)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bba1cc9c3ea9f2b5c2e2b16ac6e475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9f4a8451156c4036b42cfec99f5f3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6faec45d11006d42f053e474f4a4b504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bba1cc9c3ea9f2b5c2e2b16ac6e475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99dc4a9ee46bdd47f9491c62d00a4ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d1850b79e70c9bade75527a58b0c41.png)
您最近一年使用:0次
2024-06-04更新
|
717次组卷
|
3卷引用:湖南省长沙市第一中学2024届高三下学期模拟考试数学试卷(一)
名校
解题方法
7 . 已知三棱锥
三条侧棱
,
,
两两互相垂直,且
,
,
分别为该三棱锥的内切球和外接球上的动点,则线段
的长度的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f65a7b230807b683d18bb7415473de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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名校
解题方法
8 . 已知数列
满足
(
为正整数),
,设集合
.有以下两个猜想:①不论
取何值,总有
;②若
,且数列
中恰好存在连续的7项构成等比数列,则
的可能取值有6个.其中( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19270ac238f89bde5aeb61c622c1d68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9972b9f5d541ff043675df369de82748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a2410ce34b36954ed4923e600d42f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6225bb97266c814a33b98c1e90e03e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.①正确,②正确 | B.①正确,②错误 | C.①错误,②正确 | D.①错误,②错误 |
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2024-06-01更新
|
146次组卷
|
4卷引用:上海市格致中学2021-2022学年高二下学期期中数学试题
上海市格致中学2021-2022学年高二下学期期中数学试题(已下线)4.2等比数列及其通项公式(第1课时)(作业)(夯实基础+能力提升)-2022-2023学年高二数学精品教学课件(沪教版2020选择性必修第一册)(已下线)【练】专题5 分段数列问题上海市实验学校2023-2024学年高三下学期四模数学试题
2024高三·全国·专题练习
解题方法
9 . 罗尔定理是高等代数中微积分的三大定理之一,它与导数和函数的零点有关,是由法国数学家米歇尔罗尔于1691年提出的.它的表达如下:如果函数
满足在闭区间
连续,在开区间
内可导,且
,那么在区间
内至少存在一点
,使得
.
(1)运用罗尔定理证明:若函数
在区间
连续,在区间
上可导,则存在
,使得
.
(2)已知函数
,若对于区间
内任意两个不相等的实数
,都有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94345694d4215284c41f87146795ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e655794426cb48ec8f537baae3dd07d0.png)
(1)运用罗尔定理证明:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1486d2ae6c7e7904ab47b909039ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2982ec308d84c83d538a58dae3ff1569.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee44b0f79b66f04bde9b696c393eb47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafa44c4a404f62f54460dbcd7b8a0fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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10 . 意大利画家达·芬奇提出:固定项链的两端,使其在重力的作用下自然下垂,那么项链所形成的曲线是悬链线.1691年,莱布尼茨等得出悬链线可为双曲余弦函数
的图象,类似的可定义双曲正弦函数
.它们与正、余弦函数有许多类似的性质.
(1)类比正弦函数的二倍角公式,请写出(不证明)双曲正弦函数的一个正确的结论:
________;
(2)当
时,比较
与
的大小,并说明理由;
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2b368b26ace6c7aa1babc747110b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a6271387d2be177a6561863df3de01.png)
(1)类比正弦函数的二倍角公式,请写出(不证明)双曲正弦函数的一个正确的结论:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0604613fa3ea938e6354254e3d99d8.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd76ea82cac9d90033c324f145e13e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5890d8b411cc9c2f0884e4b1f03f5e0c.png)
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