1 . 若函数
的导数
,
的最小值为
,则函数
的零点为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef3d3f83c122e277819331c23318705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69498a7b03b1ad1426a5a11436ea407f.png)
A.0 | B.![]() | C.![]() | D.![]() |
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2 . 设正整数
,有穷数列
满足
,且
,定义积值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36bd11e8ffb70eac461dc4768b840a.png)
(1)若
时,数列
与数列
的S的值分别为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a1568c0bf07f285b2e01c3a3a55900.png)
①试比较
与
的大小关系;
②若数列
的S满足
,请写出一个满足条件的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddcaa1756eafc97696d69068689892c8.png)
(2)若
时,数列
存在
使得
,将
,
分别调整为
,
,其它2个
,令
数列
调整前后的积值分别为
,写出
的大小关系并给出证明;
(3)求
的最大值,并确定S取最大值时
所满足的条件,并进行证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83056c039e255d1ca7e26b756f3a6d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b99718e1bce4057550e1aef19c82b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36bd11e8ffb70eac461dc4768b840a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b801f41875296c26e893f492af633bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a422e11339ddc763ada97021f03722a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a1568c0bf07f285b2e01c3a3a55900.png)
①试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
②若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5769559be3487868d334c66d130360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddcaa1756eafc97696d69068689892c8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a58d2f2ef54bddedcb3ca40b1b43bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c973c75e2e9209e2a22e3deb453e0cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e57093fadaaa08e9ac73e855221525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711e95f069a685da11ff70b16504578a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d03382cb64aca02dd52d8196abb804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c5515db76e233bad7f418cfbcbc0b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f021e668a3bb0b84447138c33a6ca188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a3fc7a52b6b15e855cd22bdf8d00bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a58d2f2ef54bddedcb3ca40b1b43bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab93d9afb14d07b81567d47207c4be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab93d9afb14d07b81567d47207c4be0.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c11e6c8be2cb8384953b3f19f7b77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
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名校
解题方法
3 . 已知a,b,c为某三角形的三边长,其中
,且a,b为函数
的两个零点,若
恒成立,则M的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10921b873ec6153738ca19968f3dc6ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be131f232a7f636571607e890530a8a.png)
您最近一年使用:0次
2024-02-28更新
|
887次组卷
|
8卷引用:江苏省南通市海安高级中学2024届高三下学期开学考试数学试题
江苏省南通市海安高级中学2024届高三下学期开学考试数学试题江苏省南通市海安市2023-2024学年高三上学期期初学业质量监测数学试题河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次调研测试数学试卷(已下线)第五套 最新模拟重组精华卷(2月开学考试)(已下线)新高考预测卷(2024新试卷结构)(已下线)高二下学期第一次月考模拟卷(新题型)(导数+计数原理)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019)(已下线)大招12二次函数的零点分布问题2024届江苏省华罗庚中学高三下学期5月冲刺测试二数学试卷
解题方法
4 . “阿基米德多面体”也称为半正多面体,是由边数不全相同的正多边形为面围成的多面体,它体现了数学的对称美.如图,是一个八个面为正三角形,六个面为正方形的“阿基米德多面体”,某玩具厂商制作一个这种形状棱长为
,重量为
的实心玩具,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd6f4250ca6b1b9bce234a01f00d44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7808a98cf04a37b0358c1e855ee4347.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/37fbe650-3516-418a-b898-3bb8c8825d10.png?resizew=161)
A.将玩具放到一个正方体包装盒内,包装盒棱长最小为![]() |
B.将玩具放到一个球形包装盒内,包装盒的半径最小为![]() |
C.将玩具以正三角形所在面为底面放置,该玩具的高度为![]() |
D.将玩具放至水中,其会飘浮在水面上. |
您最近一年使用:0次
2024-02-28更新
|
894次组卷
|
3卷引用:江苏省南通市2024届高三高考考前押题卷(最后一卷)数学试题
名校
5 . 多元导数在微积分学中有重要的应用.设
是由
,
,
…等多个自变量唯一确定的因变量,则当
变化为
时,
变化为
,记
为
对
的导数,其符号为
.和一般导数一样,若在
上,已知
,则
随着
的增大而增大;反之,已知
,则
随着
的增大而减小.多元导数除满足一般分式的运算性质外,还具有下列性质:①可加性:
;②乘法法则:
;③除法法则:
;④复合法则:
.记
.(
为自然对数的底数),
(1)写出
和
的表达式;
(2)已知方程
有两实根
,
.
①求出
的取值范围;
②证明
,并写出
随
的变化趋势.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9265c54f2a96bf290388484cfd0ff47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c75f7dcce2b59c10237868c6715ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c137b971df3492a2001085d98706801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1343590f4aaf6b9e3f3c200e318bfea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43887f94250f6c073e144f2ae39b3021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8baf79cfbc5cc29029ca66632c20775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf1c89ff75dc38ce474a01c4932f8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff01089fbfd66ae3411b15e54f7a9120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef134baac9bb96324f585c5e532cbefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09df69561e70f6d8a66d32f7ffa8a60d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272a7f552e7d99ab3756c1d4e64fc355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9e8e03d12633cfe6858b8c85047100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d6ee0cf2632c76087f5bce01358ef8.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b0e3a7c0dc3c1143610f60a0fd884f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1343590f4aaf6b9e3f3c200e318bfea0.png)
(2)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18df306af443a02bf538cfc517d4a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-21更新
|
1075次组卷
|
3卷引用:江苏省海安高级中学2023-2024学年高二下学期第二次月考数学试题
江苏省海安高级中学2023-2024学年高二下学期第二次月考数学试题广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编
名校
6 . 袋中装有5个乒乓球,其中2个旧球,现在无放回地每次取一球检验.
(1)若直到取到新球为止,求抽取次数X的概率分布及其均值;
(2)若将题设中的“无放回”改为“有放回”,求检验5次取到新球个数X的均值.
(1)若直到取到新球为止,求抽取次数X的概率分布及其均值;
(2)若将题设中的“无放回”改为“有放回”,求检验5次取到新球个数X的均值.
您最近一年使用:0次
2024-02-10更新
|
1542次组卷
|
4卷引用:江苏省南通市如皋市2024届高三上学期1月诊断测试数学试题
江苏省南通市如皋市2024届高三上学期1月诊断测试数学试题湖北省孝感市高级中学2024届高三上学期期末数学试题(已下线)第七章 随机变量及其分布(单元重点综合测试)(19题新结构)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第三册)(已下线)8.2 离散型随机变量及其分布列(1)
名校
解题方法
7 . 有5辆车停放6个并排车位,货车甲车体较宽,停靠时需要占两个车位,并且乙车不与货车甲相邻停放,则共有( )种停放方法.
A.72 | B.144 | C.108 | D.96 |
您最近一年使用:0次
2024-02-10更新
|
1980次组卷
|
5卷引用:江苏省南通市如皋市2024届高三上学期1月诊断测试数学试题
江苏省南通市如皋市2024届高三上学期1月诊断测试数学试题湖北省孝感市高级中学2024届高三上学期期末数学试题(已下线)专题2.2 排列及排列数(八个重难点突破)-2023-2024学年高二数学下学期重难点突破及混淆易错规避(人教A版2019)(已下线)热点8-1 排列组合与二项式定理(10题型+满分技巧+限时检测)福建省宁德市古田县第一中学2024届高中毕业班高考前适应性测试数学试题
8 . 汽车驾驶员发现前方有障碍物时会紧急刹车,这一过程中,由于人的反应需要时间,在汽车的惯性作用下会有一个停车距离.记驾驶员的停车距离为
(单位:
),驾驶员反应时间内汽车所行距离为
(单位
),刹车距离为
(单位
),则
,其中
与刹车时的车速
单位,
满足
与刹车时的车速
的部分关系见下表:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/14c14aaa-1300-43ee-af60-f59fda312036.png?resizew=207)
(1)在坐标平面内画出
的散点图,从①
;②
③
中选择最恰当的一个函数模型拟合
与
之间的关系,并求出其解析式;
(2)在限速
的高速公路上,驾驶员遇障碍物紧急刹车,已知驾驶员的停车距离为
,请根据(1)中所求的解析式,判断驾驶员是否超速行驶.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e6151dc6ef89bc79b1ca0dc63b291e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c3c644550631be86bac4a258e957d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72b504088f9569ba1ea1ea5d89a9cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abde877ec465e7669e1c1678231ecad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![]() | 15 | 30 | 60 | 105 |
![]() | 1.25 | 5 | 20 | 61.25 |
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/14c14aaa-1300-43ee-af60-f59fda312036.png?resizew=207)
(1)在坐标平面内画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4c941b09da7316eb722fcad86399cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea53c308d542222bd32435dcbf0f9b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483e2516c014cb4d6087fbac3f26b600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07689e21c87cba68f7389a737a139deb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
(2)在限速
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30290c23cf5058b29f69803bbd434654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb83f2fc7f816c4f09e341be64519a8b.png)
您最近一年使用:0次
名校
9 . 如图,已知直线
,
分别在直线
,
上,
是
,
之间的定点,点
到
,
的距离分别为
,
,
.设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/947a1fd9-bd67-4420-9249-8d6f167bd310.png?resizew=156)
(1)用
表示边
,
的长度;
(2)若
为等腰三角形,求
的面积;
(3)设
,问:是否存在
,使得
?若存在,请求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdb9d8425d73a68731f30e0c0e22260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289a5d041c76475437bf2ab8d1169280.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/947a1fd9-bd67-4420-9249-8d6f167bd310.png?resizew=156)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73f691e91c1a725fbd6fd3d719a24b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600369eee391636a0d3ab5e9d9bf655e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
2024-01-31更新
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401次组卷
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2卷引用:江苏省南通市海安高级中学2023-2024学年高一下学期第一次月考数学试题
解题方法
10 . 某商场在元旦期间举行摸球中奖活动,规则如下:一个箱中有大小和质地相同的3个红球和5个白球,每一位参与顾客从箱中随机摸出3个球,若摸出的3个球中至少有2个红球,则该顾客中奖.
(1)若有三位顾客依次参加活动,求仅有最后一位顾客中奖的概率;
(2)现有编号为1~n的n位顾客按编号顺序依次参加活动,记X是这n位顾客中第一个中奖者的编号,若无人中奖,则记
.证明:
.
(1)若有三位顾客依次参加活动,求仅有最后一位顾客中奖的概率;
(2)现有编号为1~n的n位顾客按编号顺序依次参加活动,记X是这n位顾客中第一个中奖者的编号,若无人中奖,则记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e5e336e8d2cdd00c0f1fe7309d04c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bddf81b88cce6c7270af8fb5a99eee8.png)
您最近一年使用:0次