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1 . 若函数
的图象与函数
的图象有公切线
,且直线
与直线
互相垂直,则实数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0067b127910622f7fbc9a8256d2900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc143037f1776e2741fd8d56a4b925c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9118cc77fc0a045337745890e50cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
A.![]() | B.![]() | C.![]() ![]() | D.![]() ![]() |
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2022-07-25更新
|
1840次组卷
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6卷引用:专题3-1 切线、公切线及切线法应用 - 2
(已下线)专题3-1 切线、公切线及切线法应用 - 2(已下线)专题2-3 导数压轴小题归类(讲+练)-1(已下线)第三章 一元函数的导数及其应用 第一节 导数的概念及运算(A素养养成卷)黑龙江省哈尔滨市第三中学校2023-2024学年高二下学期第一次验收考试数学试卷江西省赣抚吉十一校2023届高三第一次联考数学(文)试题(已下线)模块四 专题5 重组综合练(黑龙江)(8+3+3+5模式)(北师大版高二)
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2 . 对于函数
和
,给出下列四个结论:
①设
的定义域为
,
的定义域为
,则
是
的真子集.
②函数
的图像在
处的切线斜率为0.
③函数
的单调减区间是
,
.
④函数
的图像关于点
对称.
其中所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0876376d0abc78d4ad8c5bbc597bde35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5c5c59bc2375e93325755a09e40d77.png)
①设
![](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/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfdd3d02b54e997cbec983d80f6bafd.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b6da436d60628bd762f3c3d9114938.png)
其中所有正确结论的序号是
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2022-06-06更新
|
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6卷引用:北京大学附属中学2022届高三三模数学试题
北京大学附属中学2022届高三三模数学试题(已下线)考向06 函数的奇偶性与周期性、对称性(重点)(已下线)专题13 导数及其应用北京卷专题10函数及其性质(填空题)北京卷专题11B指对幂函数北京卷专题12导数及其应用(选择填空题)
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3 . 已知点P为曲线
上的动点,O为坐标原点.当
最小时,直线OP恰好与曲线
相切,则实数a=___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f1dc94979ee7f94ba3f5f3ad254f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f645d4b09fba53f971172cd2602c691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024cf9810b9e312abc956648941548f3.png)
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2022-05-23更新
|
1559次组卷
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10卷引用:河北省邯郸市2022届高考二模数学试题
河北省邯郸市2022届高考二模数学试题(已下线)4.1 切线方程(精练)-【一隅三反】2023年高考数学一轮复习(提升版)(新高考地区专用)陕西省安康中学2022-2023学年高三上学期第一次检测性考试理科数学试题(已下线)考向10函数与导数(重点)-2(已下线)专题3-1 切线、公切线及切线法应用 - 2河南省许昌市禹州市高级中学2022-2023学年高二下学期第一次段考(2月)数学试题河北省邯郸市鸡泽县第一中学2024届高三上学期第二次月考数学试题上海市大同中学2023-2024学年高三三模数学试卷湖北省新高考联考协作体2021-2022学年高二下学期期末数学试题湖北省孝感市2021-2022学年高二下学期期末数学试题
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4 . 已知
,
,过原点作
图像的切线,切点为M,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8d76e423ab9015d4d3fc696579b01b.png)
(1)求
的解析式;
(2)若
的图像与
的图像有一条通过原点的公切线,求a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2dfb9619cd0fd1c9aaf63c4729b5f0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8d76e423ab9015d4d3fc696579b01b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a751619f6fe645900072be9f5eca9b97.png)
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2022-05-19更新
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874次组卷
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3卷引用:辽宁省实验中学2021-2022学年高二下学期期中数学试题
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解题方法
5 . 曲线
过点
的切线也是曲线
的切线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
___________ ;若此公切线恒在函数
的图象上方,则a的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/444c515d7d962c13ba251def136875d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8373794d772ec75ee1d82f5cb1ed7ac2.png)
您最近一年使用:0次
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6 . 集美中学高101组高二(15)班小美同学通过导数的学习,对直线与曲线相切产生浓厚兴趣,并试着定义:若曲线
与曲线
存在公共点
,且
、
在点
处的切线重合,称曲线
与
相切.现出一问题:若函数
与
相切,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53929a8f67b9aa3827fdbd73ebd265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda90af8ba1d6f9e21a49e96b709f16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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7 . 对于三次函数
,若
在
处的切线与
在
处的切线重合,则下列命题中真命题的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
您最近一年使用:0次
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8 . 双曲正弦函数
和双曲余弦函数
在工程学中有广泛的应用,也具有许多迷人的数学性质.若直线
与双曲余弦函数
和双曲正弦函数
的图象分别相交于点
、
,曲线
在
处的切线与曲线
在
处切线相交于点
,则如下命题中为真命题的有______ (填上所有真命题的序号).
①
,
;
②
;
③点
必在曲线
上;
④
的面积随
的增大而减小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3321510a9eb73909a36c084a8630e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099b9b80ed478824fa95677ebe9d5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/5963abe8f421bd99a2aaa94831a951e9.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/dad2a36927223bd70f426ba06aea4b45.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3050f406e86f0c80516a0ca8b9454f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feab64735c8c9d4efd99231a9d2e4cc3.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cdb782d4bbb34257f11bfccace6cff.png)
③点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
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9 . 某地在20年间经济高质量增长,GDP的值
(单位,亿元)与时间
(单位:年)之间的关系为
,其中
为
时的
值.假定
,那么在
时,GDP增长的速度大约是___________ .(单位:亿元/年,精确到0.01亿元/年)注:
,当
取很小的正数时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/336b39e84033e7a3d4158912179ea2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e853dac2621c68f6f9a4c8ab50215be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b28bd43d6858bfdaafcd11051251b66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/511418554ef4e80e43aa1744ce9e3a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a240b9b6cb5c6662bd7f0c7aa4180b.png)
您最近一年使用:0次
2022-05-06更新
|
1474次组卷
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7卷引用:福建省福州市2022届高三5月质量检测数学试题
福建省福州市2022届高三5月质量检测数学试题(已下线)专题08 函数模型及其应用(针对训练)-2023年高考数学一轮复习精讲精练宝典(新高考专用)(已下线)第39练 导数的概念、意义及运算陕西省西安中学2022-2023学年高二上学期第一次测试数学试题福建省永泰县第一中学2023届高三上学期10月月考数学试题(已下线)第三章 一元函数的导数及其应用 第一节 导数的概念及运算 (B素养提升卷)(已下线)第08讲 函数模型及其应用(五大题型)(讲义)
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10 . 已知抛物线
:
(
)的焦点
与圆
的圆心重合,过
的直线
与
交于
、
两点,对于下列命题:
①
;
②以
,
两点为切点引
的两条切线,两条切线交于一点
,
点必在
上;
③
的中垂线与
轴交于点
,则
;
④
为坐标原点,点
、
在
上且满足
(
,
均不与
重合)则
,
的中点轨迹方程:
.
以上说法中正确的有_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72583ae19ca43a687788658ffc1d6d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
②以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bdb006accc0b1553206855b5adf7832.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2abe13e2d4176f55f71677bbbb6eb4.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/1dde8112e8eb968fd042418dd632759e.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/b646e7630de8a801824a1c37bb7741ab.png)
以上说法中正确的有
您最近一年使用:0次
2022-04-26更新
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423次组卷
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3卷引用:四川省遂宁市2022届高三下学期三诊考试数学(文)试题