名校
1 . 已知函数
,则
在
处的导数是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf5a5b3deb7d64f28ec93505d93bd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60eeccd121aa2d2bfe10b29a058e4866.png)
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2 . 已知曲线
上有一点
,则过
点的切线的斜率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac75c24c046868cb6170f5a6e94a80b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0a8c013422a11a27bc1c160df1be0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2024高二下·全国·专题练习
解题方法
3 . 若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d0e1ec6b80f2d8d2a156277128efce.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f632c741345daba236cd2ddc87876d.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd4c710826669acbc2cc0cbcc065480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d0e1ec6b80f2d8d2a156277128efce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f632c741345daba236cd2ddc87876d.png)
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名校
解题方法
4 . 某质点的位移
(单位:
)与时间
(单位:
)满足函数关系式
,当
时,该质点的瞬时速度为
,瞬时加速度为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
______ ,数列
的前20项和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65502a7ea4d1ce6d6d8c720845c73e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518dc7e50c747e406722b7f9942e956c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50116617310d066168dca3740fe4205b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e3d64b8e329f66355a74772ed4c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed7ca096c6dcb8e7be065f4284c7aa3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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名校
5 . 法国数学家拉格朗日于1778年在其著作《解析函数论》中给出一个定理:如果函数
满足如下条件:
(1)在闭区间
上是连续不断的;
(2)在区间
上都有导数.
则在区间
上至少存在一个实数
,使得
,其中
称为“拉格朗日中值”.函数
在区间
上的“拉格朗日中值”![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)在闭区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(2)在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
则在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4c41c2f9ced5d5cf2f530bd5d880cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3e0c1b288d8cc073a1c80d16722529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
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6 . 已知
,则曲线
在点
处的切线方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0107fb8d4cb3a9b6311fa639ca514b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
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2024-04-15更新
|
862次组卷
|
3卷引用:四川省遂宁市2024届高三第二次诊断性考试数学(理)试题
名校
7 . 函数
在
处的切线方程是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6550553c1422e56af94d01bef243034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
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2024-04-13更新
|
259次组卷
|
2卷引用:江苏省南京市第五高级中学2023-2024学年高二下学期4月阶段性检测数学试卷
8 . 若函数
的导函数为
,且满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4138e3a956d50c217cdd4799ff1edd.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61930a0e2c717715517ea5603868722a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4138e3a956d50c217cdd4799ff1edd.png)
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名校
9 . 法国数学家拉格朗日于1797年在其著作《解析函数论》中给出了一个定理,具体如下.如果函数
满足如下条件.(1)在闭区间
上是连续的;(2)在开区间
上可导则在开区间
上至少存在一点ξ,使得
成立,此定理即“拉格朗日中值定理”,其中ξ被称为“拉格朗日中值”.则
在区间
上的“拉格朗日中值”![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16853b8a2118378f786e286139fc1c26.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35fbcb1106217230a817f7b10d8aa002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda16bdd2671a8e299a0d9c00504202d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16853b8a2118378f786e286139fc1c26.png)
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10 . 写出与函数
在
处有公共切线的一个函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74a01d149399210cc1ce429a5b2b20e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74a01d149399210cc1ce429a5b2b20e.png)
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