1 . 最值
(1)如果函数
在定义域内存在
,使得任意的
,总有_________ ,那么
为
在区间
上的最大值(最小值).
(1)如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03e483e8a37a8e0e1fb327f99ad93ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
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2 . 求闭区间
上函数最值的基本步骤
第一步:求
在
上的______ ;
第二步:将第一步中得到的极值与______ 比较,得到
在
上的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
第一步:求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
第二步:将第一步中得到的极值与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
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3 . 复合函数的导数
若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659c8930dab5c1e73146c215b4bf7844.png)
______ .
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b7c2e457f9c77126763cccf052fa1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659c8930dab5c1e73146c215b4bf7844.png)
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23-24高二上·江苏·课后作业
4 . 常见函数的导数
常见函数 | 导数 |
![]() | |
![]() | |
![]() | |
![]() | |
![]() | |
![]() |
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23-24高二上·江苏·课后作业
5 . 基本初等函数的导数
完成下面的表格:
完成下面的表格:
基本初等函数 | 导数 |
![]() | |
![]() | |
![]() | |
![]() | |
![]() | |
![]() | |
![]() |
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6 . 等比数列的前
项和
已知
为等比数列且公比为
,
为其前
项和.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b7a07ade5913a6e6b54dbf1c23a5f3.png)
________ 或者![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0980e3f744e203ae45c4bbb442e336.png)
________
(2)我们用方法________ 推导
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b7a07ade5913a6e6b54dbf1c23a5f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0980e3f744e203ae45c4bbb442e336.png)
(2)我们用方法
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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23-24高二上·江苏·课后作业
7 . 数学归纳法
一般地,证明一个与正整数
有关的数学命题时,可按如下两个步骤进行:
(1)证明当
时命题成立;
(2)假设当
时命题成立,证明当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
___ 时命题也成立.
根据(1)(2)就可以断定命题对应从___ 开始的所有正整数
都成立.
一般地,证明一个与正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)证明当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7236a73d373c001ecc63cd43c227bb.png)
(2)假设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef28d0b96512fc68e18a45a6f369ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
根据(1)(2)就可以断定命题对应从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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8 . 导数
(1)设函数
在区间
上有定义,
,若
无限趋近于0时,比值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6989eef65f4476379f1a16f30cf5b1.png)
_____ 无限趋近于一个常数
,则称
在
可导,并称该常数
为函数
在
处的____ ,记为
即
.
(2)
的几何意义就是曲线
在点_____ 处切线的_____ .
(3)若函数
在
内任意一点
可导,则
为
在
上的导函数.
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee49cd415b686374189f90102d23ef7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1268e217016ff7e12b9bc51341c4cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6989eef65f4476379f1a16f30cf5b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91421e7703d87617f50270178decd18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e34817c02bca54629580be8e9ea60f2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91421e7703d87617f50270178decd18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/18/fdee788f-da21-4d31-bf59-34a35094aee1.png?resizew=227)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
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9 . 曲线上一点处的切线
(1)设
为曲线
上不同于
的一点,此时直线
称为曲线的____ ,随着点
沿曲线
向点
运动,割线
在点
处附近越来越接近曲线
,当点
无限逼近点
时,直线
最终成为在点
处最逼近曲线的直线
,这条直线称为曲线在点
处的_____ .
(2)设曲线上
,
,当
无限趋近于0时,割线
的斜率______ 无限趋近于点
处切线的_____ .
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eefffa1689b5a68786b9a5875f12c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/7a5f1641947153c80b987320885a2b57.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/17/a7387044-3c3c-40c5-a84a-f850b113b736.png?resizew=218)
(2)设曲线上
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e9db72d743d71cdee7f7d70cb17381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1268e217016ff7e12b9bc51341c4cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
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10 . 瞬时速度与瞬时加速度
(1)一般地,当
无限趋近于0时,运动物体位移
的平均变化率______ 无限趋近于一个常数,那么这个常数称为物体在
时的______ .
(2)一般地,当
无限趋近于0时,运动物体速度
的平均变化率_____ 无限趋近于一个常数,那么这个常数称为物体在
时的______ .
(1)一般地,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a4958df52dd9f9cba15f4d1675fc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5451a66fb4f48811e042d8ca250f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82120861c1c4f7cc1a7a3f169f082a81.png)
(2)一般地,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a4958df52dd9f9cba15f4d1675fc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e127daca60c7927cd7a98cfbdb8d3120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82120861c1c4f7cc1a7a3f169f082a81.png)
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