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(完整word版)高等数学(上)重要知识点归纳(word文档良心出品).pdf

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1、1 高等数学（上）重要知识点归纳（粗体带下划线是重中之重，必须掌握）第一章函数的极限与连续一、极限的定义与性质1、定义(了解）2、性质(1)()()(lim0 xAxfAxfxx，其中)(x为0 xx时的无穷小。(2)(唯一性)若Axfxx)(lim0，Bxfxx)(lim0，则BA。(3)无穷小乘以有界函数仍为无穷小。二、求极限的主要方法与工具1、两个重要极限公式(1)1sinlim0(2)e)11(lim2、两个准则（了解即可）(1)夹逼准则(2)单调有界准则3、等价无穷小替换法常用替换：当0时（1)sin（2）tan（3）arcsin（4)arctan（5）)1ln(（6）1e（7）2

2、21cos1（8）nn114、分子或分母有理化法5、分解因式法6、用定积分定义三、无穷小阶的比较高阶、同阶、等价2 四、连续与间断点的分类1、连续的定义（函数在某点连续的证明）)(xf在a点连续)()()()()(lim0lim0afafafafxfyaxx2、间断点的分类其他震荡型（来回波动）无穷型（极限为无穷大第二类但不相等）跳跃型（左右极限存在可去型（极限存在）第一类五、闭区间连续函数性质1、最大值与最小值定理2、介值定理和零点定理文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C

3、9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1

4、文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:C

5、P2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1

6、Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10

7、HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B

8、5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1

9、ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K13 第二章导数与微分一、导数的概念1、导数的定义axafxfxafxafxydxdyafyaxxxaxax)()(lim)()(limlim|)(|002、左右导数左导数axafxfxyafaxx)()(limlim)(0右导数axafxfxyafaxx)()(limlim)(03、导数的几何意义kafaxfyax处的切

10、线斜率在点（等于曲线)(,)(|4、导数的物理意义加速度）速度）则若运动方程：()()()(,)()()(tatvtstvtstss5、可导与连续的关系:连续，反之不然。可导二、导数的运算1、四则运算vuvu)(vuvuuv)(2)(vvuvuvu2、复合函数求导（链式法则）设)(xfy，一定条件下xuuydxdududydxdy3、反函数求导设)()(1yfxxfy和互为反函数，一定条件下：yxxy14、求导基本公式（要熟记）见 P60-61文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R

11、9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10

12、K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码

13、:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6

14、W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P1

15、0 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V

16、6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H

17、1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K14 5、隐函数求导方法：在0),(yxF两端同时对x求导，其中要注意到：y是中间变量，然后再解出y6、对数求导法则主要用于：幂指函数求导数多个函数连乘除或开方求导数方法：先对函数式两边取对数，再用隐函数求导法得到y7、参数方程确定函数的求导)()(tyytxx设，一定条件下3)()(,ttt

18、ttttttxxttxxxyxyxxydxydyxydxdyy（可以不记公式，理解做题）8、常用的高阶导数公式（1）.)2,1,0(),2sin(sin)(nnxxn（2）.)2,1,0(),2cos(cos)(nnxxn三、微分的概念与运算1、微分定义若)(xoxAy，则)(xfy可微，记AdxxAdy2、公式：dxxfxxfdy)()(3、可微与可导的关系两者等价4、近似计算当较小时，|xdyy，xxfxxfxf)()()(文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1

19、文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:C

20、P2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1

21、Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10

22、HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B

23、5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1

24、ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C

25、9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K15 第三章微分中值定理和导数的应用一、微分中值定理1、拉格朗日中值定理)()()()()()(),abfafbfabafbffba使得：（当加上条件)()(bfaf则演变成：2、罗尔定理0)(),fba使得：（二、罗比达法则记住：法则仅能对,00型直接用，对于,0,1,000转化后用.幂指函数恒等式fggefln三、单调性判别1、,

26、0yyyy02、单调区间分界点：驻点和不可导点.四、极值求法1、极值点来自：驻点或不可导点（可疑点）.2、求出可疑点后再加以判别.3、第一判别法：左右导数要异号，由正变负为极大，由负变正为极小.4、第二判别法：一阶导等于0，二阶导不为0 时，是极值点.正为极小，负为极大.五、闭区间最值求法找出区间内所有驻点、不可导点、区间端点，比较大小.文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码

27、:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6

28、W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P1

29、0 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V

30、6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H

31、1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R

32、9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10

33、K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K16 六、凹凸性与拐点1、,0yyyy02、拐点：曲线上凹凸分界点),(00yx.横坐标0 x不外乎不存在或)(,0)(00 xfxf，找到后再加以判别0 x附近的二阶导数是否变号.文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10

34、K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码

35、:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6

36、W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P1

37、0 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V

38、6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H

39、1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R

40、9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K17 第四章（1）不定积分一、不定积分的概念若在区间I上，dxxfxdFxfxF)()(),()(亦，则称.)()(的原函数为xfxF称全体原函数F(x)+c 为 f(x)的不定积分，记为dxxf)(.二、微分与积分的互逆关系1、dxxfdxxfdxfdxxf)()()()(2、cxfxdfcxfdxxf)()()()(三、积分法1、第一类换元法（凑微分法）2、第二类换元法（去根号）三角代换根式代换3、分部积分法（

41、反对幂三指，确定u）duvuvudv4、常用的基本积分公式(要熟记).见 P143文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP

42、2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z

43、9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 H

44、S6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5

45、S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 Z

46、U5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9

47、T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K18 第四章（2）定积分一、定积分的定义niiixbaxfdxxf10)(lim)(二、

48、可积的充分条件连续或只有有限个第一类间断点.三、几何意义定积分等于面积的代数和.四、主要性质1、线性性质bababagdxkdxfkdxgkfk2121)(2、可加性babcca3、比较在a,b上，有gf，则dxgdxfbaba4、估值在a,b上，baabMdxxfabm)()()(5、积分中值定理当 f(x)在a,b上连续时：babaabfdxxf,),)()(六、变上限积分函数1、)()()()(,)(xfdttfdttfxFbaxfxaxa可导，且连续，则在若2、可导可导，则，连续，在若)()()()()()(,)(xxdttfxFxxbaxf，且)()()()()(xxfxxfxF七

49、、牛顿-莱布尼茨公式)()(|)()(,)(aFbFdxxfdxxfbaxfbbaa连续，则在若八、定积分的积分法1、换元法牢记：换元同时要换限2、分部积分法bababavduuvudv|3、特殊积分文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU

50、5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T10K1文档编码:CP2W6W1Z9P10 HS6V6B5S3H1 ZU5R9C9T

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