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(完整word版)高等数学公式大全(完整版).pdf

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1、高等数学公式导数公式：基本积分表：三角函数的有理式积分：222212211cos12sinududxxtguuuxuux，axxaaactgxxxtgxxxxctgxxtgxaxxln1)(logln)(csc)(cscsec)(seccsc)(sec)(22222211)(11)(11)(arccos11)(arcsinxarcctgxxarctgxxxxxCaxxaxdxCshxchxdxCchxshxdxCaadxaCxctgxdxxCxdxtgxxCctgxxdxxdxCtgxxdxxdxxx)ln(lncsccscsecseccscsinseccos22222222CaxxadxCx

2、axaaxadxCaxaxaaxdxCaxarctgaxadxCctgxxxdxCtgxxxdxCxctgxdxCxtgxdxarcsinln21ln211csclncscseclnsecsinlncosln22222222CaxaxaxdxxaCaxxaaxxdxaxCaxxaaxxdxaxInnxdxxdxInnnnarcsin22ln22)ln(221cossin222222222222222222222020一些初等函数：两个重要极限：三角函数公式：诱导公式：函数角 A sin cos tg ctg-sin cos-tg-ctg 90-cos sin ctg tg 90+cos-sin

3、 -ctg -tg 180-sin-cos -tg-ctg 180+-sin -cos tg ctg 270-cos -sin ctg tg 270+-cos sin-ctg -tg 360-sin cos-tg-ctg 360+sin cos tg ctg 和差角公式：和差化积公式：2sin2sin2coscos2cos2cos2coscos2sin2cos2sinsin2cos2sin2sinsinctgctgctgctgctgtgtgtgtgtg1)(1)(sinsincoscos)cos(sincoscossin)sin(xxarthxxxarchxxxarshxeeeechxshxt

4、hxeechxeeshxxxxxxxxx11ln21)1ln(1ln(:2:2:22）双曲正切双曲余弦双曲正弦.590457182818284.2)11(lim1sinlim0exxxxxx文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:

5、CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z

6、3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:

7、CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z

8、3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:

9、CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z

10、3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2倍角公式：半角公式：cos1sinsincos1cos1cos12cos1sinsincos1cos1cos122cos12cos2cos12sinctgtg正弦定理：R

11、CcBbAa2sinsinsin余弦定理：Cabbaccos2222反三角函数性质：arcctgxarctgxxx2arccos2arcsin高阶导数公式莱布尼兹（Leibniz）公式：)()()()2()1()(0)()()(!)1()1(!2)1()(nkknnnnnkkknknnuvvukknnnvunnvnuvuvuCuv中值定理与导数应用：拉格朗日中值定理。时，柯西中值定理就是当柯西中值定理：拉格朗日中值定理：xxFfaFbFafbfabfafbf)(F)()()()()()()()()(曲率：23333133cos3cos43cossin4sin33sintgtgtgtg22222

12、2122212sincossin211cos22coscossin22sintgtgtgctgctgctg文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS

13、8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H

14、6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS

15、8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H

16、6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS

17、8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H

18、6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2.1;0.)1(limMsMM:.,13202aKaKyydsdsKMMsKtgydxydss的圆：半径为直线：点的曲率：弧长。：化量；点，切线斜率的倾角变点到从平均曲率：其中弧微分公式：定积分的近似计算：bannnbannbanyyyyyyyynabx

19、fyyyynabxfyyynabxf)(4)(2)(3)()(21)()()(1312420110110抛物线法：梯形法：矩形法：定积分应用相关公式：babadttfabdxxfabykrmmkFApFsFW)(1)(1,2221均方根：函数的平均值：为引力系数引力：水压力：功：空间解析几何和向量代数：文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6

20、 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8

21、G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6

22、 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8

23、G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6

24、 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8

25、G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2。代表平行六面体的体积为锐角时，向量的混合积：例：线速度

26、：两向量之间的夹角：是一个数量轴的夹角。与是向量在轴上的投影：点的距离：空间,cos)(.sin,cos,cosPrPr)(Pr,cosPr)()()(2222222212121221221221cbacccbbbaaacbacbarwvbacbbbaaakjibacbbbaaababababababababaajajaajuABABABjzzyyxxMMdzyxzyxzyxzyxzyxzyxzyxzzyyxxzzyyxxuu（马鞍面）双叶双曲面：单叶双曲面：、双曲面：同号）（、抛物面：、椭球面：二次曲面：参数方程：其中空间直线的方程：面的距离：平面外任意一点到该平、截距世方程：、一般方程：，

27、其中、点法式：平面的方程：113,22211;,1302),(,0)()()(1222222222222222222220000002220000000000czbyaxczbyaxqpzqypxczbyaxptzzntyymtxxpnmstpzznyymxxCBADCzByAxdczbyaxDCzByAxzyxMCBAnzzCyyBxxA多元函数微分法及应用文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q

28、2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR

29、9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q

30、2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR

31、9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q

32、2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR

33、9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q

34、2zyzxyxyxyxyxFFyzFFxzzyxFdxdyFFyFFxdxydFFdxdyyxFdyyvdxxvdvdyyudxxuduyxvvyxuuxvvzxuuzxzyxvyxufztvvztuuzdtdztvtufzyyxfxyxfdzzdzzudyyudxxududyyzdxxzdz，隐函数，隐函数隐函数的求导公式：时，当：多元复合函数的求导法全微分的近似计算：全微分：0),()()(0),(),(),(),(),()(),(),(),(22),(),(1),(),(1),(),(1),(),(1),(),(0),(0),(yuGFJyvvyGFJyuxuGFJxvvxGFJxuGG

35、FFvGuGvFuFvuGFJvuyxGvuyxFvuvu隐函数方程组：微分法在几何上的应用：),(),(),(30)(,()(,()(,(2),(),(),(1),(0),(,0),(0),(0)()()()()()(),()()()(000000000000000000000000000000000000000000000000000zyxFzzzyxFyyzyxFxxzzzyxFyyzyxFxxzyxFzyxFzyxFzyxFnzyxMzyxFGGFFGGFFGGFFTzyxGzyxFzztyytxxtMtzztyytxxzyxMtztytxzyxzyxzyxyxyxxzxzzyzy、过

36、此点的法线方程：、过此点的切平面方程、过此点的法向量：，则：上一点曲面则切向量若空间曲线方程为：处的法平面方程：在点处的切线方程：在点空间曲线方向导数与梯度：文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P

37、9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文

38、档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P

39、9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文

40、档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P

41、9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文

42、档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2上的投影。在是单位向量。方向上的，为，其中：它与方向导数的关系是的梯度：在一点函数的转角。轴到方向为其中的方向导数为：沿任一方向在一点函数lyxflfljieeyxflfjyfixfyxfyxpyxfz

43、lxyfxflflyxpyxfz),(gradsincos),(grad),(grad),(),(sincos),(),(多元函数的极值及其求法：不确定时值时，无极为极小值为极大值时，则：，令：设,00),(,0),(,00),(,),(,),(0),(),(22000020000000000BACBACyxAyxABACCyxfByxfAyxfyxfyxfyyxyxxyx重积分及其应用：DzDyDxzyxDyDxDDyDxDDDayxxdyxfaFayxydyxfFayxxdyxfFFFFFaaMzxoydyxxIydyxyIxdyxdyxyMMydyxdyxxMMxdxdyyzxzAyxf

44、zrdrdrrfdxdyyxf23222232222322222D22)(),()(),()(),(,)0(),0,0(),(,),(),(),(,),(),(1),()sin,cos(),(，其中：的引力：轴上质点平面）对平面薄片（位于轴对于轴对于平面薄片的转动惯量：平面薄片的重心：的面积曲面柱面坐标和球面坐标：文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9

45、K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档

46、编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9

47、K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档

48、编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9

49、K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档

50、编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2dvyxIdvzxIdvzyIdvxMdvz

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