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2021年高等数学公式大全及常见函数图像.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|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页，共 17 页一些初等函数：两个重要极限：三角函数公式：诱导公式：函数角 A

3、sin cos tg ctg-sin cos-tg-ctg 90-cos sin ctg tg 90+cos-sin -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)(sinsinco

4、scos)cos(sincoscossin)sin(xxarthxxxarchxxxarshxeeeechxshxthxeechxeeshxxxxxxxxx11ln21)1ln(1ln(:2:2:22）双曲正切双曲余弦双曲正弦.590457182818284.2)11(lim1sinlim0exxxxxx|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页，共 17 页文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W

5、2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8

6、ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W

7、2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8

8、ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W

9、2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8

10、ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W

11、2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7倍角公式：半角公式：cos1sinsincos1cos1cos12cos1sinsincos1cos1cos122cos12cos2cos12sinctgtg正弦定理：RCcBbAa2sinsinsin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

12、。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：23333133cos3cos43cossin4sin33sintgtgtgtg222222122212sincossin211cos22coscossin22sintgtgtgctgctgctg|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页，共 17 页文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y

13、9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L

14、8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y

15、9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L

16、8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y

17、9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L

18、8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y

19、9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7.1;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：bannnbannbanyyyyyyyynabxfyyyynabxfyyynabxf)(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：

20、为引力系数引力：水压力：功：空间解析几何和向量代数：|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 4 页，共 17 页文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2

21、 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8

22、H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2

23、 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8

24、H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2

25、 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8

26、H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7。代表平行六面体的体积为锐角时，向量的混合积：例：线速度：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,cos

27、Pr)()()(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：，其中、点法式：平面的方程：113,22211;,1302),(,0)()()(12222222222222222222200000022

28、20000000000czbyaxczbyaxqpzqypxczbyaxptzzntyymtxxpnmstpzznyymxxCBADCzByAxdczbyaxDCzByAxzyxMCBAnzzCyyBxxA多元函数微分法及应用|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 5 页，共 17 页文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W

29、2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8

30、ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W

31、2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8

32、ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W

33、2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8

34、ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7zyzxyxyxy

35、xyxFFyzFFxzzyxFdxdyFFyFFxdxydFFdxdyyxFdyyvdxxvdvdyyudxxuduyxvvyxuuxvvzxuuzxzyxvyxufztvvztuuzdtdztvtufzyyxfxyxfdzzdzzudyyudxxududyyzdxxzdz，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),(yuGFJyvvyGFJyuxuGFJxvvxGFJxuGGFFvGuGvFuF

36、vuGFJvuyxGvuyxFvuvu隐函数方程组：微分法在几何上的应用：),(),(),(30)(,()(,()(,(2),(),(),(1),(0),(,0),(0),(0)()()()()()(),()()()(000000000000000000000000000000000000000000000000000zyxFzzzyxFyyzyxFxxzzzyxFyyzyxFxxzyxFzyxFzyxFzyxFnzyxMzyxFGGFFGGFFGGFFTzyxGzyxFzztyytxxtMtzztyytxxzyxMtztytxzyxzyxzyxyxyxxzxzzyzy、过此点的法线方程：、过

37、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：|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 6 页，共 17 页文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L

38、8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y

39、9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L

40、8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y

41、9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L

42、8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y

43、9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7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

44、方向导数为：沿任一方向在一点函数lyxflfljieeyxflfjyfixfyxfyxpyxfzlxyfxflflyxpyxfz),(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：DzDyDxzyxDyDxDDyDxDDDayxxdyxfaFayxydyxfFayxxdyxfFFFFFaaM

45、zxoydyxxIydyxyIxdyxdyxyMMydyxdyxxMMxdxdyyzxzAyxfzrdrdrrfdxdyyxf23222232222322222D22)(),()(),()(),(,)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：|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 7 页，共 17 页文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8

46、H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2

47、 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8

48、H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2

49、 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8

50、H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2 HG1R7H5Q9G8 ZJ4Y9S8H3H7文档编码:CX8W2B3L8F2

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