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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 14 页一阶初等函数：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-cossin ctg tg 90+cos-sin-ctg-tg 180-sin-cos-tg-ctg 180+-sin-costg ctg 270-cos-sin ctg tg 270+-cossin-ctg-tg 360-sin cos-tg-ctg 360+sin costg ctg 和差角公式：和差化积公式：2sin2sin2coscos2cos2cos2coscos2sin2cos2sinsin2cos2sin2sinsinctgctgctgctgctgtgtgtgtgtg1)(1)(sinsincoscos)cos(s
4、incoscossin)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 14 页文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10
5、O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5
6、U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G
7、2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK
8、9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W
9、6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编
10、码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A
11、3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3文档编码:CZ7A3E7W10O8 HK5U3I10G2P3 ZK9T1V1W6G3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：)()()
12、()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：.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：23333133cos3cos43cossin4sin33sintgtgtgtg222222122
13、212sincossin211cos22coscossin22sintgtgtgctgctgctg|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页，共 14 页文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8
14、 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文
15、档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7
16、A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7
17、B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K
18、8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2
19、I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8定积分的近似计算：bannnbannbanyyyy
20、yyyynabxfyyyynabxfyyynabxf)(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：。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,cosPr)()()(2222222212121221221221cbacccbbbaaacb
21、acbarwvbacbbbaaakjibacbbbaaababababababababaajajaajuABABABjzzyyxxMMdzyxzyxzyxzyxzyxzyxzyxzzyyxxzzyyxxuu|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 4 页，共 14 页文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A1
22、0 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8
23、 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文
24、档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7
25、A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7
26、B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K
27、8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2
28、I7A10 HX2P3O2O7B8 ZP7H6D7L6K8（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)()()(1222222222222222222220000002220000000000czbyaxczbyaxqpzqypxczbyaxptzzntyymtxxpnmstpzznyymxxCBADCzByAxdczbyaxDCzByAxzyxMCBAnzzCyyBxxA多元函数微分法及应用zyzxy
29、xyxyxyxFFyzFFxzzyxFdxdyFFyFFxdxydFFdxdyyxFdyyvdxxvdvdyyudxxuduyxvvyxuuxvvzxuuzxzyxvyxufztvvztuuzdtdztvtufzyyxfxyxfdzzdzzudyyudxxududyyzdxxzdz，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|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 5 页，共 14 页文档编码:CW4S3L2I7A10 HX
30、2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7
31、H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:
32、CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10
33、HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 Z
34、P7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编
35、码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A1
36、0 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8),(),(1),(),(1),(),(1),(),(1),(),(0),(0),(yuGFJyvvyGFJyuxuGFJxvvxGFJxuGGFFvGuGvFuFvuGFJvuyxGvuyxFvuvu隐函数方程组：微分法在几何上的应用：),(),(),(30)(,()(,()(,(2),(),(),(
37、1),(0),(,0),(0),(0)()()()()()(),()()()(000000000000000000000000000000000000000000000000000zyxFzzzyxFyyzyxFxxzzzyxFyyzyxFxxzyxFzyxFzyxFzyxFnzyxMzyxFGGFFGGFFGGFFTzyxGzyxFzztyytxxtMtzztyytxxzyxMtztytxzyxzyxzyxyxyxxzxzzyzy、过此点的法线方程：、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：上
38、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|精.|品.|可.|编.
39、|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 6 页，共 14 页文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4
40、S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2
41、P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H
42、6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:C
43、W4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 H
44、X2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP
45、7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8重积分及其应用：DzDyDxzyxDyDxDDyDxDDDayxxdyxfaFayxydyxfFayxxdyxfFFFFFaaMzxoydyxxIydyxyIxdyxdyx
46、yMMydyxdyxxMMxdxdyyzxzAyxfzrdrdrrfdxdyyxf23222232222322222D22)(),()(),()(),(,)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：dvyxIdvzxIdvzyIdvxMdvzMzdvyMydvxMxdrrrFddddrdrrFdxdydzzyxfddrdrdrdrrddvrzryrxzrrfzrFdzrdrdzrFdxdydzzyxfzzryrxzyxr)()
47、()(1,1,1sin),(sin),(),(sinsincossinsincossin),sin,cos(),(,),(),(,sincos222222200),(0222，转动惯量：，其中重心：，球面坐标：其中：柱面坐标：曲线积分：)()()()()(),(),(),(,)()(),(22tytxdtttttfdsyxfttytxLLyxfL特殊情况：则：的参数方程为：上连续，在设长的曲线积分）：第一类曲线积分（对弧|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 7 页，共 14 页文档编码:CW4S3L2I7A10 HX2P3O2O7B8
48、ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档
49、编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A
50、10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B8 ZP7H6D7L6K8文档编码:CW4S3L2I7A10 HX2P3O2O7B