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1、微积分公式Dx sin x=cos xcos x = -sin xtan x = sec2 xcot x = -csc2 xsec x = sec x tan xcsc x = -csc x cot x sin x dx = -cos x + C cos x dx = sin x + C tan x dx = ln |sec x | + C cot x dx = ln |sin x | + C sec x dx = ln |sec x + tan x | + C csc x dx = ln |csc x cot x | + Csin-1(-x) = -sin-1 xcos-1(-x) = -
2、cos-1 x tan-1(-x) = -tan-1 xcot-1(-x) = - cot-1 x sec-1(-x) = - sec-1 x csc-1(-x) = - csc-1 xDx sin-1 ()= ax221xa cos-1 ()=axtan-1 ()=ax22xaa cot-1 ()=axsec-1 ()=ax22axxacsc-1 (x/a)= sin-1 x dx = x sin-1 x+C21x cos-1 x dx = x cos-1 x-+C21x tan-1 x dx = x tan-1 x-ln (1+x2)+C cot-1 x dx = x cot-1 x+ln
3、 (1+x2)+C sec-1 x dx = x sec-1 x- ln |x+|+C12x csc-1 x dx = x csc-1 x+ ln |x+|+C12xsinh-1 ()= ln (x+) xRax22xa cosh-1 ()=ln (x+) x1ax22ax tanh-1 ()=ln () |x| 1ax a21 axax sech-1()=ln(+)0x1ax x1221 xxcsch-1 ()=ln(+) |x| 0ax x1221 xxDx sinh x = cosh xcosh x = sinh xtanh x = sech2 xcoth x = -csch2 xsec
4、h x = -sech x tanh xcsch x = -csch x coth x sinh x dx = cosh x + C cosh x dx = sinh x + C tanh x dx = ln | cosh x |+ C coth x dx = ln | sinh x | + C sech x dx = -2tan-1 (e-x) + C csch x dx = 2 ln | + C xxee211duv = udv + vdu duv = uv = udv + vdu udv = uv - vducos2-sin2=cos2 cos2+ sin2=1 cosh2-sinh2=
5、1 cosh2+sinh2=cosh2Dx sinh-1()= ax221xa cosh-1()= ax221ax tanh-1()= ax22xaa coth-1()=axsech-1()= ax22xaxacsch-1(x/a)= 22xaxa sinh-1 x dx = x sinh-1 x-+ C21x cosh-1 x dx = x cosh-1 x-+ C12x tanh-1 x dx = x tanh-1 x+ ln | 1-x2|+ C coth-1 x dx = x coth-1 x- ln | 1-x2|+ C sech-1 x dx = x sech-1 x- sin-1
6、 x + C csch-1 x dx = x csch-1 x+ sinh-1 x + Csin 3=3sin-4sin3 cos3=4cos3-3cos sin3= (3sin-sin3) cos3=(3cos+cos3)sin x = cos x = jeejxjx2 2jxjxeesinh x = cosh x = 2xxee 2xxee正弦定理:= =2Rsina sinb sinc余弦定理: a2=b2+c2-2bc cosb2=a2+c2-2ac cos c2=a2+b2-2ab cosabc Rsin ()=sin cos cos sin cos ()=cos cos sin s
7、in m 2 sin cos = sin (+) + sin (-) 2 cos sin = sin (+) - sin (-) 2 cos cos = cos (-) + cos (+) 2 sin sin = cos (-) - cos (+)sin + sin = 2 sin (+) cos (-) sin - sin = 2 cos (+) sin (-) cos + cos = 2 cos (+) cos (-) cos - cos = -2 sin (+) sin (-)tan ()=, cot ()= tantantantan m cotcotcotcot mex=1+x+ !
8、22x ! 33x ! nxnsin x = x-+-+ ! 33x ! 55x ! 77x )!12() 1(12nxnncos x = 1-+-+ ! 22x ! 44x ! 66x )!2() 1(2nxnnln (1+x) = x-+-+ 22x 33x 44x )!1() 1(1nxnntan-1 x = x-+-+ 33x 55x 77x ) 12() 1(12nxnn(1+x)r =1+rx+x2+x3+ -1x1! 2) 1( rr ! 3)2)(1(rrr= n ni 11= n (n+1) nii1= n (n+1)(2n+1) nii12 61= n (n+1)2 nii
9、13(x) = x-1e-t dt = 22x-1dt = x-1 dt0t0t2te0)1(lnt(m, n) =m-1(1-x)n-1 dx=22m-1x cos2n-1x dx 10x20sin= dx01)1 (nmmxx希腊字母希腊字母 (Greek Alphabets)大写小写读音大写小写读音大写小写读音, 倒数关系: sincsc=1; tancot=1; cossec=1商数关系: tan= ; cot= cossin sincos平方关系: cos2+ sin2=1; tan2+ 1= sec2; 1+ cot2= csc2; 顺位高 d 顺位低 ; 順位低順位高0* = *
10、 = = 0* = 1 01 00= ; = ; = 00)(0 e0 0e1 0e顺位一: 对数; 反三角(反双曲) 顺位二: 多项函数; 幂函数 顺位三: 指数; 三角(双曲)算术平均数(Arithmetic mean) nXXXXn.21中位数(Median)取排序后中间的那位数字众数(Mode)次数出现最多的数值几何平均数(Geometric mean)nnXXXG.21调和平均数(Harmonic mean)1.11(1121nxxxnH 平均差(Average Deviatoin)nXXni|1变异数(Variance)or nXXni21)(1)(21 nXXni标准差(Stan
11、dard Deviation)or nXXni21)(1)(21 nXXni分配机率函数 f(x)期望值 E(x)变异数 V(x)动差母函数 m(t)Discrete Uniformn1(n+1)21(n2+1)121tntteee n 1)1 (1Continuous Uniformab 1(a+b)21(b-a)2121 tabeeatbt)( Bernoullipxq1-x(x=0, 1)ppqq+petBinomialpxqn-x xnnpnpq(q+ pet)nNegative Binomialpkqx xxk1 pkq2pkqktkqep )1 ( Multinomialf(x1,
12、 x2, , xm-1)=npinpi(1-pi)三项 (p1et1+ mx mxxmpppxxxn.!.!21 21 21p2et2+ p3)nGeometricpqx-1p12pqttqepe 1Hypergeometri c nNxnkN xkn Nkn 1NnN NkPoisson! xex )1(teeNormal2)(2121x e222 21tteBeta11)1 (),(1 xxB 2)(1( Gammaxex 1)()(2 tExponentxe 121 tChi-Squared2=f(2)=212222 )(221 ennnE(2)=nV(2)=2n2)21 (n tWei
13、bullx e1111 1112221 000 000 000 000 000 000 000 000 1024 yotta Y 1 000 000 000 000 000 000 000 1021 zetta Z 1 000 000 000 000 000 000 1018 exa E 1 000 000 000 000 000 1015 peta P 1 000 000 000 000 1012 tera T 兆 1 000 000 000 109 giga G 十亿 1 000 000 106 mega M 百万 1 000 103 kilo K 千 100 102 hecto H 百
14、10 101 deca D 十 0.1 10-1 deci d 分，十分之一 0.01 10-2 centi c 厘（或写作厘 ） ，百分之一 0.001 10-3 milli m 毫，千分之一 0.000 001 10-6 micro ? 微，百万分之一 0.000 000 001 10-9 nano n 奈，十亿分之一 0.000 000 000 001 10-12 pico p 皮，兆分之一 0.000 000 000 000 001 10-15 femto f 飞（或作费 ） ，千兆分之一 0.000 000 000 000 000 001 10-18 atto a 阿 0.000 000 000 000 000 000 001 10-21 zepto z 0.000 000 000 000 000 000 000 001 10-24 yocto y
