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微积分公式Dx sin x=cos x cos x = sin xtan x = sec2 x cot x = -csc2 x sec 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 + Csin1(-x) = sin1 xcos-1(x) = p - cos-1 xtan1(x) = tan1 xcot-1(-x) = p cot-1 xsec1(x) = p sec-1 xcsc-1(-x) = - csc1 xDx sin1 ()= cos1 ()=tan1 ()=cot-1 ()=sec-1 ()=csc-1 (x/a)= sin1 x dx = x sin-1 x+C cos-1 x dx = x cos-1 x+C tan-1 x dx = x tan1 xln (1+x2)+C cot1 x dx = x cot1 x+ln (1+x2)+C sec1 x dx = x sec1 x ln |x+C csc-1 x dx = x csc-1 x+ ln x+Csinh1 ()= ln (x+) xRcosh-1 ()=ln (x+) x1tanh-1 ()=ln () |x| 1coth-1 ()=ln () x 1sech-1()=ln(+)0x1csch1 ()=ln(+) x 0Dx sinh x = cosh x cosh x = sinh x tanh x = sech2 x coth x = -csch2 x sech x = sech x tanh x csch 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 (ex) + C csch x dx = 2 ln | + Cduv = udv + vdu duv = uv = udv + vduudv = uv vducos2sin2=cos2cos2+ sin2=1cosh2-sinh2=1cosh2+sinh2=cosh2Dx sinh1()= cosh1()= tanh-1()= coth1()=sech-1()= csch-1(x/a)= sinh-1 x dx = x sinh-1 x+ C cosh1 x dx = x cosh1 x+ C tanh1 x dx = x tanh1 x+ ln 1x2|+ C coth-1 x dx = x coth1 x ln | 1-x2+ C sech1 x dx = x sech1 x sin-1 x + C csch-1 x dx = x csch-1 x+ sinh1 x + CaRcbsin 3=3sin-4sin3cos3=4cos33cossin3= (3sin-sin3)cos3=(3cos+cos3)sin x = cos x = sinh x = cosh x = 正弦定理:= =2R余弦定理: a2=b2+c2-2bc cosb2=a2+c2-2ac cosc2=a2+b22ab cossin ()=sin cos cos sin cos ()=cos cos sin sin 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 ()=ex=1+x+ sin x = x-+-+ cos x = 1+ ln (1+x) = x+-+ tan1 x = x-+-+ (1+x)r=1+rx+x2+x3+ -1x1= n= n (n+1)= n (n+1)(2n+1)= n (n+1)2(x) = x-1et dt = 22x-1dt = x1 dt(m, n) =m1(1-x)n1 dx=22m1x cos2n1x dx = dx希腊字母(Greek Alphabets)大写小写读音大写小写读音大写小写读音alphaiotarhobetakappa, sigmagammalambdataudeltamuupsilonepsilonnuphizetaxikhietaomicronpsithetapiomega倒数关系: sincsc=1; tancot=1; cossec=1商数关系: tan= ; cot= 平方关系: cos2+ sin2=1; tan2+ 1= sec2; 1+ cot2= csc2; 顺位高d顺位低 ;0 = = = 0* = = ; = ; = 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)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)调和平均数(Harmonic mean)平均差(Average Deviatoin)变异数(Variance) or 标准差(Standard Deviation) or 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 Uniform(n+1)(n2+1)Continuous Uniform(a+b)(ba)2Bernoullipxq1x(x=0, 1)ppqq+petBinomialpxqn-xnpnpq(q+ pet)nNegative BinomialpkqxMultinomialf(x1, x2, , xm-1)=npinpi(1pi)三项(p1et1+ p2et2+ p3)nGeometricpqx1HypergeometricnnPoissonNormal2BetaGammaExponentChi-Squared2=f(2)=E(2)=nV(2)=2nWeibull1 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。001 103 milli m 毫,千分之一0。000 001 106 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 1018 atto a 阿0.000 000 000 000 000 000 001 1021 zepto z 0.000 000 000 000 000 000 000 001 10-24 yocto y
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