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1、学习-好资料Dxsinx=cosxcosx=-sinxtanx=sec2xcotx=-csc2xsecx=secxtanxcscx=-cscxcotx微积分公式sinxdx=-cosx+Ccosxdx=sinx+Ctanxdx=ln|secx|+Ccotxdx=ln|sinx|+Csecxdx=ln|secx+tanx|+Ccscxdx=ln|cscxcotx|+Csin-1(-x)=-sin-1xcos-1(-x)=p-cos-1xtan-1(-x)=-tan-1xcot-1(-x)=p-cot-1xsec-1(-x)=p-sec-1xcsc-1(-x)=-csc-1xDxsin-1()=c
2、osh-1()=ln(x+x2-a2)x1xaxcos-1()=a1a2-x2sin-1xdx=xsin-1x+1-x2+Ccos-1xdx=xcos-1x-1-x2+Ctan-1xdx=xtan-1x-ln(1+x2)+Cxsinh-1()=ln(x+a2+x2)xRaxaxatan-1()=aa2+x2xcot-1()=acot-1xdx=xcot-1x+ln(1+x2)+Csec-1xdx=xsec-1x-ln|x+x2-1|+Ccsc-1xdx=xcsc-1x+ln|x+x2-1|+Cx1a+xtanh-1()=ln()|x|1a2ax-asech-1()=ln(+)0x1sec-1(
3、x)=acsc-1(x/a)=axx2-a2x-11-x2axx2x11+x2csch-1()=ln(+)|x|0axx2Dxsinhx=coshxcoshx=sinhxtanhx=sech2xcothx=-csch2xsechx=-sechxtanhxsinhxdx=coshx+Ccoshxdx=sinhx+Ctanhxdx=ln|coshx|+Ccothxdx=ln|sinhx|+Csechxdx=-2tan-1(e-x)+Cduv=udv+vduduv=uv=udv+vduudv=uv-vducos2-sin2=cos2cos2+sin2=1cschx=-cschxcothxcschxd
4、x=2ln|1+e-x1-e-2x|+Ccosh2-sinh2=1cosh2+sinh2=cosh2更多精品文档Dxsinh-1()=sinh-1xdx=xsinh-1x-1+x2+C学习-好资料x1aa2+x2sin3=3sin-4sin3cos3=4cos3-3cosxcosh-1()=a1x2-a2cosh-1xdx=xcosh-1x-x2-1+Csin3=(3sin-sin3)cos3=(3cos+cos3)xatanh-1()=aa2-x2tanh-1xdx=xtanh-1x+ln|1-x2|+Cejx-e-jxejx+e-jxsinx=cosx=coth-1xdx=xcoth-1x
5、-ln|1-x2|+C2j2xsech-1xdx=xsech-1x-sin-1x+Ccoth-1()=acsch-1xdx=xcsch-1x+sinh-1x+Cex-e-xex+e-xsinhx=coshx=22正弦定理:=2Rb2=a2+c2-2accostan()=tanatanb,cot()=1=nx-asech-1()=axa2-x2csch-1(x/a)=-axa2+x2sin()=sincoscossincos()=coscosmsinsin2sincos=sin(+)+sin(-)2cossin=sin(+)-sin(-)2coscos=cos(-)+cos(+)2sinsin=
6、cos(-)-cos(+)x2x3xnex=1+x+2!3!n!abcasinasinbsingRb餘弦定理:a2=b2+c2-2bccoscc2=a2+b2-2abcossin+sin=2sin(+)cos(-)sin-sin=2cos(+)sin(-)cos+cos=2cos(+)cos(-)cos-cos=-2sin(+)sin(-)mcotacotbmtanatanbcotacotbni=1x5x7i=n(n+1)sinx=x-x3(-1)nx2n+1n+-+3!5!7!(2n+1)!i=1i=1n(n+1)(2n+1)i=n(n+1)2(x)=tx-1e-tdt=2t2x-1ex2x
7、4x6(-1)nx2ncosx=1-+-+2!4!6!(2n)!x2x3x4(-1)nxn+1ln(1+x)=x-+-+234(n+1)!ni=1ni=123600-t21dt=(ln)x-1dt0tx3x5x7(-1)nx2n+1tan-1x=x-+-+357(2n+1)(m,n)=1xm-1(1-x)n-1dx=20p02sin2m-1xcos2n-1xdx更多精品文档学习-好资料r(r-1)2r(r-1)(r-2)(1+x)r=1+rx+x+x3+-1x12!3!=0xm-1(1+x)m+ndx希臘字母(GreekAlphabets)大寫小寫讀音大寫小寫讀音大寫小寫讀音alphaiota
8、rhobetakappa,sigmagammalambdataudeltamuupsilonepsilonzetaetanuxiomicronphikhipsithetapiomega倒數關係:sincsc=1;tancot=1;cossec=1;cot=商數關係:tan=sinqcosqcosqsinq平方關係:cos2+sin2=1;tan2+1=sec2;1+cot2=csc2順位高順位低0*=;順位高d順位低;110*=0*=00順位一:對數;反三角(反雙曲)順位二:多項函數;冪函數00=e0(-);0=e0;1=e0順位三:指數;三角(雙曲)算術平均數(Arithmeticmean)
9、X=X+X+.+X12nn中位數(Median)眾數(Mode)取排序後中間的那位數字次數出現最多的數值幾何平均數(Geometricmean)G=nXX.X12n|X-X|調和平均數(Harmonicmean)平均差(AverageDeviatoin)H=11111(+.+)nxxx12nni1n更多精品文档学习-好资料(X(X-X)2變異數(Variance)n1-X)2inorn1in-1(X-X)2(X-X)2標準差(StandardDeviation)n1inorn1in-1分配機率函數f(x)期望值E(x)變異數V(x)動差母函數m(t)npxqn-xk+x-1pkqxxx!x!.
10、x!1DiscreteUniformContinuousUniformBernoulliBinomialNegativeBinomialMultinomial12m1n1b-apxq1-x(x=0,1)xf(x1,x2,xm-1)=n!px1px2.pxm2m1(n+1)21(a+b)2pnpkqpnpi1(n2+1)121(b-a)212pqnpqkqp2npi(1-pi)1et(1-ent)n1-etebt-eat(b-a)tq+pet(q+pet)npk(1-qet)k三項(p1et1+p2et2+p3)npqx-1petGeometric1qpp21-qetxn-xnnHypergeo
11、metrickN-kkNN-nkN-1NnNPoissone-llxx!e-l(et-1)Normal12pse1x-m-()22s2emt+1s2t22BetaGamma1B(a,b)lG(a)xa-1(1-x)b-1(lx)a-1e-lxaa+balab(a+b+1)(a+b)2al2l-al-tExponentle-lx1l1l2ll-t更多精品文档学习-好资料G2Chi-Squared2=f(2)=1n2n2(c2)n2-12e-c2E(2)=nV(2)=2n(1-2t)-n211alG+1-G2+1Weibull1ae-x-bab+alG+1l221ll100000000000000
12、00000000001024yottaY10000000000000000000001021zettaZ10000000000000000001018exaE10000000000000001015petaP10000000000001012teraT兆1000000000109gigaG十億1000000106megaM百萬1000103kiloK千100102hectoH百10101decaD十0.110-1decid分，十分之一0.0110-2centic厘（或寫作厘），百分之一0.00110-3millim毫，千分之一0.00000110-6micro?微，百萬分之一0.00000000110-9nanon奈，十億分之一0.00000000000110-12picop皮，兆分之一0.00000000000000110-15femtof飛（或作費），千兆分之一0.00000000000000000110-18attoa阿0.00000000000000000000110-21zeptoz0.00000000000000000000000110-24yoctoy更多精品文档