【】:高数微积分公式大全[1]

发布时间:2022-10-10 05:39:01   来源:文档文库   
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微积分公式Dxsinx=cosxcosx=-sinxtanx=sec2xcotx=-csc2xsecx=secxtanxcscx=-cscxcotx1xDxsin-1(=22aaxxcos-1(=axatan-1(=2aax2xcot-1(=asinxdx=-cosx+Ccosxdx=sinx+Ctanxdx=ln|secx|+Ccotxdx=ln|sinx|+Csecxdx=ln|secx+tanx|+Ccscxdx=ln|cscxcotx|+Csin-1xdx=xsin-1x+1x2+Ccos-1xdx=xcos-1x-1x2+Ctan-1xdx=xtan-1x-½ln(1+x2+Ccot-1xdx=xcot-1x+½ln(1+x2+Csec-1xdx=xsec-1x-ln|x+x21|+Csin-1(-x=-sin-1xcos-1(-x=-cos-1xtan-1(-x=-tan-1xcot-1(-x=-cot-1xsec-1(-x=-sec-1xcsc-1(-x=-csc-1xxsinh-1(=ln(x+a2x2xRaxcosh-1(=ln(x+x2a2x1ax1axtanh-1(=ln(|x|<1a2aax1xa-1xcoth(=ln(|x|>12-1-1a2axacscxdx=xcscx+ln|x+x1|+Cx11x2sech(=ln(+0x12axx-1xasec-1(=axx2a2csc-1(x/a=Dxsinhx=coshxcoshx=sinhxsinhxdx=coshx+Ccoshxdx=sinhx+Cx11x2csch(=ln(+|x|>02axxduv=udv+vdu-1tanhx=sech2xtanhxdx=ln|coshx|+Ccothx=-csch2xcothxdx=ln|sinhx|+Csechx=-sechxtanhxsechxdx=-2tan-1(e-x+Ccschx=-cschxcothx1excschxdx=2ln||+C2x1e1xDxsinh-1(=sinh-1xdx=xsinh-1x-1x2+C22aaxxcosh-1(=a-1duv=uv=udv+vduudv=uv-vducos2θ-sin2θ=cos2θcos2θ+sin2θ=1cosh2θ-sinh2θ=1cosh2θ+sinh2θ=cosh2θsin3θ=3sinθ-4sin3θcos3θ=4cos3θ-3cosθsin3θ=¼(3sinθ-sin3θcos3θ=¼(3cosθ+cos3θ1xa22cosh-1xdx=xcosh-1x-x21+Ctanh-1xdx=xtanh-1x+½ln|1-x2|+Cxatanh(=2aax2-1ejxejxejxejxsinx=cosx=2j2coth-1xdx=xcoth-1x-½ln|1-x2|+Csech-1xdx=xsech-1x-sin-1x+Cxcoth(=acsch-1xdx=xcsch-1x+sinh-1x+Caxγsech-1(=22aaxaxRbcsch-1(x/a=exexexexsinhx=coshx=22bca正弦定理:===2Rsinsinsinaxax22βαc余弦定理:a2=b2+c2-2bccosαb2=a2+c2-2accosβc2=a2+b2-2abcosγ
sin(α±β=sinαcosβ±cosαsinβcos(α±β=cosαcosβsinαsinβ2sinαcosβ=sin(α+β+sin(α-β2cosαsinβ=sin(α+β-sin(α-β2cosαcosβ=cos(α-β+cos(α+β2sinαsinβ=cos(α-β-cos(α+βx2x3xne=1+x+++++2!3!n!xsinα+sinβ=2sin½(α+βcos½(α-βsinα-sinβ=2cos½(α+βsin½(α-βcosα+cosβ=2cos½(α+βcos½(α-βcosα-cosβ=-2sin½(α+βsin½(α-βtantancotcottan(α±β=,cot(α±β=tantancotcot1=ni1nn(1nx2n1x3x5x7sinx=x-+-+++(2n1!3!5!7!(1nx2nx2x4x6cosx=1-+-+++(2n!2!4!6!(1nxn1x2x3x4ln(1+x=x-+-+++(n1!234(1nx2n1x3x5x7tanx=x-+-+++(2n1357-1ri=½n(n+1i1ni2=i1n1n(n+1(2n+16ii13=[½n(n+1]2x-1-t2x-1tttedt=2edt=002Γ(x=01(lnx-1dtt1r(r12r(r1(r23m-1n-1(1+x=1+rx+x+x+-1β(m,n=x(1-xdx=22sin2m-1xcos2n-1xdx002!3!=希腊字母(GreekAlphabets大写ΑΒΓΔΕΖΗΘ小写0xm1dxmn(1xαβγδεζηθ读音alphabetagammadeltaepsilonzetaetatheta大写ΙΚΛΜΝΞΟΠ小写ικλμνξοπ读音iotakappalambdamunuxiomicronpi大写ΡΣΤΥΦΧΨΩ小写ρσ,ςsigmatauτυupsilonphiφkhiχpsiψωomega读音rho倒数关系:sinθcscθ=1;tanθcotθ=1;cosθsecθ=1商数关系:tanθ=sincos;cotθ=cossin平方关系:cos2θ+sin2θ=1;tan2θ+1=sec2θ;1+cot2θ=csc2θ順位高;顺位高d顺位低;順位低0*=110*==0*=0000=e0(;0=e0;1=e0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(Arithmeticmean中位数(Median众数(Mode几何平均数(Geometricmean调和平均数(HarmonicmeanXX1X2...Xnn取排序后中间的那位数字次数出现最多的数值GnX1X2...XnH11111(...nx1x2xni平均差(AverageDeviatoin变异数(Variance|X1nX|nX2(X1ninor(X1n2Xin1标准差(StandardDeviation(X1niX2分配DiscreteUniformContinuousUniformBernoulliBinomialNegativeBinomialMultinomial机率函数f(x1nn期望值E(x1(n+12or(X1niX2动差母函数m(t1et(1entn1etebteat(batn1变异数V(x12(n+1121ba1(a+b21(b-a212pxq1-x(x=0,1nxn-xxpqkx1kxpqxf(x1,x2,,xm-1=n!xxxp11p22...pmmx1!x2!...xm!pnpkqppqnpqkqp2q+pet(q+petnpk(1qetk三项(p1et1+p2et2+p3nnpi1pknNnpi(1-piqp2NnknN1NGeometricHypergeometricpqx-1kNkxnxNnexx!pett1qePoissonλλe(et1
NormalBetaGamma12e1x2(2μσ2et2t2121x1(1x1B(,(1(2(x1ex(x121tExponentChi-Squaredχ2=f(χ2e=1n22n222tn2E(χ=n(2n122V(χ=2ne22(12tWeibull1ex11212211110000000000000000000000001024yottaY10000000000000000000001021zettaZ10000000000000000001018exaE10000000000000001015petaP10000000000001012teraT1000000000109gigaG十亿1000000106megaM百万1000103kiloK100102hectoH10101decaD0.110-1decid分,十分之一0.0110-2centic厘(或写作「厘」,百分之一0.00110-3millim毫,千分之一0.00000110-6micro?微,百万分之一0.00000000110-9nanon奈,十亿分之一0.00000000000110-12picop皮,兆分之一0.00000000000000110-15femtof飞(或作「费」,千兆分之一0.00000000000000000110-18attoa0.00000000000000000000110-21zeptoz0.00000000000000000000000110-24yoctoy

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