微积分公式
Dxsinx=cosx
cosx=-sinx
tanx=sec2x
cotx=-csc2x
secx=secxtanx
cscx=-cscxcotx (sinxdx=-cosx+C
(cosxdx=sinx+C
(tanxdx=ln|secx|+C
(cotxdx=ln|sinx|+C
(secxdx=ln|secx+tanx|+C
(cscxdx=ln|cscx–cotx|+C sin-1(-x)=-sin-1x
cos-1(-x)=(-cos-1x
tan-1(-x)=-tan-1x
cot-1(-x)=(-cot-1x
sec-1(-x)=(-sec-1x
csc-1(-x)=-csc-1x Dxsin-1()=
cos-1()=
tan-1()=
cot-1()=
sec-1()=
csc-1(x/a)= (sin-1xdx=xsin-1x++C
(cos-1xdx=xcos-1x-+C
(tan-1xdx=xtan-1x-締n(1+x2)+C
(cot-1xdx=xcot-1x+締n(1+x2)+C
(sec-1xdx=xsec-1x-ln|x+c-|+C
(csc-1xdx=xcsc-1x+ln|x+|+C
sinh-1()=ln(x+)xR
cosh-1()=ln(x+)x≧1
tanh-1()=ln()|x|<1
coth-1()=ln()|x|>1
sech-1()=ln(+)0≦x≦1
csch-1()=ln(+)|x|>0 Dxsinhx=coshx
coshx=sinhx
tanhx=sech2x
cothx=-csch2x
sechx=-sechxtanhx
cschx=-cschxcothx (sinhxdx=coshx+C
(coshxdx=sinhx+C
(tanhxdx=ln|coshx|+C
(cothxdx=ln|sinhx|+C
(sechxdx=-2tan-1(e-x)+C
(cschxdx=2ln||+C duv=udv+vdu
(duv=uv=(udv+(vdu
→(udv=uv-(vdu
cos2θ-sin2θ=cos2θ
cos2θ+sin2θ=1
cosh2θ-sinh2θ=1
cosh2θ+sinh2θ=cosh2θ Dxsinh-1()=
cosh-1()=
tanh-1()=
coth-1()=
sech-1()=
csch-1(x/a)= (sinh-1xdx=xsinh-1x-+C
(cosh-1xdx=xcosh-1x-+C
(tanh-1xdx=xtanh-1x+?ln|1-x2|+C
(coth-1xdx=xcoth-1x-?ln|1-x2|+C
(sech-1xdx=xsech-1x-sin-1x+C
+s(csch-1xdx=xcsch-1x+sinh-1x+C
sin3θ=3sinθ-4sin3θ
cos3θ=4cos3θ-3cosθ
→sin3θ=?(3sinθ-sin3θ)
→cos3θ=?(3cosθ+cos3θ)
sinx=cosx=
sinhx=coshx=
正弦定理:===2R
餘弦定理:a2=b2+c2-2bccosα
b2=a2+c2-2accosβ
c2=a2+b2-2abcosγ
sin(α±β)=sinαcosβ±cosαsinβ
cos(α±β)=cosαcosβsinαsinβ
2sinαcosβ=sin(α+β)+sin(α-β)
2cosαsinβ=sin(α+β)-sin(α-β)
2cosαcosβ=cos(α-β)+cos(α+β)
2sinαsinβ=cos(α-β)-cos(α+β) sinα+sinβ=2sin?(α+β)cos?(α-β)
sinα-sinβ=2cos?(α+β)sin?(α-β)
cosα+cosβ=2cos?(α+β)cos?(α-β)
cosα-cosβ=-2sin?(α+β)sin?(α-β)
tan(α±β)=,cot(α±β)= ex=1+x+++…++…
sinx=x-+-+…++…
cosx=1-+-+…++…
ln(1+x)=x-+-+…++…
tan-1x=x-+-+…++…
(1+x)r=1+rx+x2+x3+…-1
=緯(n+1)
1=n(n+1)(2n+1)
=[?n(n+1)]2
Γ(x)=x-1e-tdt=22x-1dt=x-1dt
β(m,n)=m-1(1-x)n-1dx=22m-1xcos2n-1xdx=dx 希臘字母(GreekAlphabets)
大寫 小寫 讀音 大寫 小寫 讀音 大寫 小寫 讀音 Α α alpha Ι ι iota Ρ ρ rho Β β beta Κ κ kappa Σ σ,? sigma Γ γ gamma Λ λ lambda Τ τ tau Δ δ delta Μ μ mu Υ υ upsilon Ε ε epsilon Ν ν nu Φ φ phi Ζ ζ zeta Ξ ξ xi Χ χ khi Η η eta Ο ο omicron Ψ ψ psi Θ θ theta Π π pi Ω ω omega
倒數關係:sinθcscθ=1;tanθcotθ=1;cosθsecθ=1
商數關係:tanθ=;cotθ=
平方關係:cos2θ+sin2θ=1;tan2θ+1=sec2θ;1+cot2θ=csc2θ
;(順位高d順位低;
0(=(==0=
=;=;= 順位一:對數;反三角(反雙曲)
順位二:多項函數;冪函數
順位三:指數;三角(雙曲)
算術平均數(Arithmeticmean) 中位數(Median) 取排序後中間的那位數字 眾數(Mode) 次數出現最多的數值 幾何平均數(Geometricmean) 調和平均數(Harmonicmean) 平均差(AverageDeviatoin)
變異數(Variance) or 標準差(StandardDeviation) or
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) DiscreteUniform (n+1) (n2+1) ContinuousUniform (a+b) (b-a)2 Bernoulli pxq1-x(x=0,1) p pq q+pet Binomial pxqn-x np npq (q+pet)n NegativeBinomial pkqx Multinomial f(x1,x2,…,xm-1)= npi npi(1-pi) 三項(p1et1+p2et2+p3)n Geometric pqx-1 Hypergeometric n n Poisson λ λ Normal μ σ2 Beta Gamma Exponent Chi-Squaredχ2 =f(χ2)= E(χ2)=n V(χ2)=2n Weibull 10000000000000000000000001024yottaY10000000000000000000001021zettaZ10000000000000000001018exaE10000000000000001015petaP10000000000001012teraT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
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