常用的泰勒公式

e^x = 1+x+x^2/2!+x^3/3!+……+x^n/n!+……

ln(1+x)=x-x^2/2+x^3/3-……+(-1)^(k-1)*(x^k)/k(|x|<1)

sin x = x-x^3/3!+x^5/5!-……+(-1)^(k-1)*(x^(2k-1))/(2k-1)!+……。(-∞<x<∞)

cos x = 1-x^2/2!+x^4/4!-……+(-1)k*(x^(2k))/(2k)!+…… (-∞<x<∞)

tanx=x+x^3/3+2x^5/15+17x^7/315+62x^9/2835++[2^(2n)*(2^(2n)-1)*B(2n-1)*x^(2n-1)]/(2n)!+.(|x|<π

/2) arcsin x = x + 1/2*x^3/3 + 1*3/(2*4)*x^5/5 + ……(|x|<1)

arccos x = π - ( x + 1/2*x^3/3 + 1*3/(2*4)*x^5/5 + …… ) (|x|<1)

arctan x = x - x^3/3 + x^5/5 -……(x≤1)

sh x = x+x^3/3!+x^5/5!+……+(-1)^(k-1)*(x^2k-1)/(2k-1)!+…… (-∞<x<∞)

ch x = 1+x^2/2!+x^4/4!+……+(-1)k*(x^2k)/(2k)!+……(-∞<x<∞)

arcsh x = x - 1/2*x^3/3 + 1*3/(2*4)*x^5/5 - …… (|x|<1)

arcth x = x + x^3/3 + x^5/5 + ……(|x|<1)

（1+z）^m=1^m{1+m/1!*z=m*(m-1)/2!*z^2+m*(m-1)*(m-2)/3!*z^3+……},(|z|<1)