常用函数泰勒展开公式

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)!+……。(-∞cos x = 1-x^2/2!+x^4/4!-……+(-1)k*(x^(2k))/(2k)!+…… (-∞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)
sinh x = x+x^3/3!+x^5/5!+……+(-1)^(k-1)*(x^2k-1)/(2k-1)!+…… (-∞cosh x = 1+x^2/2!+x^4/4!+……+(-1)k*(x^2k)/(2k)!+……(-∞arcsinh x = x - 1/2*x^3/3 + 1*3/(2*4)*x^5/5 - …… (|x|<1)
arctanh x = x + x^3/3 + x^5/5 + ……(|x|<1)