sinx=x−x33!+o(x3)sinx=x-\frac{x^3}{3!}+o(x^3)sinx=x−3!x3+o(x3)
cosx=1−x22!+x44!+o(x4)cosx=1-\frac{x^2}{2!}+\frac{x^4}{4!}+o(x^4)cosx=1−2!x2+4!x4+o(x4)
tanx=x+x33+o(x3)tanx=x+\frac{x^3}{3}+o(x^3)tanx=x+3x3+o(x3)
arcsinx=x+x33!+o(x3)arcsinx=x+\frac{x^3}{3!}+o(x^3)arcsinx=x+3!x3+o(x3)
arctanx=x−x33+o(x3)arctanx=x-\frac{x^3}{3}+o(x^3)arctanx=x−3x3+o(x3)
ln(1+x)=x−x22+x33+o(x3)ln(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}+o(x^3)ln(1+x)=x−2x2+3x3+o(x3)
ex=1+x+x22!+x33!+o(x3)e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+o(x^3)ex=1+x+2!x2+3!x3+o(x3)
(1+x)α=1+αx+α(α−1)2!x2+o(x2)(1+x)^{\alpha}=1+{\alpha}x+\frac{\alpha(\alpha-1)}{2!}x^2+o(x^2)(1+x)α=1+αx+2!α(α−1)x2+o(x2)
