泰勒公式 sinx=x−x33!+o(x3)\sin x = x - \frac{x^3}{3!} + o(x^3)sinx=x−3!x3+o(x3) cosx=1−x22!+x44!+o(x4)\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} + o(x^4)cosx=1−2!x2+4!x4+o(x4) arcsinx=x+x33!+o(x3)\arcsin x = x + \frac{x^3}{3!} + o(x^3)arcsinx=x+3!x3+o(x3) tanx=x+x33+o(x3)\tan x = x + \frac{x^3}{3} + o(x^3)tanx=x+3x3+o(x3) arctanx=x−x33+o(x3)\arctan x = 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)