常用函数麦克劳林展开
\(\displaystyle\sin x = x-\frac{1}{3!}x^3+\frac{1}{5!}x^5+o(x^5)\)
\(\displaystyle\cos x=1-\frac{1}{2}x^2+\frac{1}{4!}x^4+o(x^4)\)
\(\displaystyle\tan x=x+\frac{1}{3}x^3+\frac{2}{15}x^5+o(x^5)\)
\(\displaystyle\arcsin x=x+\frac{1}{6}x^3+o(x^3)\)
\(\displaystyle\arctan x=x-\frac{1}{3}x^3+o(x^3)\)
\(\displaystyle\ln(1+x)=x-\frac{1}{2}x^2+\frac{1}{3}x^3+o(x^2)\)
\(\displaystyle e^x=1+x+\frac{1}{2}x^2+o(x^2)\)
\(\displaystyle (1+x)^a=1+ax+\frac{a(a-1)}{2}x^2+o(x^2)\)