常用的等价无穷小 limx→0sinx∼xlimx→0tanx∼xlimx→0arcsinx∼xlimx→0arctanx∼xlimx→0ln(1+x)∼xlimx→0(ex−1)∼xlimx→0(ax−1)∼xlnalimx→0(1−cosx)∼12x2limx→0[(1+x)a−1]∼ax\lim_{x \to 0}\sin x \sim x \\ \lim_{x \to 0}\tan x \sim x \\ \lim_{x \to 0}\arcsin x \sim x \\ \lim_{x \to 0}\arctan x \sim x \\ \lim_{x \to 0}\ln(1+x) \sim x \\ \lim_{x \to 0}(e^x-1) \sim x \\ \lim_{x \to 0}(a^x-1) \sim x\ln a \\ \lim_{x \to 0}(1-\cos x) \sim \frac{1}{2} x^2 \\ \lim_{x \to 0}[(1+x)^a-1] \sim axx→0limsinx∼xx→0limtanx∼xx→0limarcsinx∼xx→0limarctanx∼xx→0limln(1+x)∼xx→0lim(ex−1)∼xx→0lim(ax−1)∼xlnax→0lim(1−cosx)∼21x2x→0lim[(1+x)a−1]∼ax