当 \(f(x) \rightarrow 0\) 时，有：

\[\begin{align} \sin f(x) &\backsim f(x) \\ \tan f(x) &\backsim f(x) \\ \ln (1+f(x)) &\backsim f(x) \\ e^{f(x)} - 1 &\backsim f(x) \\ \arcsin f(x) &\backsim f(x) \\ \arctan f(x) &\backsim f(x) \\ \log_a (1+f(x)) &\backsim \cfrac{f(x)}{\ln a} \\ a^{f(x)} - 1 &\backsim f(x) \ln a \\ 1-\cos f(x) &\backsim \cfrac{1}{2} f^2(x) \\ \ln(f(x)+\sqrt{1+f^2(x)}) &\backsim f(x) \\ f(x) - \sin f(x) &\backsim \cfrac{1}{6} f^3(x) \\ \tan f(x) - f(x) &\backsim \cfrac{1}{3} f^3(x) \\ (1 + f(x))^ \alpha - 1 &\backsim \alpha f(x) \\ \arcsin f(x) - f(x) &\backsim \cfrac{1}{6} f^3(x) \\ f(x) - \arctan f(x) &\backsim \cfrac{1}{3} f^3(x) \\ \tan f(x) - \sin f(x) &\backsim \cfrac{1}{2} f^3(x) \end{align} \]