common uses

${\displaystyle \sin x\sim x}$${\displaystyle \tan x\sim x}$${\displaystyle \arcsin x\sim x}$${\displaystyle \arctan x\sim x}$${\displaystyle \ln (x+1)\sim x}$${\displaystyle e^x-1\sim x}$

${\displaystyle x-\sin x\sim -\frac{1}{6}{x}^3}$${\displaystyle 1-\cos x\sim \frac{1}{2}{x}^2}$

${\displaystyle a^x-1\sim x\ln a}$