When x approaches 0:
e^x- 1 ~ x；
ln(x+ 1)~ x；
sinx ~ x；
arcs inx ~ x；
tanx ~ x；
arctanx ~ x；
1-cosx ~(x^2)/2；
tanx-sinx ~(x^3)/2；
( 1+bx)^a- 1 ~ abx；
It is worth noting that equivalent infinitesimal substitution is generally used for multiplication and division, but not for addition and subtraction.
Infinitesimal is a variable with zero limit. However, a constant is a special variable, just as a straight line belongs to a curve. So constants can also be studied as variables. So -0 is a constant and can be used as an infinitesimal. On the other hand, equivalent infinitesimal can also be regarded as Taylor expansion from zero to first order.