When x→0 and x≠0, then x~sinx~tanx~arcsinx~arctanx.

x~ln( 1+x)~(e^x- 1)。

( 1-cosx)~x*x/2 .

[( 1+x)^n- 1]~nx。

loga( 1+x)~x/lna .

X power of a ~xlna.

(1/n power of (1+x) ~ 1/nx(n is a positive integer).

Related introduction

Equivalent infinitesimal is a relationship between infinitesimals, which means that if the limit of the ratio of two infinitesimals is 1 in the trend process of the same independent variable, the two infinitesimals are said to be equivalent. The equivalence relation of infinitesimals describes that two infinitesimals tend to zero at the same speed.

Equivalent infinitesimal replacement is a common method to calculate indefinite limit, which can simplify complex problems and simplify complex ones.