The equivalent substitution formula of advanced mathematics is as follows:

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).

From Taylor expansion, it can be deduced that the equivalent infinitesimal is an infinitesimal and an infinitesimal of the same order. On the other hand, equivalent infinitesimal can also be regarded as Taylor expansion from zero to first order. ?

Conditions:

1, substitution quantity, when taking the limit, the limit value is 0;

2. The substituted quantity can be replaced by equivalent infinitesimal as the multiplied or divided element, but not as the added and subtracted element.

In fact, the equivalent infinitesimal is derived from Taylor's formula, so the conclusion drawn from the equivalent infinitesimal is that multiplication and division can be changed as a whole, but addition and subtraction cannot be changed, even if they can, it is coincidental and correct. The following happened to be "right"