In using the Equivalent Infinitesimal Substitution to find the limit, 1: when x tends to 0, sin (f (x)) ~ f (x) 2: when f (x) tends to 0, sin (f (x)) ~ f (x) which is correct

In using the Equivalent Infinitesimal Substitution to find the limit, 1: when x tends to 0, sin (f (x)) ~ f (x) 2: when f (x) tends to 0, sin (f (x)) ~ f (x) which is correct

The second one is right
According to the Equivalent Infinitesimal Substitution: when t → 0, Sint ~ t
Let t = f (x) → 0, that is sin (f (x)) ~ f (x)

What is the limit of type 0 / 0, that is, infinitesimal / infinitesimal?

What you said upstairs is not necessarily right
The existence of infinitesimal / infinitesimal limit depends on what kind of infinitesimal the numerator is
If the numerator is infinitesimal of lower order of denominator, then the limit does not exist
If the numerator is infinitesimal of the same order as the denominator, the limit can be obtained by using the law of lobita
If the numerator is the infinitesimal of higher order of denominator, then the limit value is 0

Incomprehension of infinitesimal: F (x) has limit a if and only if f (x) = a + α, α is infinitesimal
What does this mean? Doesn't f (x) change

F (x) has limit a if and only if f (x) = a + α
Alpha is changing, too
It means that f (x) is very close to limit a and the difference is infinitesimal