English wording for "first level of asymptotic expansion"

Question

In French, we say that $f$ est équivalente à $g$ denoted by $f \sim g$ for a limit point $x_0$ of a topology when $$\lim\limits_{x \to x_0} \frac{f(x)}{g(x)} = 1.$$

This is the first level of asymptotic expansion in English. However it seems that the word equivalent cannot be used in English.

Is there an appropriate wording in English for "first level of asymptotic expansion"?

Answer 1

Using rrr8 comment as an answer.

You would just say $f$ is asymptotic to $g$.