Definition:Asymptotic Equality/Real Functions/Point

Definition
Let $f$ and $g$ real functions defined on a punctured neighborhood of $x_0$.

Then:
 * $f$ is asymptotically equal to $g$ at $x_0$


 * $\dfrac {\map f x} {\map g x} \to 1$ as $x \to x_0$.
 * $\dfrac {\map f x} {\map g x} \to 1$ as $x \to x_0$.

That is, the closer $x$ gets to $x_0$, the closer $f$ gets (relatively) to $g$.