The notation $f(x) = O(g(x))$ as $x \to \infty$ is used to mean that for sufficiently large values of $x$, we have $|f(x)| \leq A g(x)$ for some constant $A$.
Similarly write $f(x) = O(g(x))$ as $x \to 0$ if for $x$ sufficiently small, $|f(x)| \leq A g(x)$ for some constant $A$.