Solution
= Solution
The <Big O notation> means that there exist constants $C>0$ and $\delta>0$ such that
$$
\boxed{|f(x)|\leq C|x|^2\quad\text{whenever}\quad0<|x|<\delta}
$$
within the domain of $f$. Thus $f(x)/x^2$ stays bounded in a punctured neighbourhood of zero. It need not have a limit: $f(x)=x^2\sin(1/x)$ is one example. The statement imposes no condition on a separately assigned value $f(0)$.