Answer
$f(x)$ is continuous at $0$.
Work Step by Step
When $f(0)=\lim\limits_{x\to 0} f(x)$, then $f(x)$ will be continuous at $x=0$.
$\lim\limits_{x\to 0^{-}}f(x)=\lim\limits_{x\to 0^{-}} 3 \cos x=3\cos 0 =3*1=3$
and $\lim\limits_{x\to 0^{+}}f(x)=\lim\limits_{x\to 0^{+}} \dfrac{x^2 (x+3)}{x^2} =3+0=3$
and $\lim\limits_{x\to 0}f(x)=3$
Since, $f(0)=3$, we can see that our result satisfies the statement because $3 = 3$. Terefore, $f(x)$ is continuous at $0$.
