Let $f(x)=\left\{\begin{array}{lll}{[x]+1} & x \neq n \pi & n \in I \\ 3 & & \text { otherwise }\end{array}\right.$ and $g(x)=\left\{\begin{array}{ll}x^2+1 & x \neq 0,3 \\ 3 & x=0 \\ 5 & x=3\end{array}\right.$, the $\lim\limits_{x \rightarrow 0}(f(x))$ is, (where [.] denotes the greatest integer function)

2

$\lim\limits_{x \rightarrow 0^{+}} f(x)=2$

$\lim\limits_{x \rightarrow 0^{-}} g(x)=3 $

Hence (2) is the correct answer.