Welcome to Bytelearn!

Let’s check out your problem:

Let $g(x)=-\frac{x}{3 \sin (x-2)}$.$\newline$Select the correct description of the one-sided limits of $g$ at $x=2$.$\newline$Choose $1$ answer:$\newline$(A)$\newline$$$\begin{array}{l} \lim _{x \rightarrow 2^{+}} g(x)=+\infty \text { and } \\ \lim _{x \rightarrow 2^{-}} g(x)=+\infty \end{array}$$$\newline$(B)$\newline$$$\begin{array}{l} \lim _{x \rightarrow 2^{+}} g(x)=+\infty \text { and } \\ \lim _{x \rightarrow 2^{-}} g(x)=-\infty \end{array}$$$\newline$(c)$\newline$$$\begin{array}{l} \lim _{x \rightarrow 2^{+}} g(x)=-\infty \text { and } \\ \lim _{x \rightarrow 2^{-}} g(x)=+\infty \end{array}$$$\newline$(D)$\newline$$$\begin{array}{l} \lim _{x \rightarrow 2^{+}} g(x)=-\infty \text { and } \\ \lim _{x \rightarrow 2^{-}} g(x)=-\infty \end{array}$$