The graphs of the continuous functions $f$ (in blue), $g$ (in green), and $h$ (in red) are shown below. It is given that $\qquad f(x)\le g(x) \le h(x)~$ for all $\,x\,$ near $3$, $\qquad \displaystyle \lim_{x \to 3}f(x)=2 ~$ and $~ \displaystyle \lim_{x\to 3}~h(x)=2$. What is the value of $\displaystyle \lim_{x\to 3} ~g(x)\,$? [[☃ input-number 1]]