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 $1\,$, $\qquad \displaystyle \lim_{x \to 1}f(x)=2 ~$ and $~ \displaystyle \lim_{x\to 1}~h(x)=2\,$. What is the value of $\displaystyle \lim_{x\to 1} ~g(x)\,$? [[☃ math-keypad 1]]