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 $\displaystyle \lim_{x\to 1} ~g(x)\,$?
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