Suppose the functions $f, g$, and $h$ have the property that for all $x$ in an open interval
containing $c$, except possibly at $c$,
$
f(x) \leq g(x) \leq h(x)
$
If
$
\lim _{x \rightarrow c} f(x)=\lim _{x \rightarrow c} h(x)=L
$
then $\quad \lim _{x \rightarrow c} g(x)=L$