Let the functions in the theorem be defined as h(x), f(x), and g(x).

h(x) =< f(x) =< g(x)
lim (x->c) for all of these functions in L. (if h(x) and g(x) have the same limit, so will f(x))

How could I prove that f(x) is continuous, given that h(x) and g(x) are continuous?