Thread: About Squeeze Theorem

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?

You can't prove that "f is continuous". What you can prove is that "f is continuous at x=c".

Do you know what "f is continuous at x=c" is defined to mean?

Do you know what g(c) is? (And what's your justification for that?) What about the value of h(c)?
If so, then, given that that inequality (h(x)<=f(x)<=g(x)) holds in some neighborhood of x=c,
what can you say about f(c)?