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Math Help - About Squeeze Theorem

  1. #1
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    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?
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  2. #2
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    Re: About Squeeze Theorem

    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)?
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