The usefulness of the squeeze theorem is almost exclusively (in my experience) presented by a trig function, since the elementary functions sine and cosine are bounded; namely -1 ≤ sin x, cos x ≤ 1 for all x.(adsbygoogle = window.adsbygoogle || []).push({});

I'm looking for an example of the squeeze theorem involving elementary real-valued functions aside from trig functions. Namely, functions P, Q and F such that P(x) ≤ F(x) ≤ Q(x) for all x near some value x_{0}and P and Q have the same limits at x_{0}. Of course it is not necessary that F(x_{0}) be defined, in fact it might be a better example if it is not immediately clear how to evaluate the limit of F at x_{0}.

Probably, P and Q would be polynomials, and F is a rational function discontinuous at x_{0}.

(If you're wondering, I'm a math tutor and I want to present an example of the squeeze theorem but I haven't introduced trig functions yet. In fact I will use the squeeze theorem to develop the derivatives of the sine and cosine functions.)

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# Examples of squeeze theorem

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