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Let:limx→c g(x)=Llimx→c h(x)=Lg(x)≤f(x)≤h(x) except perhaps at x=c.Let xn be a sequence of points of (a..b) such that:∀n∈N>0:xn≠cand:limn→∞ xn=c
By Limit of Function by Convergent Sequences:
limn→∞ g(xn)=Land:limn→∞ h(xn)=L
g(xn)≤f(xn)≤h(xn)it follows from the Squeeze Theorem for Sequences of Real Numbers that:limn→∞ f(xn)=L
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In calculus, the squeeze theorem (known also as the pinching theorem, the sandwich theorem, the sandwich rule and sometimes the squeeze lemma or the "Kathy Theorem") is a theorem regarding the limit of a function. The squeeze theorem is used in calculus and mathematical analysis.
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