Overview of Sandwich Theorem or Squeeze Theorem

QUICK OVERVIEW

• If two functions squeeze together at a particular point, then any function trapped between them will get squeezed to that same point.
• The Squeeze Theorem deals with limit values, rather than function values.
• The Squeeze Theorem is sometimes called the Sandwich Theorem or the Pinch Theorem

GRAPHICAL REPRESENTATION

Formal Statement:

Suppose f(x)≤g(x)≤h(x)$f(x)\le g(x)\le h(x)$ for all x in an open interval about 
$a$ (except possibly at 
$a$ itself). Further, suppose

limx→af(x)=limx→ah(x)=L${\displaystyle \underset{x\to \mathrm{a }}{lim}f(x)=\underset{x\to \mathrm{a }}{lim}h(x)=L}$

Then, limx→ag(x)=L