The Sandwich Theorem

#calc/theorem
If $g(x)\le f(x)\le h(x)$ for all $x\ne c$ in some interval about $c$, and ${\displaystyle \underset{x\to c}{lim}g(x)=\underset{x\to c}{lim}h(x)=L}$, then ${\displaystyle \underset{x\to c}{lim}f(x)=L}$.

• Basically, all this is saying is that if two functions sandwich a third function, and they touch/almost touch at a point, then the sandwiched function, being “squished” between the two functions, also has to be at that point.

Examples