The Squeeze Theorem

If $h(x)\le f(x) \le g(x)$ for all $x$ in an open interval containing $c$ , except possibly at $c$ , and if

$$\lim_{x\to c} h(x)=L=\lim_{x\to c}g(x)$$

then $\lim_{x\to c}f(x)$ exists and is equal to $L$ .