Squeeze Theorem

Squeeze theorem: Let $(a_n)$, $(b_n)$, and $(c_n)$ be real sequences such that $a_n \le b_n \le c_n$ for all sufficiently large $n$. If $a_n \to L$ and $c_n \to L$, then $b_n \to L$.

This theorem is a standard tool for proving convergence without explicitly computing a limit, and it has an analogous form for limits at a point of functions.