Sometimes known as the Squeezing Theorem.

If

$$ g(x) \le f(x) \le h(x) $$

then

$${\lim_{ x \rightarrow a }} { g(x) }  =  {\lim_{ x \rightarrow a }} { h(x) }   =  {\lim_{ x \rightarrow a }} { f(x) }  $$