Squeeze Theorem/Functions

Theorem
Let $a$ be a point on an open real interval $I$.

Let $f$, $g$ and $h$ be real functions defined at all points of $I$ except for possibly at point $a$.

Suppose that:
 * $\forall x \ne a \in I: \map g x \le \map f x \le \map h x$
 * $\displaystyle \lim_{x \mathop \to a} \ \map g x = \lim_{x \mathop \to a} \ \map h x = L$

Then:
 * $\displaystyle \lim_{x \mathop \to a} \ \map f x = L$