Category:Squeeze Theorem for Functions

This category contains pages concerning Squeeze Theorem for Functions:

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:

$\forall x \ne a \in I: \map g x \le \map f x \le \map h x$

$\ds \lim_{x \mathop \to a} \map g x = \lim_{x \mathop \to a} \map h x = L$

Then:

$\ds \lim_{x \mathop \to a} \ \map f x = L$