Squeeze Theorem

Definition

Squeeze Theorem for Functions

Suppose $f,g,h:\mathcal{D}\to \mathbb{R}$, $L\in \mathbb{R}$, and $\forall x\in \mathcal{D}-\{a\},f(x)\le g(x)\le h(x)$

If $\underset{x\to a}{\lim }f(x)=\underset{x\to a}{\lim }h(x)=L$, then $\underset{x\to a}{\lim }g(x)=L$

Squeeze Theorem for Sequences

Suppose $(a_n),(c_n)$ be two sequences converging to $L\in \mathbb{R}$, and $(b_n)$ be a Sequence.

If $\underset{n\to \infty }{\lim }{a}_n\le \underset{n\to \infty }{\lim }{b}_n\le \underset{n\to \infty }{\lim }{c}_n$, then $\underset{n\to \infty }{\lim }{b}_n=L$