lean_workbook_plus_27728

Let $a\in\mathbb{R}$ and let $f,g,h$ be real-valued functions such that $f(x)\le g(x)\le h(x)$ for all $x$ in an open interval containing $a$ (but not necessarily at $a$ itself). If $\lim_{x\to a}f(x)=\lim_{x\to a}h(x)=L$, then $\lim_{x\to a}g(x)=L$ as well.