squeeze theorem

[Math] Limit Laws of Multivariate Function

1. Limit Laws Assume that $S\subseteq \mathbb{R}^n$ and that $\textbf{a}$ is a point in $\textbf{R}^n$ is a limit point of $S$ (for example, an interior point of $S$). Further assume that $f,g:S\to \mathbb{R}$ are functions and $L$,$M$ are numbers such that $$\lim_{\mathbf x \to \mathbf a}f(\mathbf x) = L, \qquad \lim_{\mathbf x \to \mathbf a}g(\mathbf x) = M.$$ Then $$\lim_{\textbf x \to \textb..