1. Limit LawsAssume that $S\subseteq \mathbb{R}^n$ and that $\textbf{a}$ is a point in $\mathbb{R}^n$ 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 \textbf a}[..