Limit Laws.

Let $c$ be a constant and let the limits $\lim _{x \rightarrow a} f(x)$ and $\lim _{x \rightarrow a} g(x)$ exist. Then

(a) $\lim _{x \rightarrow a}(f(x) \pm g(x))=\lim _{x \rightarrow a} f(x) \pm \lim _{x \rightarrow a} g(x)$

(b) $\lim _{x \rightarrow a}(c \cdot f(x))=c \cdot \lim _{x \rightarrow a} f(x)$

(c) $\lim _{x \rightarrow a}(f(x) \cdot g(x))=\lim _{x \rightarrow a} f(x) \cdot \lim _{x \rightarrow a} g(x)$

(d) $\lim _{x \rightarrow a} \frac{f(x)}{g(x)}=\frac{\lim _{x \rightarrow a} f(x)}{\lim _{x \rightarrow a} g(x)}$ if $\lim _{x \rightarrow a} g(x) \neq 0$.