Answer
(a) Prove Theorem 4, part 3
$\lim\limits_{x \to a}$$f(x)$ $=$ $f(a)$
$c$$\lim\limits_{x\to a}$$f(x)$ $=$ $c$$f(a)$
$\lim\limits_{x \to a}$$c$$f(x)$ $=$ $c$$f(a)$
$Proved$
$(b)$ $Prove$ $Theorem 4$ $,$ $part5$
$\lim\limits_{x \to a}$ $\frac{f(x)}{g(x)}$ $=$ $\frac{\lim\limits_{x \to a}f(x)}{\lim\limits_{x \to a} g(x)}$ $=$ $\frac{f(a)}{g(a)}$ $=$ $\frac{f}{g}$$(a)$
$Proved$
Work Step by Step
$(a)$ $Prove$ $Theorem 4$ $,$ $part3$
$\lim\limits_{x \to a}$$f(x)$ $=$ $f(a)$
$c$$\lim\limits_{x\to a}$$f(x)$ $=$ $c$$f(a)$
$\lim\limits_{x \to a}$$c$$f(x)$ $=$ $c$$f(a)$
$Proved$
$(b)$ $Prove$ $Theorem 4$ $,$ $part5$
$\lim\limits_{x \to a}$ $\frac{f(x)}{g(x)}$ $=$ $\frac{\lim\limits_{x \to a}f(x)}{\lim\limits_{x \to a} g(x)}$ $=$ $\frac{f(a)}{g(a)}$ $=$ $\frac{f}{g}$$(a)$
$Proved$
