Answer
1. $\lim\limits_{x \to c} [f(x) ±g(x)] = ∞$
2. $\lim\limits_{x \to c} [f(x)\times g(x)] = ∞, L>0$ or $\lim\limits_{x \to c} [f(x)\times g(x)] =-∞, L<0$
3. $\lim\limits_{x \to c} \frac{g(x)}{f(x)} =0$
Work Step by Step
1. $\lim\limits_{x \to c} [f(x) ±g(x)]$: Sum difference and property of limits
$\lim\limits_{x \to c} f(x)± \lim\limits_{x \to c} g(x)$
$\lim\limits_{x \to c} f(x)$ = ∞ | $\lim\limits_{x \to c} g(x) =L$
Therefore: $∞±L =∞ $
2. $\lim\limits_{x \to c} [f(x)\times g(x)]$: Product property of limits
$\lim\limits_{x \to c} f(x)\times \lim\limits_{x \to c} g(x)$
$\lim\limits_{x \to c} f(x)$ = ∞ | $\lim\limits_{x \to c} g(x) =L$
Therefore: $∞\times L =∞ $ if $L>0$ and $∞\times L =-∞ $ if $L<0$
3. $\lim\limits_{x \to c} \frac{g(x)}{f(x)} =0$: Quotient property of limits
$\frac{\lim\limits_{x \to c} g(x)}{\lim\limits_{x \to c} f(x)}$
$\lim\limits_{x \to c} f(x)$ = ∞ | $\lim\limits_{x \to c} g(x) =L$
Therefore: $\frac{L}{∞}$ = $0$
