Question

Find the limit (Picture Provided)

Answer 1

As long as $g(x)$ (or whichever function appears in the denominator) does not approach 0 as $x\to c$,

$\displaystyle\lim_{x\to c}\frac{f(x)}{g(x)}=\frac{\lim\limits_{x\to c}f(x)}{\lim\limits_{x\to c}g(x)}$

In this case,

$\displaystyle\lim_{x\to4}\frac gh(x)=\lim_{x\to4}\frac{g(x)}{h(x)}=\frac0{-2}=2$

so the answer is B.

Answer 2

ANSWER

b. 0

EXPLANATION

We use the property of limits;

$lim_{x\to 4} \frac{g}{h} (x) = lim_{x\to 4} \frac{g(x)}{h(x)}$

$lim_{x\to 4} \frac{g}{h} (x) = \frac{lim_{x\to 4}g(x)}{lim_{x\to 4}h(x)}$

Substitute,

$lim_{x\to 4} \frac{g}{h} (x) = \frac{0}{ - 2}$

Simplify;

$lim_{x\to 4} \frac{g}{h} (x) =0$