Respuesta :

LammettHash

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

[tex]\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)}[/tex]

In this case,

[tex]\displaystyle\lim_{x\to4}\frac gh(x)=\lim_{x\to4}\frac{g(x)}{h(x)}=\frac0{-2}=2[/tex]

so the answer is B.

kudzordzifrancis

ANSWER

b. 0

EXPLANATION

We use the property of limits;

[tex]lim_{x\to 4} \frac{g}{h} (x) = lim_{x\to 4} \frac{g(x)}{h(x)}[/tex]

[tex]lim_{x\to 4} \frac{g}{h} (x) = \frac{lim_{x\to 4}g(x)}{lim_{x\to 4}h(x)}[/tex]

Substitute,

[tex]lim_{x\to 4} \frac{g}{h} (x) = \frac{0}{ - 2}[/tex]

Simplify;

[tex]lim_{x\to 4} \frac{g}{h} (x) =0[/tex]

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