Given limit of f (x) = negative 4 as x approaches c and limit of g (x) = one-fifth as x approaches c. what is limit of left-bracket startfraction g (x) over f (x) endfraction right-bracket as x approaches c?

Respuesta :

It looks like we're given

[tex]\displaystyle \lim_{x\to c} f(x) = -4[/tex]

[tex]\displaystyle \lim_{x\to c} g(x) = \frac15[/tex]

Since the limit of f(x) is finite and non-zero, we have by the quotient rule for limits

[tex]\displaystyle \lim_{x\to c}\frac{g(x)}{f(x)} = \frac{\displaystyle \lim_{x\to c}g(x)}{\displaystyle \lim_{x\to c} f(x)} = \frac{-4}{\frac15} = \boxed{-20}[/tex]