Question

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? negative startfraction 20 over 1 endfraction negative five-fourths negative four-fifths negative startfraction 1 over 20 endfraction

Answer 1

Since the limit of f(x) is non-zero, the limit distributes over the quotient and

`\displaystyle \lim_(x\to c) (g(x))/(f(x)) = (\displaystyle \lim_(x\to c)g(x))/(\displaystyle \lim_(x\to c)f(x)) = (\frac15)/(-4) = \boxed{-\frac1{20}}`