Question

suppose lim[x:4,f(x)=4] and lim[x:4,g(x)= -2], find,
lim[x:4,g(x)/f(x)-1]

Answer 1

use quotient rule for taking derivative.

Answer 2

This appears to be a problem of limits. The very question states that the limits f(x)=4 and g(x)=-2 as x approaches 4 means we can assume those limits exist. Because we know:

lim f(x)/g(x) = lim f(x)/lim g(x) .... the question becomes a simple substitution problem. If lim g(x)=0, the problem wouldn't have a defined solution.

however our answer will be:

lim[x:4, f(x)/g(x) -1]

=(4)/(-2) -1

=-2-1

=-3