Answer:
1/4 = 0.25
Step-by-step explanation:
I assume you mean
lim((ln(x) - ln(4)) / (x - 4))
ln(x) - ln(4) = ln(x/4)
rule of l'hopital
lim f(x)/g(x) = lim f'(x)/g'(x)
if g'(x) <> 0
f(x) = ln(x/4)
g(x) = x - 4
ln(x)' = 1/x
ln(x/4)' = 1/x/4 × 1/4 = 1/x
(x - 4)' = 1
so,
lim f'(x)/g'(x) = 1/x / 1 = 1/x
which is for x approaching 4 : 1/4 = 0.25
