Question

find the limit using l'hospital's rule
lim x-->negative infinity (x ln(1-1/x)

Answer 1

x ln(1 - 1/x) = ln(1 - 1/x) / (1/x)
so the limit is the same as
[1/(1 - 1/x) * (1/x^2)] / (-1/x^2) = -1/(1 - 1/x)
in the limit as x→∞, that is just -1