Asked by Katy
find the limit using l'hospital's rule
lim x-->negative infinity (x ln(1-1/x)
lim x-->negative infinity (x ln(1-1/x)
Answers
Answered by
oobleck
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
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
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