lim x-> ∞ ln(x-1)-ln(x)

Question

Im stuck in this problem form my calculus hw

Answer 1

Two points to add to Michael J. Answer

1/ If you divide out  (x-1) / x  you get  1 - (1/x)

2/ Limit of the Ln = Ln of the Limit  [for continuous functions]

So  since the Limit (x => ∞) [1 - (1/x)] =  1

Then Ln 1 = 0 

With this approach there is no need for L'Hopital's Rule / No need for a Derivative

 

Answer 2

lim         ln((x - 1) / x)

x->∞

 

This will give you an indeterminate form if you plug in x=∞.  You need to take the derivative of the function.

 

lim        (1 / (x - 1)) - (1/x)   =  0

x->∞