How do you find the Limit of #(x-lnx)# as x approaches infinity?

1 Answer
Gió
Dec 12, 2016

I found #oo#

Explanation:

I tried some simple substitution to try to understand the behaviour of the function.
In particular I noticed the if #x# increases then also #ln(x)# increases BUT more slowly!
For example:
If #x=1,000# then #ln(1,000)=6.9#
If #x=1,000,000# then #ln(1,000,000)=13.8#
So I concluded that the limit should be #oo# because #x# "wins" over #ln(x)# going towards #oo#.

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