Question

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

Answer 1

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`.