Can someone tell me how to solve this problem and what the answer is.?

Question

Lim(x-ln(x^2+1))
as x approaches infinity

Answer 1

That appears not to have a limit.
Consider
lim x - lim (ln(x^2 + 1) as x goes to infinity
Both increase without bound. x increases faster than ln (x^2 + 1), so the difference is not enough to cause the function to settle down to any finite value.
Consider the graphs, sometimes that can give you a clue. When you graph this equation it does not appear to have any asymptotes, which indicate limits.
Are you missing sometihng? Like another ln? If there were an ln in front of the first x, that is,
lim (lnx - ln(x^2 + 1)) as x approaches infinity this would be a more interesting question.

Answer 2

Yes! some one definitely can.