Stuck on a basic calc problem: infinity - infinity

[Stompy]

To be exact, the limit of x - ln(x) as x approaches infinity.

I know the limit is infinity, but I can't exactly recall how to get this equation in an infinity/infinity format.

We're doing the improper integrals in Calc 2, and the problem above is obviously a precursor to that, but.. I haven't done these problems in ages so I've forgotten the more advanced methods of doing em.

I asked the teacher and he said something about factoring x, but I don't see how you can factor x out of that. You'd get x(1-?). Unless I'm missing something, you can't just pull x outta the ln.

I tried to search for this on google, but I get every problem BUT this one. Their exact search doesn't seem to process "x - ln(x)" properly.

[evil308]

factor it like your prof hinted: x(1 - (1/x)*ln(x))

1/x * ln (x) can be written as ln( x^(1/x)) if you prefer. What's the limit of x^(1/x) as x goes to infinity? Use your calculator to plug in 10^9 for x and its 1.01.. so yeah its 1.
You are left with: x(1 - ln(1))

[Stompy]

Ah yes... I don't know why I couldn't see that! (the 1/x * ln(x))

Thanks a ton