lim x -> ∞ (x - lnx)

Tedjn

Here is another approach. It is easy to show that for x > e the function (1/e)x is greater than the function ln(x) by comparing derivatives. So, for x > e, x-(1/e)x < x-ln(x), which gives a lower bound for our function. This lower bound is unbounded, which is enough to show that our original function is unbounded.

Tedjn	Here is another approach. It is easy to show that for x > e the function (1/e)x is greater than the function ln(x) by comparing derivatives. So, for x > e, x-(1/e)x < x-ln(x), which gives a lower bound for our function. This lower bound is unbounded, which is enough to show that our original function is unbounded.