# Limit of this at infinity?

1. Apr 11, 2008

### motornoob101

1. The problem statement, all variables and given/known data

$$\lim x-> \infty [x+1-ln(x+1)]$$

2. Relevant equations

3. The attempt at a solution
How does one evaluate this? I don't know how to use L'Hopital's rule on this and I have infinity- infinity, which is indeterminate. Thanks!

2. Apr 11, 2008

### HallsofIvy

Staff Emeritus
There is a fairly standard technique for going from "a-b" that leads to "$\infty$- $\infty$" to a "0/0" or "$\infty/\infty$", given in every Calculus text I know: multiply both numerator and denominator by the "conjuate" a+ b. In this case that gives
$$\frac{(x+1)^2- (ln(x+1))^2}{x+1+ ln(x+1)}$$
That is now of the form "$\infty/\infty$" and you can use L'Hopital's rule.

3. Apr 11, 2008

Ok thanks.