Evaluating the Limit of a Function at Infinity: [x+1-ln(x+1)]

[motornoob101]

Homework Statement

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

Homework Equations

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!

 

[HallsofIvy]

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.

 

[motornoob101]

Ok thanks.