well the answer is -e/2, but I can't seem to get the answer...mostly due the fact that there is a 1/x power on the 1+x polynomial and how to implement it with
L'Hopitale's rule...?
Well, so you can use l'Hopital's rule.
To get the derivative of you can use logarithmic differentiation.
Edit: My mistake: , NOT e. l'H CANNOT be used. See post #4.
The limit >is< meant to be x --> 0. so l'Hospital's Rule can be used.
To get the derivative of :
.
So the limit becomes:
.
Now show that .
Multiple applications of l'Hospital's rule is one possible approach.
Another approach is to substitute the series expansion for ln (1 + x): . This substitution is valid since the series converges for and ......