lim ((1+x)^(1/x)-e)/x can yu do it by l,hospital rule
You can but it get really nasty! Are you required to us L'Hopital's rule?
Originally Posted by prasum
It's much easier if you recognize that letting 1/x= p gives
lim(p-> infinity) (1+ 1/p)^p = e. This turns out to be, essentially, a derivative.
Originally Posted by HallsofIvy
i have done by substituting (1+x)^1/x=e^((1/x)(ln(1+x))) so appling expansion of e we get limit as -e/2 can yu please suggest graphical approach