Are you allowed to use L'Hospital's Rule? Are you allowed to use the facts that and ?
Not even sure how to approach this one:
(I have to write this without latex, since it seems to be down right now)
Show that lim (n-->infinity) (1+x/n)^n = e^x
My only thought is to restate this in a limit definition fashion, but it's not getting me anywhere:
lim (n-->infinity) n ln(1+x/n)
I know that lim (n-->infinity) (1+1/n)^n = e, but I can't seem to find the connection between these two equations.
Any help is appreciated.
Thanks!