Without using series expansion of and binomial expansion of evaluate the limit :
Also,you cannot use the L'Hospital rule.
Or avoiding series the fact that and the definition of (3rd) derivative to give:
(here denotes a function such that the limit as goes to of this function divided by goes to zero) which will allow the evaluation of the limit.
I suspect though that you might consider all this to be cheating as this is tantamount to either L'Hopital's rule and/or the use of series)