To satisfy those wishing a more strict interpretation of how the power function should act, the 2008 standard defines two additional power functions : pown ( x, n ), where the exponent must be an integer, and powr ( x, y ), which returns a NaN whenever a parameter is a NaN or the exponentiation would give an indeterminate form.
42.
:While I think there is a clever substitution to turn the first limit into the reciprocal of the second, I would tend to define a _ n = ( 1-\ tfrac1n ) ^ n, then consider \ log ( a _ n ) = \ log ( 1-\ tfrac1n ) / \ tfrac1n whose limit is an indeterminate form of \ tfrac00 and apply L'Hospital's rule.
