lim3^nn^3

As the limit is not specified, we assume that n approaches infinity.

Using L'Hopital's rule, we can rewrite the expression as:

lim (3^n) / (n^3)

Taking the derivative of both the numerator and denominator with respect to n:

lim (3^n * ln(3)) / (3n^2)

Using the limit rule for exponential functions, we know that as n approaches infinity, 3^n grows faster than any polynomial function of n. Therefore, the denominator grows much slower than the numerator, and the limit approaches infinity.

Thus, lim3^n/n^3 = infinity