Question

Evaluate the limit using L'Hospital's rule if necessary.
lim as x goes to +infinity x^(6/x)

Answer 1

I will calculate the limit of the natural log instead. The limit of x^(6/x) will be e to that power of the limit of the log.

ln x^(6/x) = (6/x)ln x = lnx/(x/6)
As x-> infinity, that becomes the limit of 6/x, which is zero

If the log of the limit is zero, the limit itself is 1.