Posted by <3 on Friday, February 19, 2010 at 1:37am.
Evaluate the limit using L'Hospital's rule if necessary.
lim as x goes to +infinity x^(6/x)

Calculus  drwls, Friday, February 19, 2010 at 4:10am
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.
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