What is the limit as x approaches 1+ of the function (lnx)^x-1?
It is in the form 0^0, but how do I rewrite it so it is in 0/0 or inf/inf form?
It is in the form 0^0, but how do I rewrite it so it is in 0/0 or inf/inf form?
1 Answer
Explanation:
Call the limit L:
Take the natural logarithm of both sides:
Now using the properties of logarithms, we can express the exponent as a product of the
Now we can express this as
which is of the form
Note that as
Therefore
We can now use L'Hôpital's Rule
Which is now of the form
Let's try L'Hôpital one more time:
Now recall that we took the natural log of the original limit, so
Therefore,