how to find lim (-ln(x))^x
x->0+
This can be done any number of ways. Here is one, first note that . Here I will use . If you would like to prove this to yourself try finding the absolute maximum of and noting its sign.
So now here is what we have
was made by the substitution and was done using the continuity of the exponential function.
So now let us note something
Cutting out the uneccessary step gives us
So this implies that
Now
So we can see that
Which by the Squeeze Theorem indicates that
So then
So we can finally conclude that