Suppose that we have $\lim_{x\to a}f(x)^{g(x)}$ with $f(a)=0$ and $g(a)=0$.
Can we say, that the value of the above limit is $0^0=1$?
Is there a counterexample?
UPDATE: I already saw examples you've provided. Is there a counterexample with continuous functions?
Counter-example: $\lim_{x\to 0} $[1-cosx$]^x$ ,where [ ] stands for greatest integer function.
Edit: Another example I found in the below linked answer : $\lim_{x\to 0+}x^\frac{1}{\ln(x)}$
A similar discussion which took place here: Zero to the zero power – is $0^0=1$?