Question

let f and g be two continuous functions and f(c)=g(c)=0
for what condition do we have \[\lim_{x\to c}(f(x))^{g(x)}=e\]

Answer 1

i think there is a mistake in this problem
i believe the condition is concerning this limit
\[\lim_{x\to c}g(x)\ln (f(x))=1\]
but then i have problem at 0 with this