suppose f is a positive function. if lim_{x->a} f(x) = 0 and lim_{x->a }g(x) = infinity, show that
lim_{x->a} [f(x)]^{g(x) }= 0
this shows that 0 to the infinite power is not an indeterminate form.

Tell your teacher that this is a well known principle.
If \(\displaystyle h(x)\le f(x)\le g(x)\) and \(\displaystyle \lim _{x \to a} h(x) = \lim _{x \to a} g(x)=L\)
then \(\displaystyle \lim _{x \to a} f(x) = L\)