Chapter 4 - Section 4.4 - Indeterminate Forms and l''Hospital''s Rule - 4.4 Exercises - Page 314: 86

$\lim\limits_{x \to a}[f(x)]^{g(x)} = 0$

$\lim\limits_{x \to a}[f(x)]^{g(x)}$ $= \lim\limits_{x \to a}[e^{ln~f(x)}]^{g(x)}$ $= \lim\limits_{x \to a}~e^{g(x)~ln~f(x)}$ $= e^{(\infty)(-\infty)}$ $= e^{-\infty}$ $= \frac{1}{e^{\infty}}$ $ = 0$