$\lim_{x \to 0} (\cos x)^{1/x^2} = \dots$ (Express as a power of $e$.)
Step-by-Step Solution
Key Concept: Let $y = (\cos x)^{1/x^2}$. Then $\ln y = \frac{\ln \cos x}{x^2}$. Expand: $\ln \cos x \approx -x^2/2 - x^4/12 - \dots$. So $\ln y \to -1/2$, giving $y \to e^{-1/2}$.
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Correct Answer: e^{-1/2}