Discussion
The value of \( \lim_{x \to 0} (\cos x)^{1/x^{2}} \) is
Answer: B
The form is \( 1^{\infty} \), so take logarithms:
\[ \ln L \;=\; \lim_{x \to 0} \frac{\ln \cos x}{x^{2}} \;=\; \lim_{x \to 0} \frac{-x^{2}/2}{x^{2}} \;=\; -\frac{1}{2}, \]
using \( \ln \cos x \approx -x^{2}/2 \). Hence \( L = e^{-1/2} \). Reading \( 1^{\infty} \) as one is the standard error, the form being indeterminate precisely because the base approaches one at a rate that matters
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