Problem

Match the following.

Column I	Column II
(A) $\lim_{x \to \infty} \left( \frac{x}{1+x} \right)^x$ equals	(p) $e^2$
(B) $\lim_{x \to -\infty} \left( \frac{1}{x} + \cos \frac{1}{x} \right)^x$ equals	(q) $e^{-1/2}$
(C) $\lim_{x \to 0} (\cos x)^{\cot^2 x}$ equals	(r) $e$
(D) $\lim_{x \to 0} \left[ \tan \left( \frac{\pi}{4} + x \right) \right]^{1/x}$ equals	(s) $e^{-1}$