Match the following

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

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) $\lim_{x\to0}(\cos x)^{\cot^2x}$ equals	(r) $e$
(d) $\lim_{x\to0}\left[\tan\left(\frac{\pi}{4}+x\right)\right]^{1/x}$ equals	(s) $e^{-1}$