Match the columns

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

Problem

Match the columns.

Column I	Column II
(a) $\lim_{x\to0}\frac{1-\cos2x}{e^{x^2}-e^x+x}$ equals	(p) $1$
(b) If $\lim_{x\to0^+}\left(\frac{(3/x)+1}{(3/x)-1}\right)^{1/x}$ can be expressed as $e^{p/q}$ , where $p$ and $q$ are relatively prime, then $p+q$ equals	(q) $2$
(c) $\lim_{x\to0}\frac{\tan^3x-\tan(x^3)}{x^5}$ equals	(r) $4$
(d) $\lim_{x\to0}\frac{x+2\sin x}{\sqrt{x^2+2\sin x+1}-\sqrt{\sin^2x-x+1}}$ equals	(s) $5$