Unanswered Limits Continuity Questions

mathop {lim }limits_{x o 0} frac{{{x^2} - 2x}}{{2sin x}} equals ...

mathop {lim }limits_{x o 0} left( {frac{{{e^x} - 1}}{x}} ight) = ...

mathop {lim }limits_{x o infty } {left[ {1 + frac{1}{{mx}}} ight]^x} equal to ...

Let and c be two vectors perpendicular to each other in the xy-plane. All vectors in the same plane having projections 1 and 2 along b and c respectively, are given by ...

mathop {lim }limits_{n o infty } frac{{{1^p} + {2^p} + {3^p} + ........ + {n^p}}}{{{n^{p + 1}}}} = a) frac{1}{{p + 1}} b) frac{1}{{1 - p}} c) frac{1}{p} - frac{1}{{(p - 1)}} d) frac{1}{{p + 2}} ...

mathop {lim }limits_{n o infty } left[ {frac{1}{n} + frac{1}{{n + 1}} + frac{1}{{n + 2}} + ....... + frac{1}{{3n}}} ight] = a) 0 b) {log _e}4 c) {log _e}3 d) {log _e}2 ...

mathop {lim }limits_{x o 0} frac{{sin (pi {{cos }^2}x)}}{{{x^2}}} = a) - pi b) pi c) frac{pi }{2} d) 1 ...