(21)原式=lim(n->∞)[(1+1/n)^(n+m)]
={lim(n->∞)[(1+1/n)^n]}^m
=e^m
(25)原式=lim(x->a)[(sinx-sina)/(x-a)]
=lim(x->a)[2cos((x+a)/2)sin((x-a)/2)/(x-2)]
=lim(x->a)[cos((x+a)/2)]*lim(x->a)[sin((x-a)/2)/(x-2)/2]
=cosa*1
=cosa
(30) 原式=lim(x->0){[2/(1+2x)]/[4sec²(4x)]} (0/0型,应用罗比达法则)
=1/2lim(x->0)[cos²(4x)/(1+2x)]
=1/2*1
=1/2