求lim sin(xy)/xy,x趋近于2,y趋近于0

题目

求lim sin(xy)/xy,x趋近于2,y趋近于0

答案

首先,你要知道极限值：lim(s->0) sin s / s = lim(s->0) cos s / 1 = cos 0 = 1 （用到了洛必达法则）lim(x->2,y->0) sin(xy)/xy = lim(y->0) sin(2y) / (2y) (换元2y = s)= lim(s->0) sin s / s = 1....