求大一高数极限习题详解

求lim(n→∞)2∧nsin(x/2∧n)极限
2024-11-22 21:02:35
推荐回答(2个)
回答1:

lim(n->∞)2^nsin(x/2^n)
设 t=1/2^n,t->0
lim(t->0) sin(xt)/t
=lim(t->0) xsin(xt)/xt
=x*1=x

回答2:

lim(n→∞)2∧nsin(x/2∧n)=lim(n→∞)xsin(x/2∧n)/(x/2∧n)=x