求lim(n→∞)2∧nsin(x/2∧n)极限
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
设 t=1/2^n,t->0
lim(t->0) sin(xt)/t
=lim(t->0) xsin(xt)/xt
=x*1=x
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第1个回答 2012-11-01
lim(n→∞)2∧nsin(x/2∧n)=lim(n→∞)xsin(x/2∧n)/(x/2∧n)=x