Lim（n→∞）2^n * sinx/(2^n)=?

Lim（n→∞）2^n * sinx/(2^n)=?

Lim（n→∞）2^n * sinx/(2^n)=Lim（n→∞）2^n *{[sinx/(2^n)]/[x/2^n]}*(x/2^n)
[sinx/(2^n)]/[x/2^n]趋向于1
所以等于x

∞
因为sinx/(2^n)是一个有界函数

Lim（n→∞）2^n * sin[x/(2^n)]
=Lim（n→∞）2^n * sin[x/(2^n)]/[x/(2^n)]*[x/(2^n)]
=Lim（n→∞）2^n *[x/(2^n)]*sin[x/(2^n)]/[x/(2^n)]
=Lim（n→∞）x*Lim（n→∞）sin[x/(2^n)]/[x/(2^n)]
=x*1
=x