lim2^nsin(x/2^n),n→无穷大,

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lim2^nsin(x/2^n),n→无穷大,lim2^nsin(x/2^n),n→无穷大,lim2^nsin(x/2^n),n→无穷大,n→无穷大,则x/2^n→0.则sin(x/2^n)等价于x/

lim2^nsin(x/2^n),n→无穷大,
lim2^nsin(x/2^n),n→无穷大,

lim2^nsin(x/2^n),n→无穷大,
n→无穷大,则x/2^n→0.则sin(x/2^n)等价于x/2^n
所以 lim 2^n·sin(x/2^n) = lim 2^n·(x/2^n)
= x