求lim2^n*sin(x/2^n)

lim(n→∞) 2^n*sin(X/2^n)
=lim(n→∞) 2^n*(X/2^n)
=X
当x→0时,sinx与x为同阶无穷小,即lim(x→0) sinx=x,记作sinx～x