高数题,谢谢了!!!!!如图

2025-05-07 18:47:18
推荐回答(1个)
回答(1):

原式
=lim(n→∞)x/2*[sin(x/2^n)/(x/2^n)]
=x/2*lim (n→∞) [sin(x/2^n)/(x/2^n)]
因为x→0时,sinx~x
所以 :sin(x/2^n)~s(x/2^n)
则limx/2*lim (n→∞) [sin(x/2^n)/(x/2^n)]=
limx/2*lim (n→∞) (x/2^n)/(x/2^n)
=x/2