cos(x/2)*cos(x/4)...cos(x/2~n)
=cos(x/2)*cos(x/4)...cos(x/2~n)*2^n*sin(x/2^n)/[2^n*sin(x/2^n)]
=sinx/[2^n*sin(x/2^n)]
分母2^n*sin(x/2^n)=x*sin(x/2^n)/(x/2^n)→x,(n→∞),
lim [cos(x/2)*cos(x/4)...cos(x/2~n)]=(sinx)/x,(n趋于无穷).
再求一道高数极限问题的解答lim [cos(x/2)*cos(x/4)...cos(x/2~n)],其中,n趋于无穷
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