问题标题:
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
问题描述:
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
邵斌彬回答:
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...
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