n趋向正无穷,求2^n(sin1/3n)的极限

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/07/08 09:47:50

n趋向正无穷,求2^n(sin1/3n)的极限
能答的都是我学长。选项分别是0，2/3,1,3/2.

当n->+∞时,
lim2^[sin(1/3n)]
=lim2^[sin(1/3n) / (1/n)]
=lim2^[(1/3) * sin(1/3n) / (1/3n)]
=2^lim[(1/3) * sin(1/3n) / (1/3n)]…………①
由于当n->+∞时,lim[sin(1/n) / (1/n)]=1
因此,①式=2^(1/3)
再问：哥，你理解错题了。是lim2^n*sin1/3n，n趋向正无穷。2的N次方乘以sin1/3n。
再答：哦哦。不好意思，题目理解有误。你是求这个？当n->+∞时，lim(2^n)* sin(1/3n)=?
再问：嗯嗯。。。继续。sin1/n这类我都不会。sin1/3n更不会
再答：当n->+∞时， lim(2^n)* sin(1/3n) =lim(2^n)/(3n) * [sin(1/3n) / (1/3n)]…………① 当n->∞时，lim [sin(1/3n) / (1/3n)] = 1 因此， ①式= lim(2^n)/(3n) = lim { (1/3n) / [2^(1/n)] } = 0

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