n趋向正无穷,求2^n(sin1/3n)的极限
问题描述：
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.
答
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)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。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)=?嗯嗯。。。继续。sin1/n这类我都不会。sin1/3n更不会当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