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.
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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.
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.
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)
2^n(sin1/3n)=e^n(sin1/3n)ln2
sin1/3n等价于1/3n
n趋向正无穷,2^n(sin1/3n)的极限为e^(ln2)/3=三次根号下3
2^n(sin1/3n)=(sin1/3n)/(1/2^n)
上式为0/0型,然后直接用洛必达法则
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.
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