极限 lim(x-->无穷)(1/n sin(n)

极限 lim(x-->无穷)(1/n sin(n)+1/n sin(1/n)+nsin(1/n))

1个回答

n趋于无穷时1/n趋于0,因此1/n和sin(1/n)都是无穷小,而sinn是有界量,根据无穷小和有界量的乘积是无穷小,可知lim(1/n)sinn=0,lim(1/n)sin(1/n)=0,而1/n趋于0时sin1/n和1/n是等价无穷小,因此limnsin(1/n)=limn(1/n)=1,所以极限=1

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