求极限lim(x→0)sinxsin(1/x);lim(x→∞)(arctanx/x)

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求极限lim(x→0)sinxsin(1/x);lim(x→∞)(arctanx/x)
求极限lim(x→0)sinxsin(1/x);lim(x→∞)(arctanx/x)

求极限lim(x→0)sinxsin(1/x);lim(x→∞)(arctanx/x)
lim(x→0)sinxsin(1/x)=0
[无穷小sinx乘以有界函数sin(1/x)]
lim(x→∞)(arctanx/x)=0
[理由同上,arctanx有界,1/x无穷小]