求当x趋向正无穷时sin(arctan(1/x))的极限

求当x趋向正无穷时sin(arctan(1/x))的极限
求当x趋向正无穷时sin(arctan(1/x))的极限

求当x趋向正无穷时sin(arctan(1/x))的极限
x趋向正无穷时sin(arctan(1/x))的极限为 0
用复合函数的极限运算法则：
lim (x-正无穷) arctan(1/x) = 0,
lim (x-正无穷) sin(arctan(1/x))=sin [ lim (x-正无穷) (arctan(1/x)) ]= sin0 =0

原式=sin(limarctan(1/x)))
=sin(π/2)
=1