x趋向于无穷时，xsin1/x的极限怎么求？

x是无穷，sin1/x不是没极限么？

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x趋源穗厅于正无穷

令a=1/雹隐x
所以原式lim(a趋于0)sina/a=1

回族野答a=1/x
则x=1/a
所以xsin(1/x)=1/a*sina=sina/a

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x→∞ ，中扒1/x→0，sin(1/x)~1/x
lim( xsin(1/x) )=lim( x*(1/枯培樱没丛x) )=lim(1)=1.

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x→∞ 1/x→0 xsin1/x =sin1/x/(1/x) ~x→0sinx/x =1

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