亲们,请问lim sin(1/x)/(1/x)= x趋向于0
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亲们,请问lim sin(1/x)/(1/x)= x趋向于0
![亲们,请问lim sin(1/x)/(1/x)= x趋向于0](/uploads/image/z/5473596-12-6.jpg?t=%E4%BA%B2%E4%BB%AC%2C%E8%AF%B7%E9%97%AElim+sin%281%2Fx%29%2F%281%2Fx%29%3D+x%E8%B6%8B%E5%90%91%E4%BA%8E0)
令t=1/x,则x->0时,有t->∞
∴limsin(1/x)/(1/x)=limsint/t
∵|sint|≤1,而t->∞
∴limsint/t=0
∴limsin(1/x)/(1/x)=limsint/t
∵|sint|≤1,而t->∞
∴limsint/t=0
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