lim(n趋向无穷)=[(5x^2+1)/(3x-1)]sin1/x=?

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lim(n趋向无穷)=[(5x^2+1)/(3x-1)]sin1/x=?
lim(n趋向无穷)=[(5x^2+1)/(3x-1)]sin1/x=?

lim(n趋向无穷)=[(5x^2+1)/(3x-1)]sin1/x=?
lim(n趋向无穷)[(5x^2+1)/(3x-1)]sin1/x
=lim(n趋向无穷)[(5x^2+1)/(3x-1)*1/x
=lim(n趋向无穷)(5x^2+1)/(3x^2-x)
=lim(n趋向无穷)(5+1/x^2)/(3-1/x)
=(5+0)/(3-0)
=5/3

应该是x趋向无穷,由于x趋向于无穷时 sin(1/x)等价与1/x,因此只要求
(5x^2+1)/(3x^2-x)的极限,上下同除以x^2,就知道这个极限为5/3.

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