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有木有大神会这道题,在线等啊?
2个回答
展开全部
lim(x->0-) e^(1/x) =0 and |sin(3/x^2)|≤1
=>lim(x->0-) e^(1/x). sin(3/x^2) =0
lim(x->0-) [ e^(1/x). sin(3/x^2) + x.arctan(1/x) ]
=lim(x->0-) x.arctan(1/x)
=lim(x->0-) x . lim(x->0-)arctan(1/x)
=0.(-π/2)
=0
=>lim(x->0-) e^(1/x). sin(3/x^2) =0
lim(x->0-) [ e^(1/x). sin(3/x^2) + x.arctan(1/x) ]
=lim(x->0-) x.arctan(1/x)
=lim(x->0-) x . lim(x->0-)arctan(1/x)
=0.(-π/2)
=0
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