t->0+
e^t = 1+ t +(1/2)t^2 + (1/6)t^3 +o(t^3)
(2+t^2).e^t
=(2+t^2).[1+ t +(1/2)t^2 + (1/6)t^3 +o(t^3) ]
= 2+ 2t +t^2 + (1/3)t^3 + t^2 +t^3 +o(t^3)
=2+2t +2t^2 + (4/3)t^3 +o(t^3)
2√(1+t^6) =2[1 + (1/2)t^6 +o(t^6) ]
(2+t^2).e^t - 2√(1+t^6) = 2t +o(t)
lim(t->0+) [ (2+t^2).e^t -2√(1+t^6) ] /(2t^3) -> +∞
希望有所帮助
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