Posted by Beta plus on Sunday, October 11, 2009 at 12:45pm.
Use l'Hôpitals rule:
1.
Lim (x->∞) (x³+3)/(2x³+4x+1)
= Lim (x->∞) (3x²)/(6x²)
= Lim (x->∞) (6x)/(12x)
= Lim (x->∞) 1/2
= 1/2
Similarly for (1-cos(x))/(x²)
= Lim (x->∞)
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