Evaluate the limits lim x^3 + 3/ x->¤ 2x^3 + 4x + 1 lim 1 - cosx / x->o x^2

Answer 1

Use l'Hôpitals rule:
1.
Lim (x->∞) (x³+3)/(2x³+4x+1)
= Lim (x->∞) (3x²)/(6x&sup2)
= Lim (x->∞) (6x)/(12x)
= Lim (x->∞) 1/2
= 1/2

Similarly for (1-cos(x))/(x²)
= Lim (x->∞)