For rational functions the limit at + or - infinity is the ratio of the highest
This should be enough to answer the question.
the key is at infinity
limc/x^n = 0
if you divide through by the highest poweed terms everything goes to 0 except the leading terms
lim(2x^3 + 3x + 1)/(x^3 +2)
=lim [x^3( 2 + 3/x^2 +1/x^3)/[x^3(1+2/x^3)]
=lim (2+3/x^2 +1/x^3)/(1+ 2/x^3)
= (2+0+0)/(1+0) = 2
so imsteas of dividing through by the highest powered terms each time we recognize we can just consider the ratio of highest powered term.
This is also true if the highest powers on top and bottom are different just consider the ratio