Limit of linear over quadratic, x->inf:

We can use the Limit at Infinity for Rational Functions. We have the case where the maximum powers in the numerator and denominator are different and the limit is dependent on the location of the largest power. Here that is in the denominator, so that the denominator grows faster than the numerator, as x increases. Hence, the limit is 0.

Another way to solve this is to divide the numerator and the denominator by the smaller of the two maximum powers of x (the value of the expression will be unchanged, just its form):

As x becomes large, the x term dominates and the 2/x term is small.