Limit of the ratio of quadratics, 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 the same and the limit is the ratio of the coefficients of the largest power:

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

As x becomes large, the terms involving x become negligible, leaving