How do you find the limit of # (3 x^4 + 4) / ((x^2 - 7)(4 x^2 - 1)) # as x approaches infinity?

Expanding the denominator gives



Then in the whole rational expression, we can divide through by . Since , we assume that , so this is legal.



As gets arbitrarily large, the rational terms in the numerator and denominator become negligible. So for large , we have



And so the limit is .