Question

How do you find the horizontal asymptote for `(3x^4 + 2x^2 + 1) / (5x^4 + x -1)`?

Answer 1

`3/5`

Explanation:

As `x` becomes larger and larger the terms other than `(3x^4)/(5x^4)` become less and less significant.

So `lim_(xto+-oo) f(x) -> (3x^4)/(5x^4) = 3/5`

Note that for both positive and negative `x` that `x^4` is positive.