How do you find the horizontal asymptote for $\frac{3 x^{4} + 2 x^{2} + 1}{5 x^{4} + x - 1}$ $(3x^4 + 2x^2 + 1) / (5x^4 + x -1)$ ?

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Answer 1 · 2016-05-17T21:21:14

$\frac{3}{5}$ $3/5$

As $x$ $x$ becomes larger and larger the terms other than $\frac{3 x^{4}}{5 x^{4}}$ $(3x^4)/(5x^4)$ 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.

Tony B

How do you find the horizontal asymptote for (3x^4 + 2x^2 + 1) / (5x^4 + x -1)3x4+2x2+15x4+x−1(3x^4 + 2x^2 + 1) / (5x^4 + x -1)?