y = 19 x
(x4 +1)[1/4]
How can I find the horizontal asymptotes?
Can I apply L'Hopital's rule?
$\displaystyle \lim_{x \to \pm \infty} \frac{19x}{\sqrt[4]{x^4+1}} =$
$\displaystyle \lim_{x \to \pm \infty} \frac{\frac{19x}{\sqrt[4]{x^4}}}{\sqrt[4]{\frac{x^4}{x^4}+\frac{1}{x^4}}} =$
$\displaystyle 19 \lim_{x \to \pm \infty} \frac{x}{|x|\sqrt[4]{1+\frac{1}{x^4}}} =$
$\displaystyle -19$ as $\displaystyle x \to -\infty$
$\displaystyle 19$ as $\displaystyle x \to \infty$