1. ## Horizontal Asymptotes.

y = 19 x
(x4 +1)[1/4]
How can I find the horizontal asymptotes?

Can I apply L'Hopital's rule?

2. ## Re: Horizontal Asymptotes.

Originally Posted by habibixox
y = 19 x
(x4 +1)[1/4]
How can I find the horizontal asymptotes?

Can I apply L'Hopital's rule?
Your function is unintelligible. Please learn to use latex. Either that or use brackets, ^ for raising to a power etc.

3. ## Re: Horizontal Asymptotes.

[(19x)/((x^4 +1)^(1/4))]
sorry.

4. ## Re: Horizontal Asymptotes.

Originally Posted by habibixox
[(19x)/((x^4 +1)^(1/4))]
sorry.
To find a horizontal asymptote, you need to consider the limit $\lim_{x \to \pm \infty} \frac{19x}{(x^4 + 1)^{1/4}}$.

It is not difficult to prove that the limit is equal to 19. Therefore ....

5. ## Re: Horizontal Asymptotes.

I can use L'Hopitals rule right? Because it would be inf/inf?

6. ## Re: Horizontal Asymptotes.

I just guessed the answers in my online hw and got 19 and -19 as the answers. But honestly I don't know how to do that... can someone show me the steps please?

7. ## Re: Horizontal Asymptotes.

$\lim_{x \to \pm \infty} \frac{19x}{\sqrt[4]{x^4+1}} =$

$\lim_{x \to \pm \infty} \frac{\frac{19x}{\sqrt[4]{x^4}}}{\sqrt[4]{\frac{x^4}{x^4}+\frac{1}{x^4}}} =$

$19 \lim_{x \to \pm \infty} \frac{x}{|x|\sqrt[4]{1+\frac{1}{x^4}}} =$

$-19$ as $x \to -\infty$

$19$ as $x \to \infty$