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Math Help - Horizontal Asymptotes.

  1. #1
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    Horizontal Asymptotes.

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

    Can I apply L'Hopital's rule?
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  2. #2
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    Re: Horizontal Asymptotes.

    Quote Originally Posted by habibixox View Post
    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.
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  3. #3
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    Re: Horizontal Asymptotes.

    [(19x)/((x^4 +1)^(1/4))]
    sorry.
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    Re: Horizontal Asymptotes.

    Quote Originally Posted by habibixox View Post
    [(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 ....
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  5. #5
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    Re: Horizontal Asymptotes.

    I can use L'Hopitals rule right? Because it would be inf/inf?
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  6. #6
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    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?
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  7. #7
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    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
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