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Math Help - Horizontal and Vertical asymptotes of a curve

  1. #1
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    Horizontal and Vertical asymptotes of a curve

    Find the horizontal and vertical asymptotes of the curve.

    y
    = 4e^x/e^x-6



    x=
    y= (smaller y - value)
    y = (larger y - value)

    How do you do this?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Horizontal and Vertical asymptotes of a curve

    I assume you mean:

    y=\frac{4e^x}{e^x-6}

    To find the vertical asymptote(s) solve:

    e^x-6=0

    To find the horizontal asymptote(s) evaluate:

    \lim_{x\to\pm\infty}\frac{4e^x}{e^x-6}
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Re: Horizontal and Vertical asymptotes of a curve

    Quote Originally Posted by Oldspice1212 View Post
    Find the horizontal and vertical asymptotes of the curve. y = 4e^x/e^x-6 How do you do this?
    Vertical asymptotes: e^x-6=0\Leftrightarrow x=\ln 6 .

    Horizontal asymptotes: f(x)=\frac{4e^x}{e^x-6}=\dfrac{4}{1-\frac{6}{e^x}}\Rightarrow \begin{Bmatrix} \displaystyle\lim_{x \to{+}\infty}f(x)=4\\\displaystyle\lim_{x \to{-}\infty}f(x)=0\end{matrix}



    Edited: Sorry, I didn't see MarkFL2's post.
    Last edited by FernandoRevilla; October 3rd 2012 at 12:17 AM.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Horizontal and Vertical asymptotes of a curve

    Hey, no worries! I make posts not seeing someone else has posted in the meantime quite frequently!
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