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Math Help - Asymptotes

  1. #1
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    Asymptotes

    I'm trying to learn how to do asymptotes and I'm having trouble with horizontal asymptotes, I'm looking for some help on them.

    So i have F(x)=3x/((x^2)+1)

    Now my brother tells me that there are no horizontal asymptotes, but the function will never touch Y=-2 or 2 so why aren't those the asymptotes. And how does one go about finding the horizontal asymptotes because honestly i don't get them at all.
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  2. #2
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    Quote Originally Posted by Mp5xm8 View Post
    I'm trying to learn how to do asymptotes and I'm having trouble with horizontal asymptotes, I'm looking for some help on them.

    So i have F(x)=3x/((x^2)+1)

    Now my brother tells me that there are no horizontal asymptotes, but the function will never touch Y=-2 or 2 so why aren't those the asymptotes. And how does one go about finding the horizontal asymptotes because honestly i don't get them at all.
    To find the horizontal asymptotes, let x approach infinity in such a way, we are left with a constant for F(x).

    Utilise

    \displaystyle\lim_{x\rightarrow\infty}\frac{k}{x}=  0


    \displaystyle\lim_{x\rightarrow\infty}\frac{\left(  \frac{1}{x}\right)}{\left(\frac{1}{x}\right)}\frac  {3x}{x^2+1}=\lim_{x\rightarrow\infty}\frac{3}{x+\f  rac{1}{x}}

    =\displaystyle\lim_{x\rightarrow\infty}\frac{3}{x}
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