1. ## 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.

2. Originally Posted by Mp5xm8
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

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

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

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