asymptote help

**ubhutto** · September 29th 2012, 08:09 AM

does (x-2) / (2x^2 +3X - 5) have any horizontal asymptote

PS i think its none.

**MarkFL** · September 29th 2012, 08:15 AM

What do you find when you evaluate:

$\lim_{x\to\pm\infty}\frac{x-2}{2x^2+3x-5}$ ?

**ubhutto** · September 29th 2012, 08:17 AM

limit of positive infinity is 0 and the limit of negative infinity is 0

**MarkFL** · September 29th 2012, 08:25 AM

Yes, so that means you have a horizontal asymptote of $y=0$ , i.e., the $x$ -axis.

**ubhutto** · September 29th 2012, 08:27 AM

thanks and if the limit of lets say f(x) is infinity does that mean that there is no horizontal asymptote.

**MarkFL** · September 29th 2012, 08:34 AM

Right. In this case there could be an oblique asymptote, but not a horizontal one.

Thread: asymptote help