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

PS i think its none.

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- Sep 29th 2012, 08:09 AMubhuttoasymptote help
does (x-2) / (2x^2 +3X - 5) have any horizontal asymptote

PS i think its none. - Sep 29th 2012, 08:15 AMMarkFLRe: asymptote help
What do you find when you evaluate:

$\displaystyle \lim_{x\to\pm\infty}\frac{x-2}{2x^2+3x-5}$ ? - Sep 29th 2012, 08:17 AMubhuttoRe: asymptote help
limit of positive infinity is 0 and the limit of negative infinity is 0

- Sep 29th 2012, 08:25 AMMarkFLRe: asymptote help
Yes, so that means you have a horizontal asymptote of $\displaystyle y=0$, i.e., the $\displaystyle x$-axis.

- Sep 29th 2012, 08:27 AMubhuttoRe: asymptote help
thanks and if the limit of lets say f(x) is infinity does that mean that there is no horizontal asymptote.

- Sep 29th 2012, 08:34 AMMarkFLRe: asymptote help
Right. In this case there could be an oblique asymptote, but not a horizontal one.