# Horizontal and Vertical asymptotes of a curve

• Oct 2nd 2012, 09:00 PM
Oldspice1212
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?
• Oct 2nd 2012, 11:07 PM
MarkFL
Re: Horizontal and Vertical asymptotes of a curve
I assume you mean:

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

To find the vertical asymptote(s) solve:

$\displaystyle e^x-6=0$

To find the horizontal asymptote(s) evaluate:

$\displaystyle \lim_{x\to\pm\infty}\frac{4e^x}{e^x-6}$
• Oct 2nd 2012, 11:15 PM
FernandoRevilla
Re: Horizontal and Vertical asymptotes of a curve
Quote:

Originally Posted by Oldspice1212
Find the horizontal and vertical asymptotes of the curve. y = 4e^x/e^x-6 How do you do this?

Vertical asymptotes: $\displaystyle e^x-6=0\Leftrightarrow x=\ln 6$ .

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

Edited: Sorry, I didn't see MarkFL2's post.
• Oct 2nd 2012, 11:20 PM
MarkFL
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! :)