# Asymptotes

• October 12th 2008, 03:21 PM
Pandora
Asymptotes
I need help with finsing the asymptotes of the graph (1 + ex)/(1 ex).
Would they be a vertical one at 0, and 2 horizontal at 1 and -1? All of this is just based on me looking at the plotted graph. Thanks

• October 12th 2008, 03:30 PM
mr fantastic
Quote:

Originally Posted by Pandora
I need help with finsing the asymptotes of the graph (1 + ex)/(1 ex).
Would they be a vertical one at 0, and 2 horizontal at 1 and -1? All of this is just based on me looking at the plotted graph. Thanks

Vertical asymptote: Solve $1 - e^x = 0: x = 0$. So the line x = 0 (that is, the y-axis) is a vertical asymptote.

Horizontal asymptotes:

$\lim_{x \rightarrow -\infty} \frac{1+e^x}{1 - e^x} = \frac{1}{1} = 1$.

$\lim_{x \rightarrow +\infty} \frac{1+e^x}{1 - e^x} = \lim_{x \rightarrow +\infty} \frac{e^{-x} + 1}{e^{-x} - 1} = \frac{1}{-1} = -1$.

So the lines y = 1 and y = -1 are horizontal asymptotes.