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Math Help - Asymptotes

  1. #1
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    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

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  2. #2
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    Quote Originally Posted by Pandora View Post
    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.
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