Results 1 to 3 of 3

Math Help - Horizontal asymptotes / infinite limits and natural log

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    2

    Horizontal asymptotes / infinite limits and natural log

    Hi. This problem simply involves finding the horizontal asymptotes of the following function. While the calculator shows two (y = 0 when x approaches negative infinity and y = 2 for positive infinity), I can only come to the conclusion that y = 2, regardless of whether X approaches positive or negative infinity.

    Function:
    Y = (2e^x) / ((e^x)-5)

    What needs to be done in order to get the result that Y approaches 0 as X approaches negative infinity? Much thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by kylera View Post
    Hi. This problem simply involves finding the horizontal asymptotes of the following function. While the calculator shows two (y = 0 when x approaches negative infinity and y = 2 for positive infinity), I can only come to the conclusion that y = 2, regardless of whether X approaches positive or negative infinity.

    Function:
    Y = (2e^x) / ((e^x)-5)

    What needs to be done in order to get the result that Y approaches 0 as X approaches negative infinity? Much thanks in advance.
    y = \frac{2 e^x}{e^x - 5} = \frac{2}{1 - 5 e^{-x}}.

    \lim_{x \rightarrow + \infty} \frac{2}{1 - 5 e^{-x}} = \frac{2}{1 - 5(0)} = 2.

    \lim_{x \rightarrow - \infty} \frac{2 e^x}{e^x - 5} = \frac{0}{0 - 5} = 0.

    The two horiziontal asymptotes are therefore y = 2 and y = 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2008
    Posts
    2
    Stupid oversight on my part. Much thanks again.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Horizontal asymptotes
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: July 13th 2010, 04:51 AM
  2. Horizontal asymptotes/limits
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 28th 2009, 09:14 PM
  3. Infinite Limits and Asymptotes
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: September 19th 2009, 11:00 PM
  4. limits of horizontal asymptotes
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 21st 2009, 07:42 PM
  5. Replies: 5
    Last Post: October 8th 2007, 05:34 AM

Search Tags


/mathhelpforum @mathhelpforum