Results 1 to 6 of 6

Math Help - Question Concerning L'Hospital's Rule

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    6

    Question Concerning L'Hospital's Rule

    Does L'Hospital's Rule still apply if the numerator and denominator go to infinity in different directions (i.e. positive infinity over negative infinity)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by cusseta View Post
    Does L'Hospital's Rule still apply if the numerator and denominator go to infinity in different directions (i.e. positive infinity over negative infinity)?
    What is the limit this is in regards to?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2011
    Posts
    6
    For example: The limit as x approaches negative infinity of ( 2x / -e^-x ).

    In this example, the numerator approaches positive infinity, but the denominator approaches negative infinity.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by cusseta View Post
    For example: The limit as x approaches negative infinity of ( 2x / -e^-x ).

    In this example, the numerator approaches positive infinity, but the denominator approaches negative infinity.
    \displaystyle\lim_{x\to\infty}-\frac{2x}{e^{-x}}=\lim_{x\to\infty}-\frac{2x}{\frac{1}{e^x}}\cdot\frac{e^x}{e^x}=\lim_  {x\to\infty}=-2xe^{x}=\cdots
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,707
    Thanks
    1470
    That is exacly the same as -\lim_{x\to\infty}\frac{2x}{e^{-x}}. In general, if one factor goes to " -\infty", you can factor out a "-1" and turn the limit into +\infty. In other words, it doesn't matter whether the limit is -\infty or +\infty.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jan 2011
    Posts
    6
    Thanks! I knew it was something ridiculously simple!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with L'Hospital's Rule question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 25th 2009, 05:37 PM
  2. Replies: 1
    Last Post: June 20th 2009, 02:08 PM
  3. L'Hospital's Rule
    Posted in the Calculus Forum
    Replies: 9
    Last Post: November 16th 2008, 09:54 AM
  4. LíHospitalís Rule
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 15th 2008, 11:44 AM
  5. L'Hospital's Rule
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 5th 2007, 02:26 PM

Search Tags


/mathhelpforum @mathhelpforum