Results 1 to 6 of 6

Math Help - Limit question

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    2

    Limit question

    Thanks for the help.

    This is a limit question that is the last on the list that I can't just figure out.

    lim x -> infinity

    (e^x + x) ^ (1/x)

    I'm sorry for the lack of formatting. When I applied math tags, it didn't come out right.

    I got as far as...

    ln(y) = (1/x) * ln(e^x + x)

    And...

    ln(y) = ln(e^x + x)/x

    Then using hospital's rule...

    lim x -> inf (1+e^x)/(x+e^x)

    What is the limit above? That looks like the only problem that's keeping me down.
    Last edited by cielroi; February 18th 2009 at 05:44 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    L'Hopital ?

    \lim_{x \to \infty} \frac{\ln(e^x + x)}{x} =

    \lim_{x \to \infty} \frac{e^x + 1}{e^x + x} =

    \lim_{x \to \infty} \frac{e^x}{e^x + 1} =

    \lim_{x \to \infty} \frac{e^x}{e^x} = 1

    \ln{y} = 1

    limit is y = e
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    2
    Oh, I forgot about using that on the second part! Thank you!!!!!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,408
    Thanks
    1294
    Quote Originally Posted by cielroi View Post
    Thanks for the help.

    This is a limit question that is the last on the list that I can't just figure out.

    lim x -> infinity

    (e^x + x) ^ (1/x)

    I'm sorry for the lack of formatting. When I applied math tags, it didn't come out right.

    I got as far as...

    ln(y) = (1/x) * ln(e^x + x)

    And...

    ln(y) = ln(e^x + x)/x

    Then using hospital's rule...

    lim x -> inf (1+e^x)/(x+e^x)

    What is the limit above? That looks like the only problem that's keeping me down.
    This is a bit messy, but I look at what happens to each part as x \to \infty.

    e^x \to \infty

    x \to \infty

    So e^x + x \to \infty.


    \frac{1}{x} \to 0.


    So we have a very big number taken to the power of a very small number (in this case, 0).

    What is anything to the power of 0?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by Prove It View Post
    This is a bit messy, but I look at what happens to each part as x \to \infty.

    e^x \to \infty

    x \to \infty

    So e^x + x \to \infty.


    \frac{1}{x} \to 0.


    So we have a very big number taken to the power of a very small number (in this case, 0).

    What is anything to the power of 0?

    \infty^0 is an indeterminate form, not 1.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1
    Quote Originally Posted by cielroi View Post
    Thanks for the help.

    This is a limit question that is the last on the list that I can't just figure out.

    lim x -> infinity

    (e^x + x) ^ (1/x)

    I'm sorry for the lack of formatting. When I applied math tags, it didn't come out right.

    I got as far as...

    ln(y) = (1/x) * ln(e^x + x)

    And...

    ln(y) = ln(e^x + x)/x

    Then using hospital's rule...

    lim x -> inf (1+e^x)/(x+e^x)

    What is the limit above? That looks like the only problem that's keeping me down.
    You need to l'Hopital again, because you have \frac{\infty}{\infty}. Then it looks like you will have to do it maybe two more times, which I think will give you \frac{1}{1} = 1 So your limit will be e^1 which = e
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: November 7th 2011, 03:27 PM
  2. Replies: 1
    Last Post: August 8th 2010, 11:29 AM
  3. limit question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 11th 2009, 08:04 PM
  4. Another Limit Question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 10th 2008, 11:38 PM
  5. Another limit question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 27th 2008, 01:02 PM

Search Tags


/mathhelpforum @mathhelpforum