Results 1 to 3 of 3

Math Help - How to use FTC in finding this limit?

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    30

    How to use FTC in finding this limit?

    \lim_{x\,\to\,\infty}e^{-e^{x}}\int_0^x e^{e^{t}}dt

    Thanks in advance.
    Last edited by xcluded; October 28th 2009 at 08:41 PM. Reason: Edit the correct question
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2009
    Posts
    80
    Quote Originally Posted by xcluded View Post
    \lim_{x\,\to\,\infty}e^{-e^{x}}\int_0^x e^{e^{t}}dt

    Thanks in advance.
    Express the limit as \lim_{x\to\infty} \frac{\int_0^x e^{e^t}dt}{e^{e^x}}. Both the numerator and denominator approach infinity, so by L'Hopital's rule and the fundamental theorem of calculus, the limit equals \lim_{x\to\infty} \frac{e^{e^x}}{e^{e^x}e^x} = \lim_{x\to\infty} e^{-x} = 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    30
    Edited.

    Thanks !
    Last edited by xcluded; October 29th 2009 at 12:15 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the limit
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 11th 2011, 07:50 AM
  2. Finding limit of this function, using Limit rules
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 27th 2011, 01:12 PM
  3. [SOLVED] Finding f(x) and g(x) - limit
    Posted in the Calculus Forum
    Replies: 7
    Last Post: December 18th 2010, 04:32 AM
  4. Finding a limit. Finding Maclaurin series.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 18th 2010, 10:04 PM
  5. help finding the following limit:
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 15th 2008, 09:25 PM

Search Tags


/mathhelpforum @mathhelpforum