1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limits again

  1. May 20, 2008 #1
    Problem: Find the limit of ln(1+e^x)/e^x as x approaches negative infinity

    I really have no idea how to do this kind of limit, so I guessed. I tried to substitute u=e^x to get ln(1+u)/u as u approaches negative infinity, then applying l'hopital's rule and eventually ended up with 1/negative infinity which is zero. This wasn't the right answer (which was 1). Appearently what I did wasn't the right thing, so what is the right way for this kind of problem?
     
  2. jcsd
  3. May 20, 2008 #2
    As x goes to infinity, we have an indeterminate form of 0/0. So apply L'Hopital's rule.

    Show us your work because using L'Hopital should have worked because you messed up your algebra.
     
  4. May 20, 2008 #3
    Ok, substituting u = e^x

    lim ln(1+u)/u as u approaches negative infinity.

    Applying lhopital's rule we have

    1/(u+1)/1

    so the limit of 1/(u+1) as u approaches negative infinity = 1/(negative infinity+1) = 1/negative infinity = 0

    Which part did I mess up?
     
  5. May 20, 2008 #4
    As x goes to negative infinity, what does u go to?
     
  6. May 20, 2008 #5
    Quit substituting, you don't need to at all.

    [tex]\lim_{x\rightarrow-\infty}\frac{\ln{(1+e^x)}}{e^x}[/tex]

    [tex]\lim_{x\rightarrow-\infty}\frac{\frac{e^x}{1+e^x}}{e^x}[/tex]

    [tex]\lim_{x\rightarrow-\infty}\frac{1}{1+e^x}[/tex]

    Answer ...
     
    Last edited: May 20, 2008
  7. May 20, 2008 #6
    Right, thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Limits again
  1. Limits again (Replies: 6)

  2. Limits again (Replies: 12)

  3. Again, Infinite Limit (Replies: 2)

  4. Limit :| (Replies: 13)

Loading...