1. Limited time only! Sign up for a free 30min personal 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!

List of indeterminate forms

  1. Jun 1, 2010 #1


    User Avatar
    Homework Helper

    Not so much a homework problem as a curiosity on my part. I chose to give a presentation recently on undefined numbers. With that, indeterminate's unsurprisingly found their way into my presentation.

    After reading up on the list of indeterminate forms, I stumbled upon the form [tex]0^\infty[/tex] and for the life of my couldn't think of any examples in limits that have this form.

    In my mind, I see such indeterminates as [tex]1^\infty[/tex] as trying to say
    "multiplying 1 by itself repeatedly obviously still gives 1, but we're trying to do it so many times that it finally equals something other than 1".
    Such an example would be e:

    [tex]\lim_{x\rightarrow \infty}\left(1+\frac{1}{x}\right)^{x}[/tex]

    Now a quick example of [tex]0^\infty[/tex] would be [tex]\lim_{x\rightarrow \infty}\left(\frac{1}{x}\right)^x[/tex]

    but in a way, I see this as "enforcing" the answer zero since this limit tends to zero much faster than [tex]\lim_{x\rightarrow \infty}\frac{1}{x}[/tex] does.

    So can anyone give me an example of such an indeterminate form that equals a finite, and possibly even infinite value.
  2. jcsd
  3. Jun 1, 2010 #2
    Re: indeterminate

    Where did you find the reference to [itex]0^\infty[/itex] as an indeterminate form? Off the top of my head, I can't think of a reason why this should be indeterminate.
  4. Jun 1, 2010 #3


    User Avatar
    Gold Member

    Re: indeterminate

    Why is [itex]1^\infty[/itex] indeterminate?

    Nevermind found it in the other thread.

    x= 1^infinity is equivalent to ln(x)= infinity*ln(1)= infinity*0=0/1/infinity = 0/0

    So is 0^infinity then equivalent to ln(x) = infinity*ln(0) = infinity*-infinity
    Last edited: Jun 1, 2010
  5. Jun 1, 2010 #4

    jack action

    User Avatar
    Science Advisor
    Gold Member

    Last edited by a moderator: May 4, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook