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Homework Help: List of indeterminate forms

  1. Jun 1, 2010 #1


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    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


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    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

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    Last edited by a moderator: May 4, 2017
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