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Indeterminate forms

  1. Apr 16, 2005 #1
    I'm having trouble recognizing when an expression produces an indeterminate form. for exampe what are the following:

    [tex]e^\infty[/tex]

    [tex]\sqrt{\infty}[/tex]

    more generally what is

    [tex]a^\infty[/tex]

    [tex]1^\infty[/tex]
     
  2. jcsd
  3. Apr 16, 2005 #2

    dextercioby

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    [itex] e^{\infty}[/itex] is something unclear...

    [tex] e^{-\infty}=0 [/tex]

    [tex] e^{+\infty}=+\infty [/tex]

    [tex] \sqrt{+\infty}=+\infty [/tex]

    As for [itex] 1^{\infty} [/itex] and the asymptotic limit of the general exponential,they require a special analysis...

    Daniel.
     
  4. Apr 16, 2005 #3
    yes i don't know why these are true
     
  5. Apr 16, 2005 #4

    dextercioby

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    Which ?The ones i wrote...?Take a look at the definition of the exponential function and expecially at the graph of [tex] e^{x} [/itex].U'll see where the first 2 come from.As for the 3-rd,i think it's an "okay" operation in [tex] \bar{\mathbb{R}} [/tex].

    Daniel.
     
  6. Apr 16, 2005 #5
    my misunderstanding stems from this problem:

    Evaluate: [tex]\lim_{x\rightarrow\infty}\frac{\sqrt{x}}{e^x}[/tex]

    i have to use L' Hopital's rule and the above ruduces to this:

    [tex]\lim_{x\rightarrow\infty}\frac{1}{2\sqrt{x}e^\infty}=0[/tex]

    now isn't [tex]0\infty[/tex] indeterminate?
     
  7. Apr 16, 2005 #6

    dextercioby

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    Where's the 0...?


    Daniel.
     
  8. Apr 16, 2005 #7
    Could he be thinking to split up the limit:

    [tex]\lim_{x\rightarrow\infty}[(\frac{1}{2\sqrt{x}})(\frac{1}{e^\infty})]=0[/tex]

    but that would give the determinant form of zero times zero, which is undoubtedly zero--- not zero times infinity.
     
  9. Apr 16, 2005 #8
    i didn't know that [tex]e^-\infty[/tex] was not equatl to [tex]e^\infty[/tex]
     
  10. Apr 16, 2005 #9

    dextercioby

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    Well,that's because u don't know how the graph of [itex] e^{x} [/itex] looks like...


    Daniel.
     
  11. Apr 16, 2005 #10
    you are totally correct. i didn't even think about looking at that graph.
     
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