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Limit of this ?

  1. Jun 30, 2006 #1
  2. jcsd
  3. Jun 30, 2006 #2

    NateTG

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    Looks like this belongs in the homework section.

    Are you familiar with l'Hospital's rule?
     
  4. Jun 30, 2006 #3
    yup i knew it , but how can we use it here ? no 0 / 0 or everlasting / everlasting ?


    / Sry didnt saw hw sec
     
  5. Jun 30, 2006 #4

    NateTG

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    No worries, just use the homework section next time.

    It's beena little while, but:
    [tex]0^\infty[/tex]
    and
    [tex]\infty^0[/tex]
    are also places that you can apply l'Hospitals rule.
    Let's say we have two functions:
    [tex]\lim_{x \rightarrow y} f(x) \rightarrow 0[/tex]
    and
    [tex]\lim_{x \rightarrow y} g(x) \rightarrow \infty[/tex]

    Then
    [tex]\lim_{x \rightarrow y} g(x)^{f(x)}=\lim_{x \rightarrow y} e^{f(x) \ln(g(x))}[/tex]
    And the exponent there is of the form:
    [tex]0 \times \infty[/tex]
     
  6. Jun 30, 2006 #5

    shmoe

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    You don't need to use l'hopital. Try pulling out the 7*8^n from inside the ().
     
  7. Jun 30, 2006 #6
    NateTg i understand what you meant.Thanks.
     
  8. Jun 30, 2006 #7
    But cant solve that : e ^ [ 2 / n . ln ( 5^n + 7.8^n ) ]

    What should i do e ^ ( fx . gx ) now ?
     
  9. Jun 30, 2006 #8

    NateTG

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    Well the limit of the exponent is the exponent of the limit, but you're better off using shmoe's technique.
     
  10. Jul 3, 2006 #9

    Alkatran

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    The first thing that jumps into my head is that the limit, if you remove the 5^n, is simply 7.8^(n*2/n) = 60.84. So, since we've ignored adding 5^n before rooting, the answer must be at least 60.84.

    There's only one answer that satisfies that, clearly demonstrating why I love multiple choice tests so much.
     
    Last edited: Jul 3, 2006
  11. Jul 3, 2006 #10

    StatusX

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    I think that's supposed to be 7*8^n, otherwise none of the choices are correct.
     
  12. Jul 5, 2006 #11
    n's going to infinity right? Easy way is piecewise. 7*8^n >> 5^n as n => infinity, so that term can be neglected (basically same is dividing out the 7*8^n, just slightly quicker and less rigorous). You get 7^(2/n)*(8^n)^(2/n) => 8^2 = 64.
     
  13. Jul 6, 2006 #12
    I don't understand the question...I don't see any lim (x->something)

    Do you mean maximum value? or the limit as x approaches infinity?

    (5^2n + 5^n * 14 * 8^n + 49 * 8 ^2n) under a n-th radical...

    I wont lie i dunno but my TI-84 does :D
     
    Last edited: Jul 6, 2006
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