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Another problem

  1. May 7, 2005 #1
    how do i find the area of a rectanglewith sides 400root of 400 raised continously to itself like x^x^x^..and 800root of 800 raised also to itself continouslylike y^y^y...
    leave answer in whole number not exponent
     
  2. jcsd
  3. May 7, 2005 #2

    dextercioby

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    What do those "..." mean...?I can assume you'd have to evaluate

    [tex] 400^{400^{400^{...}}}\cdot 800^{800^{800^{...}}} [/tex]

    Daniel.
     
  4. May 7, 2005 #3

    HallsofIvy

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    Do you have any reason to think that such a sequence converges?
     
  5. May 7, 2005 #4

    dextercioby

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    Read mathworld's page on the power tower.I'm sure u'll find the upper limit for the convergence interval,that is,of course,if u meant the infinite superpower of 400 and 800 respectively.

    Daniel.
     
  6. May 7, 2005 #5

    saltydog

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    Abia, consistent no doubt. I think you mean a power tower like:

    "The 400'th root of 400"

    [tex]\sqrt[400]{400}\approx 1.01509[/tex]

    I think that's in the range of convergence.

    Edit: The 800 one too for that matter. :smile:
     
    Last edited: May 7, 2005
  7. May 8, 2005 #6
    area of rectangle with lenght x^x^x^x^x.....
    and breath y^y^y^y^y^y..... where x is 400^ 1/400 and y is 800^ 1/800.
    leaving answer in whole number not decimal or exponent
     
  8. May 8, 2005 #7

    saltydog

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    Hello Abia. Yea, leaving it in whole numbers . . . hum . . . how about expressing the power towers in terms of Lambert W-functions (which can be done and in whole numbers), and in this way then the area is just a product of two such expressions.
     
  9. May 8, 2005 #8
    do not understand
    pls explain
     
  10. May 8, 2005 #9

    saltydog

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    Check out Power Towers, and Lambert W-functions in MathWorld. Try that first.
     
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