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-   -   Challenge: find an approximation (https://www.askmehelpdesk.com/showthread.php?t=317489)

  • Feb 15, 2009, 05:28 AM
    durexlw
    Challenge: find an approximation
    I'm looking for an approximation of the simple formula:

    Result = (47-X)/X

    For X = 1; result = 46
    For X = 2; result = 22.5
    For X = 3; result = 14.6
    For X = 4; result = 10.75
    For X = 5; result = 8.4
    For X = 6; result = 6.8

    I'd like to find an approximation that is easy and fast to calculate on the fly, it doesn't have to be accurate, the big ballpark is close enough.

    Any idea is welcome and I do mean 'any'.

    Thanks in advance,
    Andy
  • Feb 15, 2009, 07:27 AM
    galactus
    An approximation? It's pretty simple as it is.

    You could rewrite as

    By plugging in the x value, it is easy to see the result.

    Plug in x=6 and get and so on.

    Plug in 23 and get

    That appears to be easy enough and it is better than an approximation.

    I suppose I am not clear on what sort of approximation you are looking for because it is

    simplistic as is and fast to calculate 'on the fly'.
  • Feb 17, 2009, 07:45 AM
    rwinterton

    Result = (47-X)/X

    Result = 47/X - X/X = 47/X - 1

    if X is large, then 47/X becomes small and the approximation is
    Result = -1

    if X is small, then 47/X becomes large when compared to -1 and
    Result = 47/X

    if X is intermediate, you can't easily approximate.

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