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VERY ugly limit problem

  1. Feb 17, 2013 #1
    examine the limit of x→∞ of:

    (1-tanh(x))/e^(-2x) = (1- (e^x-e^(-x))/(e^x+e^(-x)))/e^(-2x)

    Rearranging a bit we get:

    e^(2x) - (e^(3x)-e^(x))/(e^x+e^(-x))

    Now plotting it in maple it seems to behave very badly, it oscillates up and down. Problem is prooving that there indeed exists no limit.

    Intuitively when x gets big the e^(3x)/(e^(x)+e^(-x)) term should approach e^(2x) - but for some reason IT DOES NOT. What is going on with this crazy function and does anyone have ideas how to proove that for a given a i can never find a delta such that lf-al ≤ δ etc etc.
  2. jcsd
  3. Feb 17, 2013 #2


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    Staff: Mentor

    According to WolframAlpha, the limit exists and it is 2. Are you sure you plotted the right function in maple?
  4. Feb 17, 2013 #3
    yes I plotted:

    (1-tanh(x))/(e^(-2x)) are u sure U plotted the right one? :) Else maybe I will resort to wolfram alpha. It seems that maple messes up sometimes. For instance it showed this as diverging too:

    e^(2x)-e^(3x)/e^x and surely that cant be right?

    edit: nvm you got me. I made a silly mistake - stupid me :(
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