# VERY ugly limit problem

1. Feb 17, 2013

### aaaa202

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. Feb 17, 2013

### Staff: Mentor

According to WolframAlpha, the limit exists and it is 2. Are you sure you plotted the right function in maple?

3. Feb 17, 2013

### aaaa202

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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