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Getting Powerful With Euler II (Posted on 2009-11-10) Difficulty: 3 of 5
Evaluate:

               (1+ x)1/x – e + e*x/2
   Limit     --------------------------
   x → 0             x2

Note: e denotes the Euler’s number.

See The Solution Submitted by K Sengupta    
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puzzling | Comment 1 of 4
A quick graph shows the answer to be 1.2 but I havent shown why.

(1+x)^(1/x) appears to approach e as x approaches 0 but if that is the case then the fraction becomes

e*x/2
-------
x^2

which obviously does not have a limit as x approaches zero.

That is probably cheating but it puzzled me.

  Posted by Jer on 2009-11-10 15:27:08
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