Evaluate:

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

Note: e denotes the Euler’s number.

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