Evaluate:

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

Note: e denotes the Euler’s number.

(In reply to puzzling by Jer)

I see more like 1.24 or 1.25.

In fact

DEFDBL A-Z
x = -.00001#
y1 = ((1 + x) ^ (1 / x) - EXP(1) + EXP(1) * x / 2) / (x ^ 2)
x = .00001#
y2 = ((1 + x) ^ (1 / x) - EXP(1) + EXP(1) * x / 2) / (x ^ 2)
PRINT (y1 + y2) / 2

finds

1.245948244750494

 

but narrowing the gap even smaller makes the y values increase a lot

Edited on November 10, 2009, 6:49 pm

Posted by Charlie on 2009-11-10 18:43:56