Evaluate:
(1+ x)
^{1/x} – e + e*x/2
Limit 
x → 0 x
^{2}
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 AZ
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 20091110 18:43:56 