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Calculus
Getting Powerful With Euler II (
Posted on 20091110
)
Evaluate:
(1+ x)
^{1/x}
– e + e*x/2
Limit 
x → 0 x
^{2}
Note
: e denotes the
Euler’s number
.
See The Solution
Submitted by
K Sengupta
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Comments: (
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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 20091110 15:27:08
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