\[ \large L = \lim_{x\to0} \dfrac{(1+x)^{1/x} - e + \frac e2 x }{x^2} \]

If \(L = ke \), where \(k \) is a real number, find the value of \(k\).

Give your answer to 3 decimal places.

If you think that the limit does not exist, enter 0.666 as your answer.

**Clarification**: \(e\) denotes Euler's number, \(e \approx 2.71828\).

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