Can you solve it?

Calculus Level 4

L=limx0((1+x)1/xe)1sinx \large L = \lim_{x\to0} \left(\frac{(1+x)^{1/x}}{e}\right)^{\dfrac{1}{\sin{x}}}

If L=ekL = e^k , where kk is a real number, find the value of kk.

Clarification: ee denotes Euler's number, e2.71828e \approx 2.71828.

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