# Can you solve it?

Calculus Level 4

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

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

Clarification: $$e$$ denotes Euler's number, $$e \approx 2.71828$$.

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