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Evaluate the following limit:
L=limx→0(sin(x)x)11−cos(x)\large L = \lim_{x\to 0} \left(\dfrac{\sin(x)}{x}\right)^{\frac{1}{1-\cos(x)}}L=x→0lim(xsin(x))1−cos(x)1
Find the value of ⌊1000L⌋\lfloor 1000L \rfloor⌊1000L⌋.
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