Limit of Exponents and Sinusoidal Functions

Calculus Level 4

Evaluate the following limit:

L=limx0(sin(x)x)11cos(x)\large L = \lim_{x\to 0} \left(\dfrac{\sin(x)}{x}\right)^{\frac{1}{1-\cos(x)}}

Find the value of 1000L\lfloor 1000L \rfloor.

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