Limit of Exponents and Sinusoidal Functions

Calculus Level 4

Evaluate the following limit:

L=lim⁡x→0(sin⁡(x)x)11−cos⁡(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.

Ariel Gershon by Ariel Gershon
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