Final answer:
The question involves finding the limit of a trigonometric function as x approaches 0, suitable for College-level Mathematics. The provided reference information is unrelated, and a proper solution requires applying L'Hopital's rule or trigonometric simplifications, which are unavailable in the given context.
Step-by-step explanation:
The subject of the question is Mathematics and the grade level is most likely College, where students deal with advanced calculus concepts such as limits involving trigonometric functions and indeterminate forms. The student is asking to find the limit of the function tan(x)*(2*(sin(x/2))^2)*(1/x3) as x approaches 0. To solve this limit, we can apply L'Hopital's rule for indeterminate forms, or try to simplify the expression and analyze the behavior as x approaches 0.
However, the information provided as a reference does not directly relate to the solving process of the given limit problem. Instead, it pertains to various other mathematical concepts such as trigonometric identities, potential energy in physics, and probability density functions. This demonstrates the necessity of understanding and applying the correct mathematical principles to solve a specific problem.
Without the proper context or additional details, I would not be able to provide a mentioned correct option in the final answer.