solving a hardcore limit with product

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Can this expression be simplified? $$\lim_{x\to0}\left(\prod^{\frac{1}{x}-1}_{i=1}\frac{1}{\sec\frac{xi\pi}{2}}\right)^x$$

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Short Answer: Yes.

Longer Answer:

  1. Rewrite sec in terms of cosine
  2. Use the fact that $y = e^{\log (y)} $ is continuous to change the product to a sum.
  3. Recognize that in the limit of the sum converges to a definite integral.
  4. Evaluate the integral.
  5. I think the answer might be 1/2, assuming no algebra errors on my part.