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Spherical Volume

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Please see the attached file for the fully formatted problems.

The sphere x20 + x21 +· · ·+x2n of radius sqrt(n) is eqiupped with its natural area, normalized so that the total area is unity. Show that the normalized volume of the spherical band where a a<=x0 <= b is
and prove that

Hint: 1 &#8722; x <= e^(&#8722;x) will be helpful at one point.

Since this is an analysis problem, please be sure to be rigorous, and include as much detail as possible so that I can understand. Please also state if you are making use of some fact or theorem. Thanks!

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Solution Summary

A spherical volume problem is solved. The solution is detailed and well-presented.

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