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Applying the generalized divergence theorem to the set M = {XЄrN: |x| < a} and , find the volume of Sn – 1 = {xЄRn: |x| = 1} in terms of the -dimensional volume of Bn = {x Є Rn: |x| <1}. (This volume is π n/2 / (n/2)! if is even and 2(n+1)/2π (n-1)/2 1∙3∙5∙. ∙ N if is odd.) |
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