where E is the region bounded by the spheres with center the origin and radii r and R, 0 < r < R, and n is an integer. (i) Evaluate the integral. (ii) For what values of n, if any, does the integral in part (i) have a limit as r → 0 + ? (iii) For what values of n, if any, does the integral in part (i) have a limit as R → ∞ ?

where E is the region bounded by the spheres with center the origin and radii r and R, 0 < r < R, and n is an integer. (i) Evaluate the integral. (ii) For what values of n, if any, does the integral in part (i) have a limit as r → 0 + ? (iii) For what values of n, if any, does the integral in part (i) have a limit as R → ∞ ?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.

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