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Jordan's Lemma and Loop Integrals

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Without evaluating the improper integrals


find the numerical value q of their quotient

by considering the loop integral

where is the semi-circular loop indented at the origin.

Explain why Jordan's Lemma (see below) is inadequate here, and write a complete formulation
of a more general Jordan's lemma which applies in this case.

Please see the attached file for the fully formatted problems.

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