Thomas Edison State University Laurent Series Residue Integration Worksheet

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1. LAURENT SERIES NEAR A SINGULARITY AT 0 Expand the function in a Laurent
series that converges for 0 < |??| < ?? and determine the precise region of convergence
cos ??
. Show the details of your work.
??4
2. ZEROS Determine the location and order of the zeros (?? + 81??)4
3. RESIDUE INTEGRATION Evaluate (counterclockwise).
???23
??? ?? 2 ?4???5 ????, ??: |?? ? 2 ? ??| = 3.2 Show the details.
4. INTEGRALS INVOLVING COSINE AND SINE Evaluate the following
2?? ??????2 ??
????
5?4 cos ??
integrals and show the details of your work. ?0

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