Complex Analysis/Exercises/Sheet 5

Exercise on Complex Analysis

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Problem (Integrals, 5 points)

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Calculate the following integrals using the Cauchy integral formula:

  1.  
  2.  
  3.   mit  ,  .

Problem (Cauchy, 10 points)

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Let  . On  , consider the function

 

Determine  . At which points of   does   have a limit?

Problem (More Integrals, 5 points)

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Use the Cauchy integral formula to determine

 

Hint: Consider   on the unit circle.

Translation and Version Control

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This page was translated based on the following Wikiversity source page and uses the concept of Translation and Version Control for a transparent language fork in a Wikiversity:

https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Übungen/5._Zettel

  • Date: 01/14/2024