Kurs:Mathematik für Anwender (Osnabrück 2011-2012)/Teil I/Arbeitsblatt 26/en

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Warm-up-exercises

Exercise

Determine the partial fraction decomposition of


Exercise

Determine the coefficients in the partial fraction decomposition of Example 26.5 by replacing with some numbers.


Exercise

Determine the complex and the real partial fraction decomposition

of


Exercise

Determine the

complex partial fraction decomposition of


Exercise

Determine the complex and the real partial fraction decomposition

of


Exercise

Determine the complex and the real partial fraction decomposition

of


Exercise

Determine the complex and the real partial fraction decomposition

of


Exercise

Determine an antiderivative of the function


Exercise

Determine an antiderivative of the function


Exercise

Determine an antiderivative of the function


Exercise

Determine an antiderivative of the function

through partial fraction decomposition.


Exercise

We consider the function

a) Determine the real partial fraction decomposition of .

b) Determine an antiderivative of for .


Exercise

Find a representation of the rational number as a sum of rational numbers, such that every denominator is a power of a prime number.




Hand-in-exercises

Exercise (4 points)

Write the rational function

in the new variables . Compute the antiderivative through the real partial fraction decomposition and through the substitution .


Exercise (4 points)

Determine the complex and the real partial fraction decomposition

of


Exercise (4 points)

Determine the complex and the real partial fraction decomposition

of


Exercise (4 points)

Determine an antiderivative of the function


Exercise (5 points)

Determine an antiderivative of the function


Exercise (1 point)

Determine an antiderivative of the function




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