Kurs:Mathematik für Anwender (Osnabrück 2011-2012)/Teil I/Arbeitsblatt 28/en

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Warm-up-exercises

Exercise

Let and consider the function

Determine the extrema of this function.


Exercise

Prove that for the factorial function the relationship

holds.


Exercise

a) Prove that for the estimate

holds.

b) Prove that the function defined by

for is increasing.

c) Prove that .

d) Prove that for the factorial function for the estimate

holds.


Exercise

Solve the initial value problem


Exercise

Solve the initial value problem


Exercise

Find all the solutions for the ordinary differential equation


Exercise

Make clear and mathematically clear to yourself that in a location-independent differential equation (i.e. does not depend on ) the difference between two solutions and does not depend on time, that is is constant. Show with an example that this may not happen in a time-independent differential equation.




Hand-in-exercises

Exercise (2 points)

Prove that for the factorial function the relationship

holds.


Exercise (3 points)

Solve the initial value problem


Exercise (3 points)

Find a solution for the ordinary differential equation


Exercise (4 points)

Solve the initial value problem




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