Die geometrische Folge beschreibt exponentielle Wachstumsprozesse (z. B. die Entwicklung von Corona-Infektionszahlen bei konstanter Reproduktionszahl R).
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Wir erklären, was arithmetische Folgen und Reihen sind und wie man letztere mit dem "kleinen Gauß" explizit berechnen kann.
We explain integration by substitution, both for definite and indefinite integrals, and work out several examples.
We explain the method of integration by parts and work out several examples.
Finding area functions and finding derivatives are inverse processes of each other. We explain this close link in detail, revealing one of the most fundamental relationships in calculus.
Three names, one idea: For a given function f find another function F, such that f is the derivative of F.
We perform a complete walk-through of a single variable optimization of an example function.
De l'Hôpital's rule helps to find limits of functions in certain "pathological" cases. The Hart-Und-Trocken-Män does not help at all.
How does a function behave if the independent variable stretches towards the boundary of the domain?
We explain what a continuous function is and how we precisely define continuity using limits of sequences.
