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Huiswerkopgave 2 ( Analyse 1 NA)
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Calculus 2 Notes (Integral Calculus)
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Huiswerkopgave 2 (AN1na)Das Aangezien we weten dat:
1. alle rationele machten (dus wortelfuncties) en alle functies van de sinus en cosinus continue zijn, waar
dan ook ze gedefinieerd zijn (dus ook in geheel ℝ)
2. gecombineerde functies van continue functies ook continue zijn zoals in Theorem 6 (p.82) van Adams
staat
3. f(x) kan bestaan uit een gecombineerde functie van rationele machtsfuncties en functies van de sinus
en cosinus
weten we dat f continue is. Echter, als f differentieerbaar is dan is f zeker continue, maar het omgekeerde
hoeft niet zo te zijn. Wat we wel weten is dat als f’ continue is, dan is f’ differentieerbaar.
Aangezien 1, 2 en 3 ook gelden voor de afgeleide van f(x), is f’ dus continue in heel ℝ en dus is f op geheel
s
ℝ differentieerbaar.
b) Eld :
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