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https://texercises.com/exercise/bogenlange/
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Exercise:
Berechne die Bogenlänge des Graphen der Funktion fx dfracbigx^ - ln xbig quad für leq x leq und vereinfache das Resultat so weit wie möglich.

Solution:
fx dfracbigx^ - ln xbig quad Rightarrow quad f'x dfracleftx - dfracxright dfracleftx - dfracxright medskip edt sqrt + bigf'xbig^ sqrtdfrac + dfrac leftx - dfracxright^ sqrtdfrac leftx + dfracxright^ ex dfrac left|x + dfracxright| ed medskip edt _^ sqrt+bigf'xbig^ mboxdx dfrac _^ left|x + dfracxright| mboxdx dfracleftdfracx^ + ln xright_^ ex dfrac + ln - - ln frac + ln approx . ed
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Exercise:
Berechne die Bogenlänge des Graphen der Funktion fx dfracbigx^ - ln xbig quad für leq x leq und vereinfache das Resultat so weit wie möglich.

Solution:
fx dfracbigx^ - ln xbig quad Rightarrow quad f'x dfracleftx - dfracxright dfracleftx - dfracxright medskip edt sqrt + bigf'xbig^ sqrtdfrac + dfrac leftx - dfracxright^ sqrtdfrac leftx + dfracxright^ ex dfrac left|x + dfracxright| ed medskip edt _^ sqrt+bigf'xbig^ mboxdx dfrac _^ left|x + dfracxright| mboxdx dfracleftdfracx^ + ln xright_^ ex dfrac + ln - - ln frac + ln approx . ed
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Attributes & Decorations
Tags
bogenintegral, bogenlänge, graph, mathematik
Content image
Difficulty
(4, default)
Points
6 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator uz
Decoration
File
Link