Exercise
https://texercises.com/exercise/taylorreihen-prufungsvorbereitung-2/
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Exercise:
Bestimme das Taylorpolynom T_x der Funktion fxsqrtx an der Stelle x_ und vereinfache es.

Solution:
Entwicklungsstelle x_ pause fx sqrtx x^frac pause quadRightarrowquad a_ dfracf! pause dfracsqrt pause medskip pause f'x dfrac x^-frac pause quadRightarrowquad a_ dfracf'! pause dfracfrac ^-frac pause dfracfrac pause dfrac medskip pause f''x -dfrac x^-frac pause quadRightarrowquad a_ dfracf''! pause dfrac-frac ^-frac pause dfrac-frac pause -dfrac medskip pause edt T_x + tfracx- - tfracx-^ pause + tfracx- tfrac - tfracx^ - x + pause tfrac + tfracx - tfracx^ + tfracx - tfrac pause -tfracx^ + tfracx + tfrac ed
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\(\LaTeX\)-Code
Exercise:
Bestimme das Taylorpolynom T_x der Funktion fxsqrtx an der Stelle x_ und vereinfache es.

Solution:
Entwicklungsstelle x_ pause fx sqrtx x^frac pause quadRightarrowquad a_ dfracf! pause dfracsqrt pause medskip pause f'x dfrac x^-frac pause quadRightarrowquad a_ dfracf'! pause dfracfrac ^-frac pause dfracfrac pause dfrac medskip pause f''x -dfrac x^-frac pause quadRightarrowquad a_ dfracf''! pause dfrac-frac ^-frac pause dfrac-frac pause -dfrac medskip pause edt T_x + tfracx- - tfracx-^ pause + tfracx- tfrac - tfracx^ - x + pause tfrac + tfracx - tfracx^ + tfracx - tfrac pause -tfracx^ + tfracx + tfrac ed
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Attributes & Decorations
Tags
mathematik, taylorreihen
Content image
Difficulty
(1, default)
Points
1 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator wg
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Link