Exercise
https://texercises.com/exercise/taylorreihen-prufungsvorbereitung-12/
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Exercise:
Stelle das Polynom px x^ + x^ - x + mit Hilfe des Satzes von Taylor in der Form px+ c_ x^ + c_ x^ + c_x^ + c_x + c_. medskip dar ohne die Potenzen auszurechnen.

Solution:
displaystyle p+x p^ + p^x + dfracp^!x^ + dfracp^!x^ + dfracp^!x^ %displaystyle p+x % _k^infty p^k x^k % _k^ p^k x^k %quad da forall k : f^kx equiv pause edatt p^x x^ + x^ - x + pause &quad &Rightarrow &quad p^ ex pause p^x x^ + x^ - pause &quad &Rightarrow &quad p^ ex pause p^x x^ + x pause &quad &Rightarrow &quad p^ ex pause p^x x + pause &quad &Rightarrow &quad p^ ex pause p^x pause &quad &Rightarrow &quad p^ edat medskippause edt px+ + x + dfrac! x^ + dfrac! x^ + dfrac! x^ ex x^ + x^ + x^ + x + ed
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\(\LaTeX\)-Code
Exercise:
Stelle das Polynom px x^ + x^ - x + mit Hilfe des Satzes von Taylor in der Form px+ c_ x^ + c_ x^ + c_x^ + c_x + c_. medskip dar ohne die Potenzen auszurechnen.

Solution:
displaystyle p+x p^ + p^x + dfracp^!x^ + dfracp^!x^ + dfracp^!x^ %displaystyle p+x % _k^infty p^k x^k % _k^ p^k x^k %quad da forall k : f^kx equiv pause edatt p^x x^ + x^ - x + pause &quad &Rightarrow &quad p^ ex pause p^x x^ + x^ - pause &quad &Rightarrow &quad p^ ex pause p^x x^ + x pause &quad &Rightarrow &quad p^ ex pause p^x x + pause &quad &Rightarrow &quad p^ ex pause p^x pause &quad &Rightarrow &quad p^ edat medskippause edt px+ + x + dfrac! x^ + dfrac! x^ + dfrac! x^ ex x^ + x^ + x^ + x + ed
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Tags
mathematik, taylorreihen
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Difficulty
(1, default)
Points
1 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator wg
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Link