Exercise
https://texercises.com/exercise/grenzwert-3/
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Exercise:
Bestimme die Konstanten alpha und beta so dass * lim_nrightarrowinfty leftsqrtn^-n^-alpha n -betaright * gilt.

Solution:
Es gilt lim_nrightarrowinfty leftsqrtn^-n^-alpha n -betaright lim_nrightarrowinfty leftn^left-fracnrightright^frac-alpha n -beta ^frac lim_nrightarrowinfty nleft-fracn+On^-right-alpha n -beta lim_nrightarrowinfty left^frac-alpharight n -frac^frac-beta &mustbe . Daher muss alpha ^frac quadmboxund beta -frac ^frac sein.
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Exercise:
Bestimme die Konstanten alpha und beta so dass * lim_nrightarrowinfty leftsqrtn^-n^-alpha n -betaright * gilt.

Solution:
Es gilt lim_nrightarrowinfty leftsqrtn^-n^-alpha n -betaright lim_nrightarrowinfty leftn^left-fracnrightright^frac-alpha n -beta ^frac lim_nrightarrowinfty nleft-fracn+On^-right-alpha n -beta lim_nrightarrowinfty left^frac-alpharight n -frac^frac-beta &mustbe . Daher muss alpha ^frac quadmboxund beta -frac ^frac sein.
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  1. Grenzwert by TeXercises
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analysis, grenzwert, konstante, limes, mathematik
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(5, default)
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5 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
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