tx · 8FpwboX8xYxyfhVR9gLgg5Qby9b5ZVgTeo594GmphSjk
3N9ttyLcRwDo7L4EmJkbS3ZFuQJygivupsL: -0.00500000 Waves
2024.11.25 17:56 [3387088] invoke 3N9ttyLcRwDo7L4EmJkbS3ZFuQJygivupsL > 3N9tKixzqTYWnEXQxrDQ5pBTGvQd6sFsvmV commitTask()
3N9tKixzqTYWnEXQxrDQ5pBTGvQd6sFsvmV: checked_out_by_92ovWCy1Zf8CSsTLLLssC74m8yn5yPMqVp9fmVacou97_chatgpt_Cq8BogobKC2aWf4zRQ97HC7c8W27jmpAdgB7GHP7Bz98_GwAQybf677Q8jDYJ7x9GQTR8A5kyGEXtUmgbWGxovnAP: null == null
3N9tKixzqTYWnEXQxrDQ5pBTGvQd6sFsvmV: Cq8BogobKC2aWf4zRQ97HC7c8W27jmpAdgB7GHP7Bz98_GwAQybf677Q8jDYJ7x9GQTR8A5kyGEXtUmgbWGxovnAP_commit_timestamp_chatgpt: 1732546610266 == 1732546610266
3N9tKixzqTYWnEXQxrDQ5pBTGvQd6sFsvmV: Cq8BogobKC2aWf4zRQ97HC7c8W27jmpAdgB7GHP7Bz98_GwAQybf677Q8jDYJ7x9GQTR8A5kyGEXtUmgbWGxovnAP_commit_height_chatgpt: 3387088 == 3387088
3N9tKixzqTYWnEXQxrDQ5pBTGvQd6sFsvmV: Cq8BogobKC2aWf4zRQ97HC7c8W27jmpAdgB7GHP7Bz98_GwAQybf677Q8jDYJ7x9GQTR8A5kyGEXtUmgbWGxovnAP_result_chatgpt: "Die Regel von L'Hospital ist eine Methode in der Mathematik, speziell in der Differentialrechnung, zur Berechnung von Grenzwerten von Funktionen. Sie ist besonders nuetzlich fuer den Fall, dass die direkte Berechnung eines Grenzwertes auf einen unbestimmten Ausdruck wie 0/0 oder / fuehrt. Die Regel besagt, dass wenn die Funktionen f(x) und g(x) an einer Stelle a differenzierbar sind und der Grenzwert von f(x)/g(x) als x gegen a strebt ein unbestimmter Ausdruck ist, dann kann dieser Grenzwert durch den Grenzwert der Ableitungen der Funktionen gefunden werden:
\[
\lim_{{x \to a}} \frac{f(x)}{g(x)} = \lim_{{x \to a}} \frac{f'(x)}{g'(x)},
\]
vorausgesetzt, dass der rechte Grenzwert existiert oder gegen unendlich geht. Diese Regel kann unter bestimmten Bedingungen mehrfach angewendet werden, falls der Grenzwert der Ableitungen weiterhin unbestimmte Ausdruecke erzeugt." -> "The rule of L'Hospital, also known as L'Hopital's Rule, is a method in calculus used to evaluate limits of indeterminate forms. Specifically, when evaluating a limit that produces the indeterminate form 0/0 or /, L'Hopital's Rule can be applied. The rule states that:
\[
\lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)},
\]
provided that the limits on the right-hand side exist or reach infinity. Here, \( f(x) \) and \( g(x) \) are functions that are differentiable near \( c \) except perhaps at \( c \) itself, and \( f'(x) \) and \( g'(x) \) are their derivatives. The rule can be applied repeatedly if the limit still results in an indeterminate form after applying it once.
This rule is a powerful tool for solving limits and is named after the French mathematician Guillaume de l'Hpital, who published the rule in the 17th century. However, it is worth noting that the rule was actually discovered by the Swiss mathematician Johann Bernoulli."
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