3N9tKixzqTYWnEXQxrDQ5pBTGvQd6sFsvmV · data · 8AWtnRJqTdZ5ENKjePSZHUBsr4FxfHgcrAs2r54wCNMe_Hi8zo1vvbUZ7UHqRZUVZyRTM1KrsQ6CnpuMhQ3G2GMHo_result_chatgpt
{
"8AWtnRJqTdZ5ENKjePSZHUBsr4FxfHgcrAs2r54wCNMe_Hi8zo1vvbUZ7UHqRZUVZyRTM1KrsQ6CnpuMhQ3G2GMHo_result_chatgpt": "The rule of L'Hospital (or L'Hopital) is a method in calculus used to determine the limit of indeterminate forms like \( \frac{0}{0} \) or \( \frac{\infty}{\infty} \). It was developed by the French mathematician Guillaume de l'Hpital.
The rule states that if you have a limit of the form:
\[ \lim_{x \to c} \frac{f(x)}{g(x)} \]
and both \( f(x) \) and \( g(x) \) approach 0 or both approach infinity as \( x \) approaches \( c \), then the limit can be computed as:
\[ \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x to c} \frac{f'(x)}{g'(x)} \]
**if** the limit on the right-hand side exists or reaches infinity.
This rule is particularly useful because it simplifies the evaluation of limits that are otherwise difficult or impossible to evaluate using standard algebraic techniques alone. The application of L'Hospital's Rule can often be iterated if the resulting limit is still an indeterminate form."
}
Changelog:
{
"2024.09.16 14:19": "The rule of L'Hospital (or L'Hopital) is a method in calculus used to determine the limit of indeterminate forms like \( \frac{0}{0} \) or \( \frac{\infty}{\infty} \). It was developed by the French mathematician Guillaume de l'Hpital.
The rule states that if you have a limit of the form:
\[ \lim_{x \to c} \frac{f(x)}{g(x)} \]
and both \( f(x) \) and \( g(x) \) approach 0 or both approach infinity as \( x \) approaches \( c \), then the limit can be computed as:
\[ \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x to c} \frac{f'(x)}{g'(x)} \]
**if** the limit on the right-hand side exists or reaches infinity.
This rule is particularly useful because it simplifies the evaluation of limits that are otherwise difficult or impossible to evaluate using standard algebraic techniques alone. The application of L'Hospital's Rule can often be iterated if the resulting limit is still an indeterminate form."
}
