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muzz
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can somebody explain what is the L hospital rule.. where does it come from and what's it mean?
muzz said:can somebody explain what is the L hospital rule.. where does it come from and what's it mean?
The L Hospital Rule, also known as L'Hôpital's rule, is a mathematical rule used to evaluate limits involving indeterminate forms. It is named after French mathematician Guillaume de l'Hôpital.
The L Hospital Rule was first published in the book Calculus of Newton and of L'Hôpital in 1696 by Guillaume de l'Hôpital. However, it is believed that he learned the rule from his teacher, Johann Bernoulli, who in turn learned it from Leibniz.
The L Hospital Rule states that for functions f(x) and g(x), if the limit of f(x) divided by g(x) as x approaches a certain value is an indeterminate form (such as 0/0 or ∞/∞), then the limit of the quotient of the derivatives of f(x) and g(x) will be the same.
The L Hospital Rule is important because it provides a method for evaluating limits that would otherwise be difficult or impossible to solve algebraically. It is particularly useful in calculus and other areas of mathematics that involve limits and derivatives.
One common misconception about the L Hospital Rule is that it can be used to evaluate any limit involving a quotient of functions. However, it can only be used in specific cases where the limit is an indeterminate form. Additionally, some people may mistakenly believe that the rule is named after a hospital, rather than a person.