Meaning of L'Hôpital's rule | Babel Free

Definitions

1. Alternative letter-case form of L'Hôpital's rule.
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2. The rule that the limit of the ratio of two functions equals the limit of the ratio of their derivatives, usable when the former limit is indeterminate and the latter limit exists.

Equivalents

Examples

“In this section, we shall describe a useful method for finding limits that is known as L’Hôpital’s Rule. Actually, there are several versions of L’Hôpital’s Rule and the formal statements of these will appear in the form of propositions or as a part of some remarks.”

“In each of the examples presented in this section, L’Hôpital’s Rule is used to find a limit that exists.”

“Modern examples involving L’Hôpital’s Rule frequently involve transcendental functions, but Leibniz’ calculus at this time was only a calculus of algebraic expressions.”

“Many times a simple algebraic manipulation will put a limit into a form that we can study using l’Hôpital’s Rule.”

“Notice that if you put x = 3, then both top and bottom of the fraction are 0. This means we can use l’Hôpital’s Rule.”

“To resolve a limit involving an indeterminate form, we sometimes need to apply l’Hôpital’s Rule more than once.”

“Many times, the limit of an exponential form can be determined by applying l'Hôpital's rule to the logarithm of the desired function.”

“There are a number of applications of limits in physical chemistry, and l’Hôpital’s rule is useful in some of them.”

“We will discuss the proof of l’Hôpital’s rule later in this section.”

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