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L'Hôpital's rule (/ ˌ l oʊ p iː ˈ t ɑː l /, loh-pee-TAHL) or L'Hospital's rule, also known as Bernoulli's rule, is a mathematical theorem that allows evaluating limits of indeterminate forms using derivatives. Application (or repeated application) of the rule often converts an indeterminate form to an expression that can be easily ...
For the limiting case as → 1, L'Hôpital's rule shows that the utility function becomes linear in wealth; and for the limiting case as goes to 0, the utility function becomes logarithmic: () = (+). Decreasing, constant, and increasing absolute risk aversion
When =, using l'Hôpital's rule shows that this simplifies to the case of log utility, u(c) = log c, and the income effect and substitution effect on saving exactly offset. A time-varying relative risk aversion can be considered.
The book includes the first appearance of L'Hôpital's rule. The rule is believed to be the work of Johann Bernoulli, since l'Hôpital, a nobleman, paid Bernoulli a retainer of 300₣ per year to keep him updated on developments in calculus and to solve problems he had. Moreover, the two signed a contract allowing l'Hôpital to use Bernoulli's ...
Guillaume François Antoine, Marquis de l'Hôpital [1] (French: [ɡijom fʁɑ̃swa ɑ̃twan maʁki də lopital]; sometimes spelled L'Hospital; 7 June 1661 – 2 February 1704) [a] was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞.
The rule can be thought of as an integral version of the product rule of differentiation; it is indeed derived using the product rule. The integration by parts formula states: ′ = [() ()] ′ () = () () ′ ().
The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions include: The partial sums (the Taylor polynomials) of the series can be used as approximations of the function ...
Michel de l'Hôpital ({1506–1573), French lawyer, diplomat and chancellor Guillaume de l'Hôpital (1661–1704), French mathematician L'Hôpital's rule , in mathematics