l'Hôpital's rule (redirected from L'Hopital's rule)

L'Hôpital's rule

Procedure of differential calculus for evaluating indeterminate forms such as 0/0 and ∞/∞ when they result from attempting to find a limit. It states that when the limit of f(x)/g(x) is indeterminate, under certain conditions it can be obtained by evaluating the limit of the quotient of the derivatives of f and g (i.e., f′(x)/g′(x)). If this result is indeterminate, the procedure can be repeated. It is named for the French mathematician Guillaume de L'Hôpital (1661–1704), who purchased the formula from his teacher the Swiss mathematician Johann Bernoulli (1667–1748).

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l'Hôpital's rule [lō·pē·tälz ‚rūl]

(mathematics)

A rule useful in evaluating indeterminate forms: if both the functions ƒ(x) andg(x) and all their derivatives up to order (n- 1) vanish atx=a, but thenth derivatives both do not vanish or both become infinite atx=a, thenƒ⁽ⁿ⁾denoting thenth derivative.